PHYSICAL AND GEOCHEMICAL IMPACTS OF IMPURE CO2 ON STORAGE IN DEPLETED HYDROCARBON RESERVOIRS AND SALINE AQUIFERS
Zaman ZiabakhshGanji
Cover page: the image is modified version by author from an Iranian power plant (http://www.sabainfo.ir )
© Zaman ZiabakhshGanji, Amsterdam, the Netherlands, 2015.
Physical and geochemical impacts of impure CO2 on storage in depleted hydrocarbon reservoirs and saline aquifers
Ph.D. Thesis, VU Universiteit Amsterdam
ISBN/EAN: 978-90-9028887-1
Cover and layout design: Z. ZiabakhshGanji,
The research reported in this thesis was carried out as a part of the CATO-2 programme (CO2 capture, transport and storage in the Netherlands). Their financial support is gratefully acknowledged.
VRIJE UNIVERSITEIT
Physical and geochemical impacts of impure CO2 on storage in depleted hydrocarbon reservoirs and saline aquifers
ACADEMISCH PROEFSCHRIFT
ter verkrijging van de graad Doctor aan de Vrije Universiteit Amsterdam, op gezag van de rector magnificus
prof.dr. F.A. van der Duyn Schouten, in het openbaar te verdedigen
ten overstaan van de promotiecommissie van de Faculteit der Aard- en Levenswetenschappen
op vrijdag 27 maart 2015 om 11.45 uur in de aula van de universiteit,
De Boelelaan 1105
door
Zaman ZiabakhshGanji geboren te Babol, Iran
promotor: prof.dr. P.J. Stuijfzand copromotor: dr. H. Kooi
Examination committee:
prof.dr. S. M. Hassanizadeh
prof.dr. P.L.J. Zitha
prof.dr. M. Blunt
dr. B.M. van Breukelen
dr. T.J. Tambach
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\ÇÇÉätà|ÉÇ |á ZÉwËá vâáàÉÅ
i
Table of Contents
Contents Page
Chapter 1
General Introduction
1.1. Background………………………………………………………………….............. 3
1.2. Principle of Carbon dioxide Capture and Storage (CCS)……………………………. 4
1.3. CCS in practice around the globe……………………………………………………. 5
1.4. CCS in The Netherlands……………………………………………………………... 6
1.5. Research objective…………………………………………………………………… 8
1.6. Outline of this thesis…………………………………………………………………. 9
Chapter 2
An Equation of State for thermodynamic equilibrium of gas mixtures and brines
2.1. Introduction…………………………………………………………………………... 13
2.2. Thermodynamic Model……………………………………………………………... 15
2.2.1 Equilibrium between AqP and NaqP…………………………………….. 15
2.2.2. Non aqueous phase……………………………………………………….. 17
2.2.3. Aqueous phase……………………………………………………………. 19
2.3. Model Calibration………………………………………………………………….... 20
2.4. Solving the model equations for systems consisting of single or mixed gases……… 24
2.5. Results and Discussion……………………………………………………………… 25
2.6. Concluding remarks………………………………………………………………….. 36
ii
Appendix 2-A…………………………………………………………………………….. 37
Chapter 3
Sensitivity of Joule-Thomson cooling to impure CO2 injection in depleted gas reservoirs
3.1. Introduction………………………………………………………………………….. 43
3.2. Modelling Approach…………………………………………………………………. 45
3.2.1. Governing equations…………………………………………………….. 46
3.2.2. Calculation of the transport properties for the NaqP……………………. 47
3.2.2.1. Specific heat capacity and Joule-Thomson coefficient……….......... 47
3.2.2.2. Density and compressibility………………………………………… 50
3.2.2.3. Viscosity……………………………………………………………. 52
3.2.3. AqP Properties………………………………………………………….. 53
3.3. Model Set up…………………………………………………………………………. 55
3.4. Results………………………………………………………………………………... 56
3.4.1. Comparison with existing solutions for pure CO2 injection……………. 56
3.4.2. Sensitivity to impurity; constant pressure injection…………………….. 57
3.4.3. Sensitivity to impurity; constant rate injection…………………………. 60
3.4.4. The relative role of individual thermo-physical properties…………….. 63
3.5. Discussion and conclusions………………………………………………………….. 66
Appendix 3-A…………………………………………………………………………….. 67
Appendix 3-B…………………………………………………………………………….. 70
Appendix 3-C…………………………………………………………………………….. 74
iii
Chapter 4
Sensitivity of the CO2 storage capacity of underground geological structures to the presence of SO2 and other impurities
4.1. Introduction…………………………………………………………………………. 79
4.2. Method……………………………………………………………………………….. 81
4.2.1. Volumetric Storage Trapping Capacity (STCV)……………………….. 81
4.2.2. Solubility Storage Trapping Capacity (STCS)…………………………. 82
4.3. Results and Discussion………………………………………………………………. 84
4.3.1. Support for the applicability of the NaqP model……………………….. 84
4.3.2. Effect of impurities on the STCV………………………………………. 86
4.3.4. Effect of impurities on STCS…………………………………………… 90
4.3.5. Potential use of the positive effect of SO2………………………………. 92
4.4. Conclusion……………………………………………………………………………. 94
Chapter 5
Sensitivity of the geochemical response of a saline aquifer to the presence of impurities in the stored CO2
5.1. Introduction………………………………………………………………………….. 99
5.2. Methods……………………………………………………………………………… 101
5.2.1. General modelling approach…………………………………………… 101
5.2.2. Mineral composition and initial formation water chemistry…………… 102
5.2.3. Reactions………………………………………………………………. 103
5.2.4. Further assumptions and model discretization…………………………. 105
5.2.5. Model experiments…………………………………………………….. 106
iv
5.2.6. Porosity changes………………………………………………………... 107
5.3. Results………………………………………………………………………………... 108
5.3.1. Impacts on pH…………………………………………………………… 108
5.3.2. Impacts on mineral dissolution and precipitation……….……….…… 110
5.3.3. Impacts on porosity……………………………………………………… 114
5.3.4. Grid convergence and domain size influences………………………….. 115
5.4. Discussion and Conclusions………………………………………………………… 116
5.4.1. Summary of the geochemical impacts…………………………………... 116
5.4.2. Possible significance of the predicted impacts………………………….. 117
Chapter 6
Summary
6.1. Conclusions………………………………………………………………………….. 121
6.2. Recommendations…………………………………………………………………… 123
Chapter 7
Samenvatting
7.1. Conclusies…………………………………………………………………………… 127
7.2. Aanbevelingen………………………………………………………………………. 129
Chapter 8
Bibliography 133
Acknowledgments 151
Chapter 1
Introduction
Chapter 1 3
1.1. Background
Greenhouse gases play a crucial role in the Earth’s climate system. Without greenhouse gases, the average global surface temperature would by about -19 °C, which is 33 °C lower than the present average of 14 °C (IPCC, 2005). Increasing concentrations of greenhouse gases in the atmosphere, and notably of carbon dioxide (CO2) (figure 1.1), are therefore considered an important driver of global warming and regional climate change (IPCC, 2005). Rising of global average sea level due to widespread melting of snow and ice provides strong evidence that the atmosphere is heating up and the climate system is warming (IPCC, 2005). In spite of ongoing investigation and continuing debate, there is broad scientific consensus that human activities are the main reasons for global warming since the beginning of the industrial revolution in 1750 (IPCC, 2005; Treut et al., 2008; Buckingham & Turner, 2008). As a result of the increasing worldwide energy demands, the amount of CO2 in the atmosphere has grown exponentially; 40 % of CO2 in the atmosphere is attributed to the burning of fossil fuels (DOE, 2012). Figure 1.1 shows the increase of atmospheric CO2 as measured at the meteorological station at Mauna Loa, Hawaii, since the mid-20th century, including the superimposed seasonal fluctuations.
Fig. 1.1: Atmospheric CO2 concentrations as measured at Mauna Loa, Hawaii. (modified after NOAA, 2014)
Apart from CO2, the potential greenhouse gases CH4 and N2O have also increased considerably over the last century, as recently documented by the World Meteorological Organization (WMO, 2014). While CO2 is mainly emitted by point sources such as power plants and at industrial sites, CH4 and N2O are mostly produced in agriculture, for instance in paddy-fields, and by cattle breeding and nitrogen fertilization. Globally averaged mole fractions of CO2, CH4 and N2O reached new record highs in 2013, with CO2 at 396 ppm, CH4 at 1824 ppb (part per billion) and N2O at 325.9 ppb. These
Introduction 4
values are 142 %, 253 % and 121 %, respectively, of pre-industrial levels (WMO, 2014). Moreover, the annual CO2 concentration rise of 2.9 ppm from 2012 to 2013 was the largest increase since 1984 (WMO, 2014). There is broad consensus that the trend of rising CO2 levels should be reversed by cutting of emissions of CO2 and other greenhouse gases, and the following general measures have been proposed (IPCC, 2007):
Improving the energy efficiency of existing technologies: reducing the consumption of carbon-based fuels (e.g. hybrid cars, power plants).
Using alternative energy sources: solar and wind power and geothermal energy.
Capturing and storing carbon dioxide (CO2) for long periods of time (hundreds of years) in geological formations.
1.2. Principle of Carbon dioxide Capture and Storage (CCS)
CCS generally involves capture of CO2 at major stationary sources such as power plants, subsequent transport of the CO2 in pipe lines or ships to storage sites, and then injection in the underground geological structures (figure 1.2). Important geological target structures for CO2 sequestration are saline aquifers (Chadwick et al., 2007; Ofori et al., 2011), depleted hydrocarbon reservoirs (Damen et al., 2005; Velasquez et al., 2006; Arts et al., 2008, 2012) and unmineable coal seams (Bergen et al., 2009). Injection and storage in undepleted hydrocarbon reservoirs, including coal beds, can be of particular interest to simultaneously enhance production of oil (CO2-EOR) or gas (CO2-EGR in gas reservoirs and ECBM in coal beds).
Fig. 1.2: General schematic diagram of CCS (IPCC, 2005)
Chapter 1 5
Depleted or almost depleted gas/oil reservoirs are important targets for storage because knowledge of the reservoirs generally is quite extensive due to the large amounts of data acquired during the exploitation stage (Li et al., 2006). Due to their widespread occurrence, deep brine aquifers could theoretically host a significantly greater amount of CO2 than hydrocarbon reservoirs (IPCC, 2005), and deep brine aquifers also can often be found near CO2 point sources, which would limit needs for transport infrastructure. Hydrocarbon reservoirs have the advantage of (i) a proven track record for being able to contain low density fluids (gas/oil) for millions of years, (ii) high effective stress levels due to hydrocarbon production (reducing the risk of leakage), and (iii) more comprehensive knowledge of reservoir and caprock properties through exploration and production.
The following four basic mechanisms of CO2 trapping are distinguished (Gaus et al., 2008):
Structural trapping: The injected CO2 can accumulate and become trapped beneath a low-permeability caprock. In aquifer storage the CO2 tends to migrate upward by buoyancy because the density of the (supercritical) CO2 is less than that of the ambient groundwater or brine. This form of trapping poses the greatest potential risk of escape to the surface or shallower subsurface levels if the caprock integrity is not secure due to fractures or leaking well bores for example.
Residual fluid trapping: During its migration through the reservoir small bubbles of CO2 can snap off and stay behind in the pores together with formation water. This form of trapping is particularly relevant in aquifer storage. In the long term, some or all of this CO2 may dissolve in formation brine. This form of trapping poses relatively small risks of leakage from the reservoir.
Solubility trapping: CO2 can be trapped by dissolution in the formation water which initially fills the pores of the storage formation (groundwater, or residual capillary water). The solubility of CO2 is highly dependent on temperature and pressure (Chapter 3). This form of trapping poses very small risk of leakage.
Mineral trapping: When CO2 dissolves in brine it forms a weak carbonic acid. Over a long time this weak acid can react with the minerals in the reservoir, binding CO2 to the rock in the form of precipitated carbonate minerals. This process can be fast or slow depending on the geochemistry of the rock and water at a specific storage site. If minerals have formed and the system CO2-brine-rock has equilibrated, CO2 is bound for long periods of time in the solid phase. This clearly is a safe form of trapping.
1.3. CCS in practice around the globe
Although geological CCS is a relatively new concept, enhanced oil recovery through injection of miscible or immiscible CO2 without the prime objective to store CO2 was already applied 37 years ago on a commercial scale in Canada and North America (Procesi et al., 2013). Since then, CO2-EOR has seen continued usage, for instance at the Weyburn oil field in southern Saskatchewan, Canada (Stevens et al., 2005) and at the Permian Basin oil fields in USA where naturally sourced CO2 from
Introduction 6
New Mexico and Colorado is injected. Apart from these injection or storage applications in hydrocarbon reservoirs, over the last decades more than ten CCS projects involving storage in saline aquifers have been implemented by governments and industries (Procesi et al., 2013) (figure 1.3). Acid-gas disposal (H2S and CO2) in the Alberta Basin (Canada) (Bachu & Gunter, 2004; Bachu et al., 2005) was the first injection of CO2 into saline aquifers in the early 1990s. The first dedicated CO2
storage in an aquifer started in 1998 at the Sleipner field in the North Sea (Torp & Gale, 2003) followed in 2008 by storage at Snøhvit, Norway (Maldal & Tappel, 2004). Demonstration projects for storage in depleted gas reservoirs started in 2004 at the K12-B gas field in The Netherlands (Van der Meer et al., 2004) and in the Otway Basin, Australia, in 2008 (Sharma et al., 2007).
Currently, only three projects are active in Europe (Sleipner and Snøhvit, Norway, K-12-B offshore gas field in the Dutch sector of the North Sea) and 19 projects are planned to start in 2015–2016 (Procesi et al., 2013).
Fig. 1.3: The map shows an overview of the active CCS projects around the world, update to 15th January 2013 (modified after Procesi et al., 2013).
1.4. CCS in The Netherlands
The first, and still only, active CO2 storage project in The Netherlands is that of the K-12B field in the North Sea, about 150 km northwest of Amsterdam (http://www.co2-cato.org/) (figure 1.3). At this site, CO2 is separated from the produced natural gas, which contains too high a CO2 content (13%) to allow transport through the pipeline infrastructure. Since 2004, the captured CO2 is re-injected in the reservoir (Rotliegend) at a depth of about 4 km. Until 2010 approximately 80.000 ton CO2 has been re-injected.
Chapter 1 7
Fig. 1.4: Oil and gas fields in the Netherlands (modified after Tambach et al., 2015)
Introduction 8
Figure 1.4 shows that the Netherlands has a large number of reservoirs that can potentially be used for CO2 storage. At present, the ROAD (Rotterdam Capture and Storage Demonstration) project is one of the few projects in the European Union that are still running for large scale demonstration of CCS. ROAD involves plans to capture about 1.1 million ton of CO2 per year for 5 years from an E.ON coal fired power plant, transport it over a distance of about 26 km, and store it in the offshore depleted gas reservoir P-18 (figure 1.4), operated by TAQA. Earlier plans to establish pilot projects involving storage in gas reservoirs onshore (Barendrecht and in northern parts of The Netherlands), have been called off.
In parallel with these CCS projects, in 2004 the CATO (Dutch acronym for CO2 Capture, Transport and Storage) research and development programme was initiated. This programme had a focus on fundamental research. In 2009 this programme was followed up by CATO-2 (http://www.co2-cato.org/) with the additional aim to facilitate and enable integrated development of CCS demonstration sites in the Netherlands. The CATO programmes involve academic and industrial partners and knowledge institutes. The research presented in this thesis was conducted within the CATO-2 framework and contributed to work package 3.2 on reservoir behavior.
1.5. Research objective
Comprehensive understanding and prediction of physical and chemical processes during and following injection of CO2 in depleted gas reservoirs and saline aquifers are important for the assessment of the performance and impacts of planned and existing CCS projects. Over the last decade significant improvements have been made in numerical modeling of the complex, coupled processes involved. Among the many remaining issues where progress is still called for, is the consistent simulation of impacts of gas mixtures. In particular the presence of ‘impurities’ or ‘co-contaminants’ in the injected CO2 stream that are retained from the source gases (flue-gas, acid gas), such as N2 , Ar, O2 and SO2,and in-situ gases (e.g. CH4 , H2S) have the potential, upon dissolution in the pore water, to alter aqueous and water-mineral reactions. Evaluation of the impacts of the presence of such components on subsurface storage is also important because they modify fluid properties (e.g. density and viscosity) of the gas/liquid streams which influences transport of gas and brine and the pressure and temperature response of the storage reservoir. Knowledge of the consequences of impurities in the CO2 stream is of particular interest as high-level purification of CO2 is costly and injection of co-contaminants with the CO2 may therefore reduce the front-end processing costs of CCS. These costs of purification of CO2 are estimated to represent about ¾ of the total costs of CCS (Metz et al., 2005).
The main objective of this PhD thesis is to contribute to the quantitative understanding of the impact of impurities on reservoir storage behavior. The work that is presented focuses on the impact of impurities on:
the solubility of CO2 in formation brine (and solubility trapping) for a wide range of pressure and temperature conditions.
Chapter 1 9
the physical properties of the gas mixture and the density of the non-aqueous phase CO2 (and stratigraphic and residual trapping).
the thermal response of depleted gas reservoirs to CO2 injection with special attention for the influence of gas expansion/compression (Joule-Thomson effect).
water rock-interaction and associated changes in storage reservoir porosity with special attention for storage in aquifers.
An overarching question in all of the analyses is to what extent the presence of impurities has negative or beneficial consequences for the storage aspect of CCS.
1.6. Outline of this thesis
The thesis is structured as follows:
In chapter 2, a new thermodynamic model (Equation of State, EOS) is presented for calculations of solubility of gas mixtures in brine over a wide range of pressure, temperature and salinity of brine. This EOS includes CO2, SO2, H2S, CH4, O2 and N2 but some other gases can be readily added. Also the accuracy and validation of this EOS is investigated using experimental data and existing EOS’s.
In chapter 3 the thermal consequences of impure CO2 are studied using a coupled heat and mass transport model. First of all, methods are presented to calculate transport properties such as density, viscosity, heat capacity and Joule-Thomson coefficient of single gas and mixtures of gases for both aqueous and non-aqueous phases. Then it is shown how impurities can affect both the spatial extent of the zone around the well-bore in which Joule-Thomson cooling is induced and the magnitude of the cooling.
In chapter 4 other physical effects of impure CO2 are addressed. In this chapter we investigate the impact of the presence of impurities in the injected CO2 stream on solubility trapping (aqueous phase trapping) and volumetric trapping (trapping in the non-aqueous phase), for a wide range of pressure and temperature.
In chapter 5 chemical effects of impurities on the reservoir rocks (minerals and porosity) and brine composition are studied using the EOS presented in Chapter 2 and the geochemical modelling code PHREEQC. Focus is the long-term, geochemical impacts of impure CO2 storage in a saline aquifer. The mineralogy of the aquifer is adopted from the Triassic Hardegsen Formation at the P-18 field in the Dutch offshore.
Finally, chapter 6 provides an overview of the general conclusion of this thesis and also lists recommendations for useful future work on the research topic.
Introduction 10
Chapter 2
An Equation of State for thermodynamic equilibrium of gas
mixtures and brines
Part of this chapter is based on:
Ziabakhsh-Ganji, Z., Kooi, H., (2012). An Equation of State for thermodynamic equilibrium of gas mixtures and brines to allow simulation of the effects of impurities in subsurface CO2 storage. International Journal of Greenhouse Gas Control, 11S, 21-34.
Chapter 2 13
Abstract
In this chapter as an important step towards evaluation of the impact of gas mixtures on these processes, a new Equation of State (EOS) has been developed which allows accurate and efficient modeling of thermodynamic equilibrium of gas mixtures and brines over a large range of pressure, temperature and salinity conditions. Presently the new EOS includes CO2, SO2, H2S, CH4 and N2. This model is based on equating the chemical potentials in the system, using the Peng–Robinson EOS to calculate the fugacity of the gas phase. It is shown that the model performs favorably with respect to existing EOS’s and experimental data for single gas systems and accurately reproduces available data sets for gas mixtures. Preliminary analysis shows, amongst others, that CO2 solubility is most sensitive to CH4 admixture and least sensitive to the presence of SO2 in the injected gas.
2.1. Introduction
There is broad consensus that anthropogenic emission of carbon dioxide (CO2) into the atmosphere is an important driver of global warming and regional climate change and that the current trend of increasing CO2 emissions should be reversed (IPCC, 2007). Carbon dioxide capture and storage (CCS) is a significant component of the portfolio of mitigation technologies required to achieve such reversal (Smith et al., 2009). CCS generally involves capture of CO2 at major stationary sources such as power plants and injection in underground geological structures such as saline aquifers, depleted hydrocarbon reservoirs, or producing hydrocarbon reservoirs to enhance oil or gas recovery. Depths greater than 800 m are generally needed for aquifers to allow CO2 to be sequestered in supercritical and hence, fairly dense state (Bachu & Adams, 2003). While demonstration projects for storage in depleted gas/oil reservoirs have started only recently, the number of aquifer storage pilots conducted on various continents is progressively growing since first injection in a saline aquifer overlying the Sleipner field in the North Sea began in 1998 (AAAS, 2009; http://www.globalccsinstitute.com).
Coeval with these developments, efforts are ongoing to study the processes and factors that control the injectivity, containment, and long-term safety of geological storage. Numerical models play an important role in these efforts and are essential, together with experimental studies, to help develop a comprehensive understanding of the complex, coupled physico-chemical processes at play in subsurface storage. Over the last decades, capabilities of these numerical simulators have been progressively improving and they have been used to clarify key system behaviours such as the role of heterogeneity and density influences on spreading of CO2 (Bachu, 2008), the pressure response of aquifers (Birkholzer et al., 2009), the thermal response of depleted gas reservoirs (Oldenburg et al., 2009), and CO2-brine-mineral chemical reactions (White et al., 2005; André et al., 2007; Gaus, 2010).
While simulation of injection of pure, dry CO2 and its interaction with aquifer/reservoir constituents is well developed, capabilities to investigate presence and impacts of other (gaseous) components than CO2 are still limited. These additional components can either be so-called impurities or co-
An Equation of State for thermodynamic equilibrium of gas mixtures and brines 14
contaminants (SO2, H2S, N2, NOx) retained from the original flue-gases from which CO2 was separated, or pre-injection in-situ gases in the reservoir (Ghaderi et al., 2011) or aquifer, notably methane (CH4).Evaluation of the impacts of the presence of such components is important because they modify dynamical and thermal properties (viscosity, density, Joule-Thomson coefficient) of the gas/liquid streams, chemical partitioning among the CO2-rich phase and brine, and brine mineral reactions (Jacquemet et al., 2009; Gaus, 2010). Moreover, knowledge of the consequences of impurities in the CO2 stream is of particular interest as high-level purification of CO2 is costly and injection of co-contaminants with the CO2 may therefore reduce the front-end processing costs of CCS (Knauss et al., 2005).
Simplified approaches to evaluate the impacts of additional gases have been used in a couple of studies. Gunter et al. (2000) performed batch-type modeling (without transport) of geochemical interaction of carbonate minerals with brine containing dissolved H2S and H2SO4 (latter can be considered to be derived from SO2–brine system). However, CO2 was not included and concentrations of the acid gases were not obtained from solubility calculations. Knauss et al. (2005) used a more comprehensive approach involving 1D transport modeling, simulating the response of an aquifer to injection of a brine pre-equilibrated with imposed fugacities of CO2, H2S and SO2. Here, the separate non-aqueous (gas-mixture) phase was not considered in transport and simplifications were involved regarding activity calculations. Xu et al. (2007) further improved on this by simulating injection of pure CO2 together with an H2S and SO2 equilibrated brine. In their simulations the ECO2N module (equation of state) of the TOUGH2 code (Pruess, 2004) handles equilibrium calculations of the CO2-H2O-NaCl system during transport. However, presence of non-aqueous H2S and SO2 in the CO2-stream could not be modeled explicitly.
To further extend simulation-capabilities for analyzing the impacts of associated gases in subsurface CO2 storage, there is a need for efficient and accurate equations of state (EOS) that model the thermodynamic equilibrium of a large suite of gas mixtures and brines with a wide range of composition (Jacquemet et al., 2009). Some authors such as Zhang et al. (2011) have used a modified version of the TMVOC simulator of the TOUGH2 family to model the fate and transport of co-injected H2S with CO2 in deep saline formations. Battistelli and Marcolini (2009) recently took an important step by presenting an EOS module (TMGAS) for the TOUGH2 reservoir simulator (Pruess et al., 1999) that handles mixtures of several inorganic gases and hydrocarbons. They showed TMGAS reproduces density, viscosity and specific enthalpy data for several binary gas mixtures and does well in predicting solubility of several pure gases (CH4, CO2, H2S) in brine and in predicting water content of pure CO2. Moreover, they demonstrated injection of a H2S-CO2 mixture in a hydrocarbon reservoir containing methane does alter behaviour compared to pure CO2 system modeling. Battistelli et al. (2011) have used TMGAS-TOUGHREACT to model the injection of an acid gas mixture (CO2+H2S+CH4) into a high-pressure under-saturated sour oil reservoir. Geloni et al. (2011) have used the same software to analyse the effect of CO2 +CH4 in rock and cement and caprock around the wellbore in an exploited hydrocarbon reservoir. Unfortunately, TMGAS still is proprietary software. Moreover, not all details of the EOS appear to have been disclosed in publication(s), which makes it not easily available or reproducible for broader academic investigations in CCS.
Chapter 2 15
In this chapter, we present a new or alternative Equation of State (EOS) which, similar to TMGAS, allows accurate and efficient modeling of thermodynamic equilibrium of gas mixtures and brines over a large range of pressure (up to 600 bar), temperature (up to 110 C) and salinity (up to 6 m) conditions. Presently the model includes CO2, SO2, H2S, CH4 and N2, but the suite of gases can be readily extended. Non-NaCl brines can be handled and activity of aqueous species is based on the Pitzer formalism for high ionic strength. In the following we first present the EOS in detail. Then we show that the model performs favourably with respect to existing EOS’s and experimental data for single gas systems and accurately reproduces available data sets for gas mixtures. Focus is on solubility of impurities and special attention is paid to SO2 which is likely to have prominent geochemical impacts (Knauss et al., 2005; Xu et al., 2007). Finally, we illustrate that CO2 solubility is most sensitive to CH4 admixture and least sensitive to the presence of SO2 in the injected gas mixture.
2.2. Thermodynamic Model
The model describes thermodynamic equilibrium between a non-aqueous phase (NaqP), basically a multi-component mixture that can be in gas, supercritical or condensed conditions, and an aqueous phase (AqP), that may include dissolved hydrocarbons (here methane) and gases in addition to water and dissolved solids. The EOS does not include solid/minerals as a separate phase.
2.2.1 Equilibrium between AqP and NaqP
Thermodynamic equilibrium implies that the chemical potential of each component in the AqP and the NaqP are equal. For the NaqP phase we use
0( , ) ( , ) ln( )NaqPNaqPT P T P RT f , (1)
where is chemical potential and 0 is chemical potential at reference temperature, R is the gas
constant, T is temperature, P is pressure, and f is fugacity which is equal to
f P y (2)
where is the fugacity coefficient, y is the mole fraction of the component in the NaqP and P is total
pressure. The chemical potential of the AqP is written in terms of activity a rather than fugacity.
0( , ) ( , ) ln( )AqPAqPT P T P RT a , (3)
Equating the two chemical potentials gives
0 0( , ) ( , )lnAqP NaPT P T P a
RT P y(4)
An Equation of State for thermodynamic equilibrium of gas mixtures and brines 16
In terms of equilibrium constant this reads0K
0 00( , ) ( , )
lnAqP NaPT P T PK
RT, (5)
By using 0HNwkK
(Prausnitz et al., 1986) Eqs. (4) and (5) yield
H
Nw ak P y (6)
where is the number of moles per kilogram of water (55.508) and Nw Hk is Henry’s constant. We
further use a Nw x , which is reasonable because the solubility of the gas species is small (Spycher
et al., 2005). The effect of salt is accounted for in the activity coefficient of the gas species, (Eq.
26). Therefore the final equation for dissolved gas yields (Akinfiev & Diamond, 2003; Zirrahi et al., 2012)
HP y k x (7)
Hence, for each gas we have
i i H i i iNaqP AqPP y k x (8)
where subscript i denotes individual gases like except water. Similar to
Battistelli and Marcolini (2009), we ignore binary interaction between different dissolved gases in the aqueous phase. Therefore, the activity coefficient in Eq. (8) for individual gas species does not depend on presence of other gases. This assumption is an important one in the present EOS since it allows use of a rather simple, non-iterative solving method.
2 2 2 2 4, , , ,CO SO N H S CH
Since the EOS should be able to quantify thermodynamic equilibrium between gas mixtures and brine, water is an important system component. For equilibrium between H2O in the AqP and the NaqP we follow the approach of Spycher et al. (2003):
2 ( ) 2 ( )l gH O H O (9)
2 ( )
2
2 ( )
gH OH O
H O l
fK
a (10)
where is Spycher’s ‘true equilibrium constant’, f is the fugacity of NaqP water, and a is the activity of AqP water. The equilibrium constant of water is a function of temperature and pressure as given by Eq. (11)
K
Chapter 2 17
2
2 2
000, , exp H O
H O H O
P P VK T P K T P
RT(11)
where T is temperature in K;2H OV
0P
is the average partial molar volume of the water in the AqP over the
pressure interval from to which is equal to 18.1; is a reference pressure, which is assumed to
be 1 bar. The equilibrium constant at reference pressure
P 0P
2
00,H OK T P is obtained from
2
0 2 4 2log 2.209 3.097 10 1.098 10 2.048 10 ,H OK 7 3 (12)
where is temperature in (Spycher et al., 2003). By combining (10), (11) and (2) we obtain C
2 2 2
2
2
00expH O H O H O
H OH O
K a P P Vy
P RT(13)
At the range of consideration for pressure and temperature (5 - 110 ), the solubility of gases in water is low, and the activity of the water component can be approximated by its mole fraction in the liquid phase. Therefore, in Eq. (13) the effect of dissolved salt is accounted for in the activity of water. Using these considerations yields
C
2
2 2
00 exp H O2 2H O H O
P P VK x
RT H O H OPy (14)
Eq. 14 is used in the model for equilibrium of H2O in the system. For the full set of equilibrium equations, Eq. 14 is combined with Eq. 8.
2.2.2. Non aqueous phase
In Eqns. (8) and (14) the fugacity coefficient must be derived from PVT or PVT-X properties of brines and different gas mixtures by utilizing an equation of state. There are many EOS’s in the literature. Some authors such as Duan and Sun (2003) and Duan and Mao (2006) used a virial like equation of state. However the complexity of the equation makes it not very practical for our aims. Cubic equations in volume were developed and improved over the last century. Redlich and Kwong (1949) (RK) and Peng Robinson (1976) (PR) are well-known examples. Other examples are the equations of Schmidt-Wenzel (1980) and Soave Redlich-Kwong (1972) which basically are modifications of the Van der Waals EOS. Still other studies used a modified form of RK to represent the properties of gas mixtures such as CO2-H2O (Spycher et al., 2003; King et al., 1992; Zirrahi et al, 2010; Hassanzadeh et al., 2008). Similar to Battistelli and Marcolini (2009), we use the classical Peng-Robinson (1976) EOS. Although the PR EOS is more elaborate than, for instance, RK, it has the advantage that is has greater accuracy around the liquid-vapour boundary.
An Equation of State for thermodynamic equilibrium of gas mixtures and brines 18
In our model, calculation of the fugacity coefficient in the non aqueous phase is as follows. The compressibility factor obeys
3 2 2 2 31 2 3Z B Z A B B Z AB B B 0 (15)
Parameters A and B are a function of pressure and temperature and are defined as follows
2
a T PA
RT(16)
bPBRT
(17)
where
2 2
0.45724 c
c
R Ta T TP
(18)
0.07780 c
c
RTbP (19)
and
2
21 0.37646 1.4522 0.26992 1c
TTT
(20)
where is the acentric factor. To calculate the fugacity coefficient for each species, i , in gas
mixtures, we use standard simple mixing rules and binary interaction coefficients (Prausnitz et al., 1986).
i j iji j
a y y a , 1ij i j ija a a k , i ii
b b y (21)
22.414ln ( 1) ln ln
2.828 0.414
j ijji i
i
y aB BA ZZ Z B BB B B a Z B
(22)
The binary interaction coefficients for CO2-SO2, CO2-H2S, CO2-CH4 and CO2-N2 were obtained from Li and Yan (2009). As observed by Spycher et al. (2003) the current approach neglects the mole fraction of water in the mixing rule (same as assuming infinite dilution of NaqP H2O). This is practical since it reduces iteration demands as will be explained in the section on model calibration.
Chapter 2 19
To obtain the proper value of Z in Eq. (22), we follow the approach described by Danesh (1998). When Eq. (15) has three roots, the intermediate one is ignored and the root yielding the lowest Gibbs
free energy between the remaining two is selected. Let Zh and Zl be the two real roots with hGRT
and
lGRT
being the Gibbs free energy, and where the subscripts denote the high and low Z value
respectively. The difference in Gibbs free energy is given by:
1 2
2 2
( ) ln ln1
h l l lh l
h l
G G
1
h
h
Z B Z B ZAZ Z BRT Z B B Z B Z B
(23)
where 1 and 2 for Peng-Robinson EOS are 1 2 and 1 2 respectively. If h lG GRT
in Eq.
(23) is positive Zl is selected; otherwise Zh is the correct root.
2.2.3. Aqueous phase
In the next step of model development, Henry’s constant, H ik , and the activity coefficient, i , on the
right-hand side of Eq. (8), need to be quantified. For the temperature and pressure dependency of Henry’s constant, we use a correlation established by Akinfiev and Diamond (2003). The correlation is a virial-like equation for the thermodynamic properties of the aqueous phase species at infinite dilution and requires but a few empirical parameters (constrained by experimental data), and these parameters are independent of temperature and pressure
0 02 2ln( ) (1 ) ln ln 2H H O H O H
RTk fMw
02O B (24)
where is a constant for each dissolved gas in water, T is temperature in K; and 02H Of and 0
2H O
0
are
fugacity and density of pure water, respectively. For calculation of properties of pure water we use the
correlation of Fine and Millero (1973); see Appendix A. It should be noted that we quantify 2H Of
using Eq. (A6) because Eq. (22) is not sufficiently accurate for pure water. In Eq. (24) B (cm3.g-1)stands for the difference in interaction between dissimilar solvent molecules (Akinfiev & Diamond, 2003) and is calculated as follows
310B PT
(25)
where (cm3. g-1) , (cm3. K0.5. g-1) and (bar-1) denote adjustable parameters. In the original
version of Eq. (25) (Akinfiev & Diamond, 2003, their Eq. (15)) the term P does not occur. It is added here specifically for SO2 to allow for the fact that the solubility of this species is two to three
An Equation of State for thermodynamic equilibrium of gas mixtures and brines 20
orders of magnitude higher than other considered gas species. For the latter we, therefore, set 0 .It should further be noted that we only used the parameter values for Eqs. (24) and (25) tabu by Akinfiev and Diamond (2003) as initial guesses, and obtained new estimates of these parameters for the pressure and temperature ranges of interest during calibration (new parameter values are listed in Table 2.2).
For calculat
lated
ilar
(26)
ion of the activity coefficient of the various gas species, we developed an approach sim
A C
where subscript of mC and mA denote anions and cations molality respectively,
to Duan and Sun (2003). Reduction of the activity coefficient due to interaction with solute present in the brine (Pitzer, 1973), is based on a virial expansion of Gibbs excess energy
ln 2 2i C i C A i A A C iC A C A
m m m m
i C and i A C are
) we second and third-order interaction parameters respectively. Following Duan and Sun (2003 also
assume 0i A . Temperature and pressure dependency of the interaction parameters is modelled
using
3 5 81 2 4 6 7 9 102 2Par( , ) ln
630c c c PP TT P c c T c P c c c T P cT P T P T
PT
where is either
(27)
Par( , )T P or , P is pressure in bar and T is temperature in K and the ,ic i
.
1..10
Followingare con ch are cal late by using a fitting procedure and are given in Table 3
Duan and Sun (2003) we reduce the number of interaction parameters by using i C i Na
stants whi cu d
, and by
interpreting m for the second-order interaction term in terms of equivalents pe ine (that
is, molality ltiplied by valency). For the third-order interaction parameters we assume
i A C i Na Cl
C
mu
r mass of br
while maintaining molalities in Eq. (26). For instance, for a brine containing
potassium and magnesium salts, Eq. (26) effectively gives sodium, calcium,
ln 2 2 2i i Na Na Ca K Mg i Na Cl Cl Na K Mg Cam m m m m m m m m (28)
It may be worthy to note that, in contrast to Duan and Sun (2003) who use different equations for the
.3. Model Calibration
east Square (WNLS) method was used in model calibration. Calibration for
pressure and temperature dependency for the various gas species, we use the single form shown in Eq. (27). Furthermore, it may be pointed out that in the absence of dissolved salts (gas dissolution in pure water), Eq. (26) yields activity coefficients equal to 1.
2
The Weighted Nonlinear Leach gas component (CO2, CH4, N2, H2S, SO2) was conducted in two steps. First, the parameters in the Henry constant (Eqs. (24) and (25); , , and ) and the binary interaction coefficient between
Chapter 2 21
H2O and the gas species (Eq. (21)) were obtained using experimental data for equilibrium with pure water. Second, the parameters in the relationship quantifying the activity coefficient (Eq.
(27); , 1..10ic i ) were determined from data for brine-gas systems. The calibration targets
(expe a sets) that were used were obtained from the literature listed in Table 2.1. rimental dat
Table 2.1: Experimental data used in calibration of the model
CO2
Authors Solution (M = mol. K -1)g
T (K) P (bar)
Wiebe and Gaddy (1939) Wiebe and Gaddy (1940)
Todheide and Franck (1963) Za 1) wisza and Malesinska (198
Müller et al. (1988) King et al. (1992) Drummond (1981)
Nighswander et al. (1989) Rumpf et al. (1994)
Prutton and Savage (1945)
WaterWaterWaterWaterWaterWater
3 23–373
0–6. Cl 5 m Na0–0. aCl 17 m N
4–6 m NaCl 0–3.9 m CaCl2
285–313 323–623 323–473 373–473 288–298 290–673 353–473 313–433 348–394
25–710 25–510
2 00–35001– 54 3– 80
60–250 35–400 20–100 1– 100 10–700
H S2
Selleck et al. (1952)Lee and Mather (1977) Gillespie et al. (1982)
Drummond (1981) Suleimenov & Krupp (1994)
Xia et al. (2000)
WaterWaterWater
0– l 6 m NaC0– 2. Cl5 m Na4–6 m NaCl
310.15–443.15 283.15–453.15 311.15-477.15 373.15-653.15 393.15-593.15 313.15–398.15
6-210 1-70
10-210 6-200 0-140
10-100
N 2
Goodman and Krase (1931) Wiebe et al. (1932) Wiebe et al. (1933)
Saddington and Krase (1934) Smith et al. (1962)
O’Sullivan and Smith (1970) Alvarez and Prini (1991)
Chapoy et al. (2004)
WaterWaterWaterWater
0–6. Cl 2 m Na0–4. Cl 6 m Na
WaterWater
273.15–442.15 298.15
298.15–373.15 338 15 .15–513.
303.15 324.65–398.15 33 6.3–636.5
274.19–363.02
101.3–303.9 25.33–1013.25 25.33–1013.25
101.3–304 11–72.6
101.3–616.1 5.34–256
9.71–70.43
CH4
Michels et al. (1936)
Dodson and Standing (1944) Culberson et al. (1950)
Culberson and Mcketta (1951) Duffy et al. (1961)
O’Sullivan and Smith (1970)
Water1.01–6.59 m aCl N2.91–2 aCl2.93 m C
0.0–0.6 m brine WaterWaterWater
0.5– aCl 6.1 m N0–7. Cl235 m Ca
Water
298.15–423.15 298.15–423.15
298.15 311.15–394.15
298.15 298.2–444.3
298 15.15–303.303.15
298.15–303.15 324 15
40.6–469.1 41.8–456.0 56.2–209.9
35–345 36.2–667.4 2
.65–398.
2.3–689.13.17–51.71 214.8–957.5
3.2–74.8 101.3–616.1
An Equation of State for thermodynamic equilibrium of gas mixtures and brines 22
continued from pervious page…
Am )irijafari and Campbell (1972Blanco and Smith (1978)
Namiot et al. (1979) Blount and Price (1982)
Crovetto et al. (1982) S )toessell and Byrne (1982b
Cramer (1984)
Yarym 985)-Agaev et al. (1Yokoyama et al. (1988)
Lekvam and Bishnoi (1997) Song et al. (1997)
Dhima et al. (1998) Kiepe et al. (2003)
Wang et al. (2003) Chapoy et al. (2005)
1.01–4.4 m NaCl 1Water
1.0 m CaCl20–1. aCl 54 m N0–5.9 m NaCl
WaterWater
0–4. Cl 0 m Na0–4 Cl .0 m K
0–2.16 m MgCl20–2.0 m CaCl2
Water0.81–4.7 m NaCl
WaterWaterWaterWaterWaterWater
0.99- l 3.99 m KCWaterWater
324.65 8.15 –39310.93 4.26 –34298.2–398.2
323–623 372.15–513.152 97.5–518.3
298.15 298.15 298.15 298.15 298.15
27 7.2–573.227 7.2–573.2298.2–338.2
298.15–323.15298.15–323.15273.2–290.2
344 313–473
313.5 3.19 1–372 83.2–303.2
275.11–313.11
101.3 .1 –61641.4– 44.7 3
101–608 295
75–1570 13.2 .51 7–6424.1–51.7 24.1–51.7 24.1–51.7 24.1–51.7 24.1–51.7 11–132 19–124 25–125 30–80
5 .67–90.8234.5
200–1000 3 .4–93
4.2–97.9 2 0–400.39.7–180
O2
Geng & Duan (2010) Water0-6 m Na l C
273.15-513 1-600
SO2
Rumpf & Maurer (1992) Xia et al. (1999)
Water2.942–5.928 m NaCl
293.15–413.15 0.1–25 313–393 0.1-37
CO2+CH4+H2S
Huang et al. (1985) Water 37.8–176.7 48.2–173.1
hese include both solubility data for the gas species in the aqueous phase and data on H2O vapour
Table 2.2: Calibrated parameter values for
Tcontent in the non aqueous phase. The optimized parameter values are listed in Tables 2.2 – 2.5.
Hk for various species (Eq. (24))
Gas
CO2 -0.114 35 -5.279 63 6.187 05 0 967H 0.77357854 0.27049433 0.27543436 0 2SSO2 0.198907 -1.552047 2.242564 -0.0 09847N2 -0.008194 -5.175337 6.906469 0
CH4 -0.092248 -5.779280 7.262730 0
O2 0.290812 -1.862778 3.9917226 0
Chapter 2 23
Table 2.3: Calibrated second-order interaction parameters ( ) for various gases (Eq. (27))
cons nt ta2CO Na 2SO Na 2N Na 2H S Na 4CH Na 2O Na
1c -0.0653 -5.0962E-2 -2.0934 1.0366 -5.707E-1 0.20
2c 1 3 -1 .6791E-4 2.8865E-4 .1445E-3 .1785E-3 7.300E-4 0
3c 40.839 0 3.9139E+2 -1.7755E+2 1 .5177E+2 0
4c 0 0 -2.9974E-7 -4.5313E-4 3.1927E-5 0
5c 0 1.11 2 45E- 0 0 0 0
6c -3. 9 E-2 -1.59 E-5 -1.64 E-5 267 0 18 0 27 0
7c 0 -2.48 E-5 78 0 0 0 0
8c 2. 11 E-2 57 0 0 0 0 0
9c 6. 5486E-6 0 0 0 0 0
10c 0 0 0 4.77 1 51E+ 0 0
Table 2.4: Calibrated third-order interaction arameters ( p ) for various gases (Eq. (27))
Constant 2CO Na 2SO Na 2N Na 2H S Na 4CH Na 2O Na
1c -1. 14 2 -7.146E-3 -6.398E-3 -0.01027 -2.999E-3 -1.28E-2 46E-
2c 2. 828E-5 0 0 0 0 0
3c 0 0 0 0 0 0
4c 0 0 0 0 0 0
5c 0 0 0 0 0 0
6c 1. 3 -2 98E 0 0 0 0 0
7c 0 0 0 0 0 0
8c -1. 43 2 49E- 0 0 0 0 0
9c 0 0 0 0 0 0
10c 0 0 0 0 0 0
Table 2.5: Calibrated binary interaction coefficients
CO2 H2S S 2O N 2 CH4 O2
H2O 0. -1 9 0.32 0.19014 0.105 .1032 547 47893 0.9
An Equation of State for thermodynamic equilibrium of gas mixtures and brines 24
2.4. Solving the model equations for systems consisting of single or mixed gases
For single gas-brine systems, partitioning of the gas species and H2O among the aqueous and non-aqueous phase can be directly obtained from the following equations. The determination of the phase composition for single gas – brine systems is non iterative because of the assumptions made that the fugacity of the gas in NAqP does not depend on composition, but can be computed accounting only for know P and T (illustrated here for CO2).
2
22
2
2 2
2 22
00
1
1 exp
CO
CO
CO
H CO
H O
H O H O CO
H O H CO
Pk
yK P P V P
P RT k2
(29a)
2
222
2
22 2 2
2 22
00
1
1
1 exp
CO
CO
CO
CO
H COCOCO
H CO H O H O CO
H O H CO
PkP
xk K P P V P
P RT k2
(29b)
Eq. (29) is obtained by combination of Eqs. (8) and (14) and using the fact that
2 2 2 2, ,1, 1i ii CO H O i CO H O
x y (30)
For gas mixtures the method is a little different. Because the number of equations and the number of unknowns (mole fraction of each species in gas and liquid phase) are not equal, Vapour-Liquid flash calculations are used (Danesh, 1998). First the mole fraction of each component in the total system, zi,(feed) is defined. The problem is to solve for xi and yi for given P, T, and salt molality. To do this, the Rachford-Rice equation
1
10
1 1
Ni i
Vi i
z KK n
(31)
is solved for nV, the mole fraction of NaqP in the system (value between 0 and 1). In Eq. (31) Ki-valuesare defined as follows:
2 2 2 2 4 2, , , , , , ,ii
i
yK i H O N O CO CH H S Sx 2O (32)
According to Eq. (14) the K-value for water is
Chapter 2 25
2
2
2
2
00 exp H OH O
H OH O
P P VK
RTK
P(33)
And according to Eq. (8) for other components, the K-value is
2 2 2 4 2, , , , , , 2iH i
ii
kK i N O CO CH H S SO
P(34)
With the known value of nV , Ki’s and zi’s, the mole fraction of each phase are subsequently obtained from
1 1i
i Vi
zxK n
,1 1
i ii V
i
K zyK n
. (35)
In the case of gas mixtures the binary interaction between dissolved gases in the aqueous phase is ignored (Battistelli & Marcolini, 2009). Binary interaction coefficients for CO2-SO2, CO2-H2S, CO2-CH4, CH4-H2S and CO2-N2 for the non-aqueous phase are adopted from Li and Yan. (2009), while the gas-H2O interaction coefficients, listed in Table 2.5 are known from model calibration. It may be worthwhile repeating that in the mixing rule (Eq. (21)) the mole fraction of water has been neglected. This is convenient since it eliminates the need for iteration procedures.
2.5. Results and Discussion
In this section the model performance is assessed and illustrated by showing: (1) results of calibration, (2) comparison with existing models for H2O-NaCl-CO2 and H2O-CaCl2 -CO2 systems (Spycher et al., 2003; Spycher & Pruess, 2005; Duan & Sun, 2003; Duan & Mao, 2006; Mao & Duan, 2006), and (3) how model predictions for gas mixtures compare with experimental data.
CO2-brine
In figure 2.1 a comparison is shown of the model with respect to experimental data used in the calibration for pure water. Both CO2 solubility and water content in the CO2-rich phase are shown for different temperatures.
Figure 2.2 demonstrates that our model predictions are virtually identical to those of Spycher et al. (2003; 2005) and Duan and Sun (2003) for different brines up to pressures of 600 bars.
An Equation of State for thermodynamic equilibrium of gas mixtures and brines 26
0 100 200 300 400 500 600 7000
1
2
3
4
5T=298.15 K (a)
P (bar)
x CO
2*100
0 100 200 300 400 500 600 7000
0.005
0.01
0.015
0.02
0.025
0.03T=298.15 K (b)
P (bar)
y H2O
in C
O2
0 100 200 300 400 500 600 7000
1
2
3
4
5T=304.19 K (c)
P (bar)
x CO
2*100
0 100 200 300 400 500 600 7000
0.01
0.02
0.03
0.04
0.05T=304.19 K (d)
P (bar)
y H2O
in C
O2
0 100 200 300 400 500 600 7000
1
2
3
4
5T=308.15 K (e)
P (bar)
x CO
2*100
0 100 200 300 400 500 600 7000
0.01
0.02
0.03
0.04
0.05
0.06T=308.15 K (f)
P (bar)
y H2O
in C
O2
0 100 200 300 400 500 600 7000
1
2
3
4
5T=313.15 K (g)
P (bar)
x CO
2*100
0 100 200 300 400 500 600 7000
0.02
0.04
0.06
0.08T=313.15 K (h)
P (bar)
y H2O
in C
O2
Fig. 2.1: Comparison between results for the new EOS (solid lines) and experimental data (symbols) for CO2solubility (left panels) and H2O content of the CO2-rich phase (right panels) for various temperatures. The data shown are identical to those used by Spycher et al. (2003; their Appendix A).
Chapter 2 27
0 100 200 300 400 500 600 7000
1
2
3
4
5T=323.15 K (i)
P (bar)
x CO
2*100
0 100 200 300 400 500 600 7000
0.02
0.04
0.06
0.08
0.1
0.12
0.14T=323.15 K (l)
P (bar)
y H2O
in C
O2
0 100 200 300 400 500 600 7000
1
2
3
4
5T=333.15 K (m)
P (bar)
x CO
2*100
0 100 200 300 400 500 600 7000
0.05
0.1
0.15
0.2
0.25T=333.15 K (n)
P (bar)
y H2O
in C
O2
0 100 200 300 400 500 600 7000
1
2
3
4
5T=348.15 K (o)
P (bar)
x CO
2*100
0 100 200 300 400 500 600 7000
0.1
0.2
0.3
0.4T=348.15 K (p)
P (bar)
y H2O
in C
O2
0 100 200 300 400 500 600 7000
1
2
3
4
5T=353.15 K (q)
P (bar)
x CO
2*100
0 100 200 300 400 500 600 7000
0.1
0.2
0.3
0.4
0.5T=353.15 K (s)
P (bar)
y H2O
in C
O2
Fig. 2.1: continued
An Equation of State for thermodynamic equilibrium of gas mixtures and brines 28
0 100 200 300 400 500 600 7000
1
2
3
4
5T=366.45 K (w)
P (bar)
x CO
2*100
0 100 200 300 400 500 600 7000
0.02
0.04
0.06
0.08
0.1
0.12
0.14T=366.45 K (x)
P (bar)
y H2O
in C
O2
0 100 200 300 400 500 600 7000
1
2
3
4
5T=373.15 K (y)
P (bar)
x CO
2*100
0 100 200 300 400 500 600 7000
0.05
0.1
0.15
0.2T=373.15 K (z)
P (bar)
y H2O
in C
O2
Fig. 2.1: continued
0 100 200 300 400 500 600 7000
0.5
1
1.5
2
2.5
P (bar)
x CO
2* 10
0
(a)
New ModelSpycher & Pruess (2005)Duan & Sun (2003)
280 300 320 340 360 3801.4
1.6
1.8
2
2.2
2.4
T (K)
x CO
2* 10
0
P=300 bar, m= 2 M (b)
New ModelSpycher & Pruess (2005)Duan & Sun (2003)
Fig. 2.2: Comparison between results for the new EOS (solid lines) and predictions of the EOS’s of Spycher et al. (2005) and Duan and Sun (2003) (symbols) for CO2 solubility as function of (a) pressures at 90°C and 2 m salinity of NaCl (b) temperature at 300 bar and 2 m salinity of NaCl. (c) Same for the EOS of Spycher et al. (2005) and 76°C and various salinity of CaCl2.
0 100 200 300 400 500 600 7000
0.5
1
1.5
2
2.5
P (bar)
x CO
2* 10
0
T=349.15 K (c)
m= 1.05m= 2.3m= 3.95
Chapter 2 29
Table 2.6: Absolute deviation (AD %) from experimental data for the new model and for the models of Spycher et al. (2003) and Duan and Sun (2003).
T (K) P bar 2
100COx New Model Spycher et al. (2003)
Duan and Sun (2003)
323.15 25.3 0.774 2.550519 1.720475 2.456373 323.15 40.5 1.09 6.983281 6.886282 7.069009 323.15 50.6 1.37 0.250958 0.607855 0.465618 323.15 68.2 1.651 0.787999 1.83888 1.273293 323.15 75.3 1.75 0.410151 1.682105 1.01269 323.15 101.33 1.98 0.425269 1.674057 1.368011 323.15 111 2.10 2.974057 2.164378 2.227906 323.15 121 2.14 2.906066 2.367484 2.407302 323.15 141.1 2.17 1.233456 0.969925 1.091927 323.15 152 2.174 0.007072 0.154437 0.004453 323.15 200 2.30 0.528422 0.530476 0.780196 323.15 304 2.457 0.945205 0.980066 0.862124 323.15 405.3 2.606 1.094991 1.218304 1.505869 323.15 500 2.80 1.321428 1.187714 0.402989 323.15 608 2.868 1.041145 1.074843 2.563775 323.15 709.3 2.989 0.931 0.741758 2.914181 AAD 1.219551 1.289952 1.420286
exp exp exp exp% 100 | ( ) / |, % 100 | ( ) / | /cal calAD x x x ADD x x x N
The Spycher model forms the basis of the ECO2N-EOS module in TOUGH2 (Pruess, 2005). To allow a further quantitative comparison with these models, we calculated the absolute deviation (AD) of these models and our model with respect to experimental data shared by all studies. Table 6 shows that our model performs favourably with respect to the existing ones. Table 2.6 only gives results for a small selection of data. For the full data set of 405 measurements the (average absolute deviation) AAD value of our model is about 8.3%.
H2S-brine
For H2S our model shows good agreement with the solubility model of Duan et al. (2007) (Figure 2.3a) and with experimental data for the mole fraction of water in the gas phase (Søreide & Whitson, 1992) (Figure 2.3b).
Figure 2.4a highlights the importance of accounting for non-ideality of H2O in the non-aqueous phase as we do in our model. The figure indicates that the assumption of ideal mixing for water in the gas-rich phase strongly underestimates the actual water content at relatively high pressures. Figure 4b illustrates model behaviour with respect to H2S solubility in brine for various salinities.
An Equation of State for thermodynamic equilibrium of gas mixtures and brines 30
0 50 100 150 200 2500
1
2
3
4
5
6
7
8
P (bar)
x H2S
* 10
0
T= 333.15 K (a)
m= 0m= 2m= 4m= 6
0 50 100 150 200 2500
0.02
0.04
0.06
0.08
0.1
0.12
P (bar)
y H2O
in H
2S
(b)
T=304.15 KT= 344.15 KT= 364.15 K
Fig. 2.3: (a) Comparison between results for the new EOS (solid lines) and predictions of the EOS of Duan et al. (2007) (symbols) for H2Ssolubility in NaCl brines with different salinities and at a temperature of 333.15 K. (b) Comparison between results for the new EOS (solid line) and experimental data (Søreide & Whitson, 1992) for H2O content in the H2S-rich phase.
0 20 40 60 80 100 120 1400
0.02
0.04
0.06
0.08
0.1
0.12(a)
T= 343.15 K
T= 363.15 K
P (bar)
y H2O
in H
2S
0 50 100 150 200 2500
1
2
3
4
5
6
7
8
P (bar)
x H2S
* 10
0
T= 363.15 K
(b)
m= 0m= 2m= 4m= 6
Fig. 2.4: (a) Comparison between results for the new EOS (solid lines) and Duan et al. (2007) data (symbols) for H2S solubility in NaCl brines at 363.15 K for various salinities. (b) Comparison between results for the new EOS (solid lines), and AQUAlibrium (2010) software-predicted (symbols) water content in the H2S-rich phase. The dashed lines illustrate that if ideal mixing would be assumed for calculation of water content in the H2S-rich phase, the model would yield too low values for pressures exceeding about 40 bar.
Chapter 2 31
SO2-brine
Experimental data on SO2-water or SO2-brine systems are very scarce. Figures 2.5a and 2.5b show how the model compares with respect to the data reported in the two studies listed in Table 2.1. It should be noted that although the model fit is good, predictions at pressures beyond about 10 bar are not well constrained and, hence, are associated with relatively large uncertainty.
0 5 10 15 20 25 30 350
5
10
15
20
25
P (bar)
x SO
2* 10
0
(a)
T=313.15T=343.15T=363.15
0 5 10 15 20 25 30 350
5
10
15
20
25
P (bar)
x SO
2* 10
0
m= 2.942
m= 5.928
(b)
T=313.15T=323.15
Fig. 2.5: Comparison between results for the new EOS (solid lines) and experimental data (symbols) for SO2. (a) Solubility in pure water; data from Rumpf et al. (1992). (b) Solubility in NaCl brines for different salinity and temperature; data from Xia et al. (2000).
N2-brine
Figure 2.6a demonstrates model-predicted solubilities of N2 show good correspondence with solubilities by Mao and Duan (2006) for a large range of salinities. Model performance with regard to experimental data for the mole fraction of water in rich N2 phase (Namiot & Bondareva 1959) is illustrated in Figure 2.6b.
An Equation of State for thermodynamic equilibrium of gas mixtures and brines 32
0 100 200 300 400 500 6000
0.5
1
1.5
2
2.5
3
3.5
P (bar)
x N2*
1000
(a)m= 0
m= 2m= 4m= 6
0 20 40 60 80 100 120 1400
0.05
0.1
0.15
0.2
0.25(b)
P (bar)
y H2O
in N
2Fig. 2.6: (a) Comparison between results for the new EOS (solid lines) and predictions of the EOS of Mao and Duan (2006) (symbols) for N2 solubility in NaCl brines with different salinities and at a temperature of 333.15 K.
(b) Comparison between results for the new EOS (solid line) and experimental data (Namiot & Bondareva 1959) (symbols) for water content in the N2-rich phase at 366.45 K.
CH4-brine
Figure 2.7 depicts model performance for methane. Both the correspondence with the existing model of Duan and Mao (2006) (Figure 2.7a) and experimental data (Olds et al., 1949) are very satisfactory.
0 100 200 300 400 500 600 7000
1
2
3
4
5
P (bar)
x CH
4* 10
00
(a)m= 0m= 1m= 2m= 4m= 6
0 100 200 300 400 500 600 7000
0.01
0.02
0.03
0.04
0.05(b)
P (bar)
y H2O
in C
H4
Fig. 2.7: (a) Comparison between results for the new EOS (solid lines) and predictions of the EOS of Duan and Mao (2006) (symbols) for CH4 solubility in NaCl brines with different salinities and at a temperature of 333.15 K.
(b) Comparison between results for the new EOS (solid line) and experimental data (Olds et al. 1949) (symbols) for water content in the CH4 -rich phase at 377.59 K.
Chapter 2 33
O2-brine
Figure 2.8 illustrates the model performance for Oxygen. A favorable agreement has been observed between existing model of Geng and Duan (2010) and results of this model.
0 50 100 150 200 250 300 350 4000
2
4
6
8
10
P (bar)
x O2*
1000
m= 0
(a)
T=273.15T=303.15T=333.15T=363.15
260 280 300 320 340 360 3800
2
4
6
8
10
T (K)
x O2*
1000
(b)
P= 10 barP= 50 barP= 100 barP= 200 barP= 400 bar
0 50 100 150 200 250 300 350 4000
1
2
3
4
5
6
7
P (bar)
x O2*
1000
m= 1
(c)
T=273.15T=303.15T=333.15T=363.15
260 280 300 320 340 360 3800
1
2
3
4
5
6
7
T (K)
x O2*
1000
(d)
P= 10 barP= 50 barP= 100 barP= 200 barP= 400 bar
0 50 100 150 200 250 300 350 4000
1
2
3
4
5
P (bar)
x O2*
1000
m= 2
(e)
T=273.15T=303.15T=333.15T=363.15
260 280 300 320 340 360 3800
1
2
3
4
5
T (K)
x O2*
1000
(f)
P= 10 barP= 50 barP= 100 barP= 200 barP= 400 bar
0 50 100 150 200 250 300 350 4000
0.5
1
1.5
2
2.5
P (bar)
x O2*
1000
m= 4
(g)
T=273.15T=303.15T=333.15T=363.15
260 280 300 320 340 360 3800
0.5
1
1.5
2
2.5
T (K)
x O2*
1000
(h)
P= 10 barP= 50 barP= 100 barP= 200 barP= 400 bar
Fig. 2.8: Comparison between results for the new EOS (solid lines) and predictions of the EOS of Geng and Duan (2010) (symbols) for O2 solubility in NaCl brines with different salinities and temperature.
An Equation of State for thermodynamic equilibrium of gas mixtures and brines 34
Gas mixture-brine
We have been able to find two studies with relevant experimental data regarding equilibrium conditions for brine and gas mixtures (Huang et al. 1985; Qin et al. 2008). The system of Huang et al. (1985) is for a 3-component gas mixture consisting of CO2, CH4 and H2S with mole fractions of 0.6, 0.3 and 0.1 respectively. This gas mixture is equilibrated with various amounts of water. Data and model performance is shown in Figure 2.9. It should be noted that the experimental data (Huang et al., 1985) were not involved in the model calibration, which was done for single gas-brine systems only.
40 60 80 100 120 140 160 1800
5
10
15
20
25
P (bar)
x CO
2* 10
00
(a)T=310.95T=380.35
40 60 80 100 120 140 160 1800
5
10
15
20
25
30
35
P (bar)
y H2O
* 10
00 in
mix
ture
(b)T=310.95T=380.35
Fig. 2.9: Comparison between results for the new EOS (solid lines) and experimental data (symbols) for a three-component gas mixture consisting of CO2, CH4 and H2S with mole fractions of 0.6, 0.3 and 0.1, respectively. (a) Solubility of CO2 in pure water; experimental data from (Huang et al., 1985). (b) H2O content of the gas mixture (NaqP); experimental data from (Huang et al., 1985).
The favourable correspondence between data and model therefore provides some confidence that the employed method for handling gas mixtures is adequate.
0.55 0.6 0.65 0.7 0.75 0.8 0.850.9
1
1.1
1.2
1.3
1.4
1.5
1.6
nCH
4
/(nCH
4
+ nCO
2
)
(Py C
H4/x
CH
4)1
P= 205 barP= 303 barP= 402 barP= 499 bar
0.55 0.6 0.65 0.7 0.75 0.8 0.850.5
0.6
0.7
0.8
0.9
1
1.1
1.2
nCH
4
/(nCH
4
+ nCO
2
)
(Py C
O2/x
CO
2)1
Fig. 2.10: According to our EOS CH4 solubility increases in the presence of CO2 (a) and CO2 solubility increases in the presence of CH4. This behavior is shown here for T=375 K and is consistent with behavior inferred in an experimental study by Qin et al. (2008). For the horizontal axis, n denotes the amount of gas species in the system in moles.
Chapter 2 35
The system of Qin et al. (2008) is for a 2-component gas mixture consisting of CO2 and CH4. Their experimental data showed that CO2 solubility (defined as the reciprocal of apparent Henry’s law
constant,2 2
1
CO COP y x ) increases in the presence of CH4. Similarly, CH4
solubility,4 4
1
CH CHP y x , was shown to increase in the presence of CO2. Figure 2.10 shows that our
model reproduces this behaviour. Unfortunately, we could not test our model against their measurements in detail because the amount of water in the experimental system was not reported.
Finally, we used our model to investigate the sensitivity of CO2 solubility to the presence of various impurities. Figure 2.11 shows the impact of 5% (by weight) admixture of each of the ‘contaminant’ gases (as listed in Table 2.7) on the mole fraction of carbon dioxide in the aqueous phase.
Table 2.7: Weight fraction in the composition of injected gas (before equilibration with water)
Gas Case 1 Case 2 Case 3 Case 4 Case 5
CO2 95 95 95 95 95SO2 5 0 0 0 0N2 0 5 0 0 0
H2S 0 0 5 0 0CH4 0 0 0 5 0O2 0 0 0 0 5
Results show that CO2 mole fraction in the aqueous phase is most sensitive to CH4 admixture and least sensitive to the presence of SO2 in the injected gas.
0 100 200 300 400 500 600 7000
0.5
1
1.5
2
2.5
3
3.5
P (bar)
x CO
2*100
T= 323.15 K
Pure CO25% H2S5% SO25% N25% CH45% O2
Fig. 2.11: Results for mole fraction of CO2in the aqueous phase for the gas mixtures listed in Table 7.
An Equation of State for thermodynamic equilibrium of gas mixtures and brines 36
2.6. Concluding remarks
In CCS or acid gas disposal, and natural gas sweetening and gas transportation, accurate estimation of water content in the non-aqueous phase as well as solubility of gases in water/ brine is important. In this chapter, a new EOS has been presented which quantifies the thermodynamic equilibrium between gas mixtures and brines. Presently the model includes CO2, O2, SO2, H2S, CH4 and N2, but the suite of gases can be readily extended. Non-NaCl brines can be handled and activity of aqueous species is based on the Pitzer formalism for high ionic strength. This model predicts the water content in non-aqueous phase and composition of the various gas components in both the aqueous and non-aqueous phase at moderate temperatures (5 – 110 °C), a wide pressure range (1– 600 bar) and various salinities (0 – 6 m).
The model predictions are consistent with existing EOS’s and experimental data for single gas systems and accurately reproduces available, albeit still very limited data sets for gas mixtures. Analysis shows, amongst others, that the amount of dissolved CO2 is most sensitive to CH4 admixture and least sensitive to the presence of SO2.
An important assumption of the EOS is that it neglects binary interaction between dissolved gases in the aqueous phase. This allows use of a simple, non-iterative solving method. More comprehensive experimental data for gas mixtures are needed to ascertain the validity of this assumption. It should be further noted that uncertainty of model predictions will be strongly correlated with the P and T ranges of experimental data of the various gas species used in model calibration.
The EOS may be suitable for incorporation in reactive transport simulators in order to address, for instance, the chemical impact of co-components. Presently the model includes fugacity calculations using the Peng-Robinson EOS. However, it can be easily modified to include another EOS. In that case the model calibration parameters would have to be re-calculated. We did so for the modified RK EOS (Spycher et al., 2003), but for H2S the prediction of the water content proved to be considerably less accurate than for the PR EOS.
A key advantage of the present model is that it is fairly simple and non-iterative and fully explicated, which makes that it can be readily adopted for use in other studies.
Chapter 2 37
Appendix 2-A
For calculation of properties of pure water we use the correlation of Fine and Millero (1973)
00
21 2
,V PV VB A P A P
(A1)
0 2
3 4 5
(1 18.159725 3 ) /(0.9998396 18.224944 3 7.922210 655.44846 9 149.7562 12 393.2952 15 ),
V e ee e e
e(A2)
2 319654.320 147.037 2.21554 1.0478 2 2.2789 5 ,B e 4e
4e
(A3)
2 31 3.2891 2.3910 3 2.8446 4 2.8200 6 8.477 9 ,A e e e
4
(A4)
2 32 6.245 5 3.913 6 3.499 8 7.942 10 3.299 12 ,A e e e e e (A5)
where is temperature in and C 1/V is the reciprocal of the density of pure water in cubic
centimeter per gram.
For the fugacity of pure water we use the relation of King et al. (1992)
02 exp /H O s sf P P P v RT (A6)
where v is molar volume, calculated by multiplying molecular weight of water (18.0152) by V in Eq.
A1. For calculation of sP we utilize Shibue’s (2003) correlation
1.5 3 3.5 4 7.51 2 3 4 5 6ln S c
c
P T a a a a a aP T
(A7)
where 1 / cT T and and are critical temperature and pressure of water. cT cP
1 2 3 4 5
6
7.85951783, 1.84408259, 11.7866497, 22.6807411, 15.9618719,1.80122502
a a a a aa
An Equation of State for thermodynamic equilibrium of gas mixtures and brines 38
PART I PHYSICAL EFFECTS
Chapter 3
Sensitivity of Joule-Thomson cooling to impure CO2 injection in
depleted gas reservoirs
Part of this chapter is based on:
Ziabakhsh-Ganji, Z., Kooi, H., (2014). Sensitivity of Joule-Thomson cooling to impure CO2 injection
in depleted gas reservoirs, Applied Energy, 113, 434-451.
Chapter 3 43
Abstract
Depleted hydrocarbon reservoirs are key targets for geological storage of CO2. It is well known that Joule-Thomson cooling can potentially occur in reservoirs during CO2 injection. In this chapter we investigate the impact of the presence of other gases (impurities) in the injected CO2 stream on Joule-Thomson cooling. A coupled heat and mass transport model is presented that accurately accounts for the pressure-, temperature-, and gas-compositional influences on the thermo-physical transport properties such as density, viscosity, specific heat capacity and Joule-Thomson coefficient. With this model it is shown that impurities affect both the spatial extent of the zone around the well bore in which Joule-Thomson cooling is induced and the magnitude of the cooling. SO2 expands the zone of cooling, O2, N2, and CH4 contract this zone, and H2S has a very small influence on the spatial extent of cooling. These relative behaviours are primarily controlled by the impact of the impurities on the specific heat capacity of the gas mixtures.
The influence of impurities on the magnitude of cooling also depends on the operational conditions of gas injection. Enhanced cooling is caused by O2, N2, and CH4 in combination with constant pressure injection, while for constant rate injection cooling enhancement is minimal or absent. Presence of SO2
strongly suppresses Joule-Thomson cooling at low injection temperatures. Apart from the Joule-Thomson coefficient, the density of the gas mixture plays an important role in controlling these thermal responses.
The thermal risks associated with impure gas injection appear small. Enhanced cooling >5 K requires high-pressure, low-temperature injection in a low permeability reservoir and presence of O2, N2, and/orCH4 in the injectate. Co-injection of SO2 has clear beneficial thermal consequences for low-temperature injection, by suppressing Joule-Thomson cooling, and may therefore be of special interest to help bring down the costs of CO2 sequestration in depleted gas reservoirs.
3.1. Introduction
For the assessment of the performance and impacts of planned and existing Carbon Capture and Storage (CCS) projects, extensive understanding and prediction of the fate and behaviour of CO2
during and following injection is very important (Benson et al., 2005). In CCS, CO2 is injected in underground geological structures such as depleted or producing hydrocarbon reservoirs, or in saline aquifers. The CO2 that is injected is captured at major emitters such as power plants, or separated from the hydrocarbons extracted from natural gas at producing oil or gas fields. While the number of storage pilots conducted in saline aquifers is progressively growing since the first injection in a saline aquifer overlying the Sleipner field in the North Sea began in 1998 (Procesi et al., 2013), demonstration projects for storage in depleted gas reservoirs have started only recently. The few hydrocarbon reservoir projects reported in the literature include the K12-B gas field (Van der Meer et al., 2004) and the CO2CRC Otway Basin Project (Sharma et al., 2007).
Sensitivity of Joule-Thomson cooling to impure CO2 injection in depleted gas reservoirs 44
Because in-situ investigation of the behaviour and fate of CO2 in gas reservoirs is very limited and exceedingly costly, both laboratory studies and numerical models play an important role in CCS research. Over the last decades, capabilities of numerical simulators have been progressively improving and they have been used to clarify key system behaviours both for injection of pure CO2
and for impure CO2 containing other gases. Examples of system behaviours for pure CO2 that have been addressed through numerical modelling include the role of heterogeneity and density influences on spreading of CO2 (Bachu, 2008), the pressure response of aquifers (Birkholzer et al. 2009), and CO2-brine-mineral chemical reactions (White et al., 2005; André et al., 2007; Gaus 2010; Raoof et al., 2012). For mixtures of CO2 with other gases, special attention has been paid to geochemical impacts of SO2 (Knauss et al., 2005; Xu et al., 2007) and the stripping of H2S from the CO2 stream during its migration in an aquifer (Bachu & Adams, 2003; Ghaderi et al., 2011) and the impact of H2S on CO2
storage capacity during injection of acid gas (Bachu & Adams, 2003; Zhang et al., 2011) in saline aquifers. Compared to studies of CO2 storage in saline aquifers, the number of modelling studies addressing CO2 injection in depleted gas reservoirs is presently limited (Oldenburg, 2003; Oldenburg et al., 2004; Ramazanov & Nagimov, 2007; Pruess, 2008).
One of the key issues of CCS in depleted gas reservoirs is the reservoir thermal response, in particular the Joule-Thomson cooling (JTC) associated with the expansion of the injected gas when it spreads into a low-pressure reservoir. In earlier research, it was suggested that if JTC is large, it might compromise well injectivity by reducing reservoir permeability through formation of hydrates and freezing of residual water (Oldenburg, 2007; Mathias et al. 2010). Additionally, the idea was mentioned that fracturing due to thermal stresses may affect the transmission properties of the reservoir (Oldenburg, 2007). Only a few studies have addressed the JTC effect. Ramazanov and Nagimov (2007) developed an analytical model to estimate the temperature response of a gas-saturated reservoir to temporal changes in bottomhole pressure. Oldenburg (2007) has presented numerical simulations with the TOUGH2/EOS7C code (Oldenburg et al., 2004) to investigate the impact of various reservoir parameters on the temperature distribution resulting from CO2 injection in a gas reservoir. His modelling showed that a large pressure drop (about 50 bars) from the injection well to the reservoir can induce a significant temperature decline in the reservoir of more than 20 °C as a result of the JTC effect. Furthermore he showed that for a given injection rate, low reservoir permeability and high porosity enhance the magnitude of JTC, but temperatures low enough to freeze water or form hydrates were not predicted. Mathias et al. (2010) derived an analytical solution for the reservoir temperature as a function of radial distance from a CO2-injection well by assuming steady-state flow in the reservoir, constant thermo-physical properties and by ignoring thermal conduction. They showed that their analytical solution compares favourably with the numerical results obtained by Oldenburg (2007). Singh et al. (2011; 2012) developed a numerical model which includes mixing of injected CO2 and pre-existing gas (methane) in the reservoir, and the model accounts for the influence of the properties (density, viscosity) of the gas mixtures on the non-isothermal processes, including JTC. However, to what extent the thermal impact of the gas mixing in their model is important is not explicitly shown.
Chapter 3 45
In this chapter we assess the thermal effect of impure gas injection where the CO2 stream contains additional gases - these are commonly referred to as co-contaminant gases or impurities - such as H2S, CH4, SO2, N2 and O2. The first two of these gases (H2S, CH4) are usually associated with CO2 in acid gas that is produced in hydrocarbon production units and that can be used in CCS. The other gases are common components of flue gas captured at major CO2 emitters such as power plants (Wang et al., 2012). Although direct storage of these unpurified gases may have various undesirable effects (Wang et al., 2012), allowing these impurities to be stored together with CO2 is of great interest as it would reduce the cost of CO2 capture and the whole CCS chain.
The chapter is organized as follows. First, we elucidate the modelling approach, the governing equations for coupled heat and mass transport and the way in which the thermo-physical properties are calculated. Then, the results of sensitivity analyses are presented which illustrate the impact of the various gases on JTC, and the general behaviours are discussed. Finally, we summarize our findings in the conclusion section.
3.2. Modelling Approach
In order to evaluate the thermal impacts of injection of impure CO2, we adopted similar reservoir conditions and injection scenarios as those used in previous studies of JTC for injection of pure CO2
(Oldenburg, 2007; Mathias et al. 2010). This has the obvious advantage that it allows efficient comparison with results of these previous studies. For the reservoir, a 1D radial domain is used, extending horizontally from the injection well. Initial reservoir conditions are homogeneous, and responses for both constant pressure and constant mass-rate injection scenarios are investigated. Although these conditions clearly are idealized, model simulations are considered appropriate to illustrate the essential generic features of JTC; evaluation of detailed responses of specific reservoirs might necessitate consideration of reservoir-specific parameterizations and 2D or 3D geometries, but these are considered beyond the scope of the present evaluation.
The gas (-mixture) that is injected is a single-phase dry gas (without H2O). However, once injected, the gas is assumed to interact with an aqueous phase (AqP) in the form of residual brine that is present in the reservoir. This interaction includes dissolution of the various gas species in the brine. This is considered an essential part of the modelling approach since it allows us to include the influences of compositional changes of the migrating gas mixture on its thermo-physical properties. In the model calculations we not only quantify the compositional influences on the Joule-Thomson coefficient of the non-aqueous phase (NaqP) gas mixture, but also on its viscosity, density and heat capacity. The species exchange is handled by an equation of state (EOS) for equilibrium between gas mixtures and brine which we developed previously and which has been published separately (Ziabakhsh-Ganji & Kooi, 2012). Similar to Oldenburg (2007), we assume the brine to be immobile. Furthermore, we ignore progressive reduction of brine content and formation dry-out around the injection well due to evaporation of H2O into the migrating CO2-rich phase. For the moderate temperature conditions (< 100 ºC) considered in the present study, the water content of the NaqP is very small. So is the influence of this water content on JTC, as was confirmed by tests we conducted comparing thermal
Sensitivity of Joule-Thomson cooling to impure CO2 injection in depleted gas reservoirs 46
responses for dry and ‘wet’ CO2, where we found a maximum difference of 0.05 ºC. Similar to ECO2N (Pruess, 2005), an EOS used in the TOUGH2 code, we therefore ignore the influence of water content on the NaqP transport properties. In contrast to Mathias et al. (2010) and similar to Oldenburg (2007), our approach includes non-steady heat and mass flow in the reservoir; that is, both pressure (P)and temperature (T) are evolving with time.
3.2.1. Governing equations
In this paragraph the energy balance equation and the mass balance equation that are employed in the model are elucidated. For the assumptions outlined above, the energy balance equation takes the following form
1AqP
r Pr NaqP NaqP NaqP TNaqP
S H S P C T v H K Tt
(1)
where the subscripts AqP, NaqP and r refer to the AqP (brine and dissolved gases) and the NaqP (gas
mixture), and the solid phase (rock) respectively. and are porosity, bulk thermal conductivity,
andTK
, H and S are the density, enthalpy and saturation of each phase respectively. In Eq. (1) it is
implicitly assumed that local equilibrium is established. The first term on the right-hand side of Eq. (1) shows that advective heat transport is only considered for the non-aqueous phase because the brine is assumed immobile. Appendix C shows how Eq. (1) follows from the more fundamental energy balance equation in terms of internal energy.
The total derivative of enthalpy is given by
P JT PdH C dT C dP (2)
where JT is the Joule-Thomson coefficient and PC is the specific heat capacity. Mass conservation is
represented by
0AqP
NaqP NaqPNaqP
S vt
(3)
where the specific volumetric velocity is given by Darcy’s law, i.e., NaqPv
NaqPNaqP
kv P (4)
where k is permeability and is viscosity.
By combination of Eqs. (3) and (4) we have
Chapter 3 47
21 AqP NaqP NaqPAqP AqP NaqP AqP NaqP NaqP
NaqP NaqP NaqP
S CS C P Pk k t
P (5)
where1C
P is the compressibility of the AqP or NaqP. Eqs. (1), (2) and (5) should be solved
simultaneously while the transport properties C , , PC , JT and are a function of pressure (P)
and temperature (T) and the compositions of both AqP and NaqP. The compositions of both phases are handled by our previous published EOS (Ziabakhsh-Ganji & Kooi, 2012). The transport properties are calculated as explained in the next sections. Evidently, viscosity of the AqP is not relevant in the current model because residual brine is assumed to be immobile. Eq. (C14) in Appendix 3-C provides the equivalent form of the heat transport equation Eq. (1) in terms of dependent variables P and Tonly.
3.2.2. Calculation of the transport properties for the NaqP
For reasons of consistency, to calculate the transport properties for the NaqP, we used the Peng-Robinson EOS, because the PR-EOS also is the basis of our previous model (Ziabakhsh-Ganji & Kooi, 2012) for composition calculations.
3.2.2.1. Specific heat capacity and Joule-Thomson coefficient
Specific heat capacity is calculated using the following relationships
0P P PC DC C ,
2 2
2 2
0.414ln2 2 2.4142 2P
R M N T d a Z BDC RM A Z B dT Z Bb
,
2 22Z BZ BMZ B
,B daNRb dT
,
(6)
where Z, A, B, a and b are the PR-EOS parameters which, together with a full derivation of the Eq. 6,
are introduced in Appendix A. In Eq. (6) PDC is the departure function of specific heat capacity. The
departure function is defined as the difference between the property as computed for an ideal gas (here
) and the property of the species in the real case for any temperature T and pressure P. For the ideal
gas, the temperature of the triple point of water (T=273.16 K) is the reference temperature in this
work. We quantify the ideal gas specific heat capacity, 0 , using a polynomial function with
coefficients introduced by Poling et al. (2000). Table 3.1 shows the polynomial expression, and lists the coefficients for the various gases which are studied in this work.
0PC
PC
Sensitivity of Joule-Thomson cooling to impure CO2 injection in depleted gas reservoirs 48
Table 3.1: Ideal Gas Heat Capacities (Poling et al., 2000) 0 2 3 4 -1 -1
0 1 2 3 4/ ,PC R a a T a T a T a T J mol K .
Gas 0a 31 10a 5
2 10a 83 10a 11
4 10a
CO2 3.259 1.356 1.502 -2.374 1.056 CH4 4.568 -8.975 3.631 -3.407 1.091 H2S 4.266 -3.438 1.319 -1.331 0.488 O2 3.630 -1.794 0.658 -0.601 0.179 N2 3.539 -0.261 0.007 0.157 -0.099
SO2 4.417 -2.234 2.344 -3.271 1.393 H2O 4.395 -4.186 1.405 -1.564 0.632
The Joule-Thomson (JT) coefficient is calculated as follows
2 2
2 22 2
1 2( ) 2 2
2
JTP
daTRT dTV b V bV b V
a T V bC RTV b V bV b
,ZRTV
f
P(7)
where is molar volume. The first and second derivative oV T with respect to temperature in
Eqs. (6) and (7) for pure components are quantified us
a
ing
( )c
c
da T a Ta a TdT TT
(8)
2
2 0.52c
c c
d a T a T a Ta
dT TT T T. (9)
Table 3.2 shows that JT coefficients calculated with this method agree with those obtained from the NIST database and the EOS7C equation of state to within 10% for pure CO2.
Table 3.2: Joule Thomson coefficients for pure CO2 derived from this work and other sources
T (K) P (bar) This work EOS7C/PR(Oldenburg, 2007)
NISTa Atkins (1990)
348.15 1 0.790 0.820 0.742 -348.15 10 0.782 0.816 0.742 -348.15 20 0.773 0.813 0.740 -348.15 30 0.760 0.807 0.736 -348.15 40 0.746 0.798 0.730 -348.15 70 0.686 0.742 0.694 -348.15 90 0.619 0.671 0.645 -300.15 1 1.096 1.060 1.075 1.095
Chapter 3 49
Figure 3.1 presents the Joule-Thomson inversion curves calculated for various the gases considered in
this study. The curves trace the points in pressure-temperature space for which 0JT (zero-value-
contour). These points were obtained by solving
0V T
P PT VT V
(10)
for the PR-EOS. For each gas, positive values of the JT coefficient correspond to the zone enclosed by the inversion curve while negative values occur on the other, “outer” side of the zero-contour. Positive and negative values of the JT coefficient indicate a cooling and warming response, respectively, when the gas expands, which is the dominant process in the present analysis of gas injection. The rectangle in figure 3.1 indicates typical pressure and temperature ranges encountered in hydrocarbon reservoirs. For these pressure and temperature conditions JT coefficients have positive values for CO2 and most other gases. For SO2, however, negative values are predicted for relatively low temperature conditions.
0 200 400 600 800 1000 12000
200
400
600
800
1000
1200
1400
1600
1800
P (bar)
T (K
)
CO2
CH4
O2
H2S
SO2
N2
Fig. 3.1: Joule Thomson inversion curves for various pure gases derived from this work.
For the mixture we use standard simple mixing rules and binary interaction coefficients, , (Li &
Yan, 2009)
ijk
1 1
( ) ( ) 1mix i j i j iji j
a T x x a T a T k ,1
n
mix i ii
b x b (11)
where the first and second derivative of mixa T with respect to temperature are
Sensitivity of Joule-Thomson cooling to impure CO2 injection in depleted gas reservoirs 50
1 1 1 1,
N N N N
m i j ij m ii j i j
a x x a a x j ijx a (12)
2
"3/ 2
2 21 1,
4 2i j i j i j i j i j j iij ij i j j i
ij iji ji j
a a a a a a a a a a a ak ka a
a aa a
a a a a . (13)
The binary interaction coefficients, , for CO2-SO2, CO2-H2S, CO2-CH4, CO2-N2, and CO2-O2 for the
non-aqueous phase are adopted from Li and Yan (2009).
ijk
3.2.2.2. Density and compressibility
It is well known that the PR-EOS, as well as other classical EOS’s, provide a good fit of the vapour pressure for most substances, but that the prediction of molar volume and, hence, density, are rather poor. Over the years, several improved methods for density modelling have been developed. Here we use the method proposed by Mathias et al. (1989), which is an extension of the simpler ‘volume-shift method’ of Peneloux et al. (1982). Hence, we calculate density of the NaqP from
PR
MwV c
(14)
where Mw is the molecular weight, is the molar volume calculated directly from the PR-EOS, and c is a correction factor or volume shift. The correction factor proposed by Mathias et al. (1989) is
/PRV ZRT P
20.41 ,
0.41
PR
c PRT
V Pc fRT V
(15)
where is the fitting parameter which is constant for a gas species and is obtained by regression of
density data; , is the bulk modulus, and where cf is given by
3.946c cf V b (16)
and where b is the co-volume (Eq. (19) in chapter 2) and is the molar volume in the critical point.
Following Mathias et al. (1989), for mixtures the quantities
cVPRV and are determined by the mixing
rule chosen for the PR-EOS (here Eq. (11)) while the correction factor for the mixture, , is
obtained usingmixc
Chapter 3 51
1
n
mix i ii
x , ,,1
n
c mix i cii
V xV (17)
where ix is the mole fraction of each component in the mixture. The molecular weight for the mixture
is similarly averaged. The compressibility of a NaqP follows directly from its definition, 1C
P,
and the density of the NaqP defined above, and yields
1 PRPRC V
V c Pc . (18)
The Weighted Nonlinear Least Squares (WNLS) method was used to determine i for the gases
addressed in the present study. Density data from the NISTa (http://webbook.nist.gov/chemistry/fluid/)
database were used as targets. Resulting i -values are listed in Table 3.3 for temperature range 5 to
110 C and pressures up to 700 bar.
Table 3.3: Constants fitting parameter for correct density calculation for PR EOS
Gas CO2 CH4 H2S O2 N2 SO2
3.38936396 6.404378 3.939035 5.174887 6.852653 1.443083
0 200 400 600 800 10000
200
400
600
800
1000
1200
P (bar)
ρ (k
g/m
3 )
(a)
NISTaPeneloux et al. (1982)Mathias et al. (1989)PR EOS
0 200 400 600 800 10000
500
1000
1500
P (bar)
ρ (k
g/m
3 )
(b)
CH4N2O2SO2H2S
Fig. 3.2: Comparison between (a) Mathias et al. (1989) (dash line) and Peneloux et al. (1982) (solid line) and PR-EOS (dot dot) approaches with NITSa database (symbols) for CO2 density in NaqP (left-hand side panel) at 313.15 K and various pressure (b) Mathias et al. (1989) (solid line) NITSa database (symbols) for density of pure SO2, H2S, N2, O2 and CH4 in NaqP.
Figure 3.2 illustrates the performance of the present model for all pure gases considered in this work at a temperature of 313.15 K. Included in figure 3.2a are predictions for the uncorrected PR-EOS and for the Peneloux et al. (1982)method, which highlights the superior performance of Mathias et al.’s (1989)
Sensitivity of Joule-Thomson cooling to impure CO2 injection in depleted gas reservoirs 52
method. Figures 3.3a to 3.3f show that density predictions correspond quite closely with NISTb (2007) data for binary mixtures of CO2 and other gas species.
0 20 40 60 80 1000
200
400
600
800
1000
1200
xCH
4
ρ (k
g/m
3 )
(a)
P= 100 barP= 300 barP= 600 bar
0 20 40 60 80 1000
200
400
600
800
1000
1200
xH
2S
ρ (k
g/m
3 )
(b)
P= 100 barP= 300 barP= 600 bar
0 20 40 60 80 1000
200
400
600
800
1000
1200
xN
2
ρ (k
g/m
3 )
(c)
P= 100 barP= 300 barP= 600 bar
0 20 40 60 80 1000
200
400
600
800
1000
1200
xO
2
ρ (k
g/m
3 )
(d)
P= 100 barP= 300 barP= 600 bar
Fig. 3.3: Comparison between new model based on Mathias et al. (1989) (solid line) NITSb (2007) database (symbols) for mixture density of (a) CH4and CO2 (b) H2S and CO2 (c) N2 and CO2 (d) O2 and CO2 (e) SO2 and CO2 at 313.15 K.
0 20 40 60 80 100
600
800
1000
1200
1400
1600
xSO
2
ρ (k
g/m
3 )
(e)
P= 100 barP= 300 barP= 600 bar
3.2.2.3. Viscosity
For calculation of NaqP dynamic viscosity the one-parameter Friction Theory Model (FTM) (Quinones-Cisneros et al., 2001) was used. The method is detailed in Appendix 3-B. For all pure components, sixteen adjustable parameters were calibrated using the Weighted Nonlinear Least Squares method and NISTa viscosity data. Inferred parameter values are listed in Table 3.4. For binary mixtures of CO2 and other gases three parameters (Table 3.5) were optimized using NISTb (2007) data. The model performance is again illustrated for 313.15 K in figure 3.4. Similarly accurate predictions are obtained for other temperatures.
Chapter 3 53
0 200 400 600 8000
1000
2000
3000
4000
5000
P (bar)
μ (m
icro
Poi
se)
(a)
CO2
CH4
O2
N2
SO2
H2S
0 20 40 60 80 1000
500
1000
1500
2000
xH
2S
μ (m
icro
Poi
se)
(b)
0 20 40 60 80 1000
500
1000
1500
xN
2
μ (m
icro
Poi
se)
(c)
0 20 40 60 80 1000
500
1000
1500
xO
2μ
(mic
roP
oise
)
(d)
0 20 40 60 80 1000
500
1000
1500
xCH
4
μ (m
icro
Poi
se)
(e)
0 20 40 60 80 1000
1000
2000
3000
4000
5000
xSO
2
μ (m
icro
Poi
se)
(f)P= 100 barP= 300 barP= 600 bar
Fig. 3.4: (a) Comparison between FTM (solid line) NITSa database (symbols) for viscosity of pure CO2, SO2,H2S, N2, O2 and CH4 in NaqP (left-hand side panels) at 313.15 K and various pressure. And Comparison between FTM (solid line) NITSb (2007) database (symbols) for mixture viscosity of (b) H2S and CO2 (c) N2 and CO2 (d) O2 and CO2 (e) CH4 and CO2 (f) SO2 and CO2 at 313.15 K.
3.2.3. AqP Properties
For calculation of the AqP density, AqP , as a function of temperature, pressure, dissolved gases and
brine salinity, we have utilized an approach similar to Battistelli and Marcollini (2009), and which is an extension of the method of Garcia (2001) who only considered brine-CO2 -mixtures. The effect of dissolved gases is quantified by
2 2
1
1
nH O H O s s Aq
AqP AqP i iib
x Mw x MwMw V x , (19)
where b is the pure brine (without dissolved gases) density, computed using a correlation proposed by
Rowe and Chou (1970). The subscript refers to the salt and the x’s are the mole fractions of each component in the aqueous phase which are calculated with the EOS developed by Ziabakhsh-Ganji
and Kooi (2012) and is the molar volume of each dissolved component in pure water, calculated
s
AqV
Sensitivity of Joule-Thomson cooling to impure CO2 injection in depleted gas reservoirs 54
from a correlation by Akinfiev and Diamond (2003) for various dissolved gases in pure water. The
compressibility, , follows directly from density through its definition. The specific heat capacity,
, was obtained from Eq. (A19), and the correlation of Lorenz and Muller (2003) for the enthalpy
H of the AqP. Similar to (Battistelli & Marcolini, 2009), influences of dissolved gases have been ignored. Parameterization of the pure water specific heat capacity is provided in Table 3.1.
AqPCAqPPC
Table 3.4: Constants for f-theory for PR EOS
Gas CO2 CH4 H2S O2 N2 SO2
ca -0.13236 -0.13129 -0.14048 -0.16391 -0.15118 -0.1262
rc 1.225E-02 0.01188 1.20E-02 1.26E-02 1.24E-02 1.19E-02
rrc 1.112E-03 1.782E-4 1.24E-03 8.89E-04 8.14E-04 7.65E-04
,0,0a -4.656-02 -4.87E-2 -4.89E-02 -5.00E-02 -4.97E-02 -4.89E-02
,1,0a 0.30366 0.27269 0.27046 0.25883 0.26301 0.27143
,1,1a -1.086E-04 -3.756E-04 -1.03E-04 -1.11E-04 -1.11E-04 -1.27E-04
,2,0a -4.48E-02 -4.48E-02 -4.48E-02 -4.48E-02 -4.48E-02 -4.48E-02
,2,1a 4.089E-05 4.089E-05 4.09E-05 4.09E-05 4.09E-05 4.09E-05
,2,2a 4.642E-07 -6.812E-07 2.85E-07 -3.08E-06 -1.72E-06 1.56E-07
,0,0r -0.59302 -0.37592 -0.37778 -0.13347 -0.14524 -0.36185
,1,0r 0.29427 0.61477 0.60339 0.886717 0.90443 0.63125
,1,1r -6.126E-05 1.54E-03 -6.28E-05 -5.96E-05 -5.95E-05 -7.61E-05
,2,0r -7.902E-02 -7.90E-02 -7.95E-02 -7.90E-02 -7.90E-02 -7.90E-02
,2,1r 3.724E-05 3.7231E-05 3.72E-05 3.72E-05 3.72E-05 3.72E-05
,2,2r 3.14E-06 -3.131E-06 5.78E-07 -5.97E-06 -4.18E-06 5.62E-07
,2,1rr -3.47E-06 -1.97E-06 -4.19E-08 -4.07E-06 -4.19E-06 -8.89E-07
Table 3.5: Tuning parameters, , and K for mixture of CO2 and other gases. ,1cK ,2c
Gas CH4 SO2 H2S N2 O2
-1.2058 1.64848 0.3 0.3 0.3
,1cK 1.0955 4.27528 3.97225 4.31387 4.3080
,2cK 7.4709 3.67528 3.97225 4.31387 4.3080
The Joule-Thomson coefficient of the AqP was calculated from
Chapter 3 55
01AqP
JT AqPP
T
H HC P
, (20)
where is again obtained from Lorenz and Muller (2003). H
3.3. Model Set up
The model equations were solved in a 1D radial domain extending horizontally from the screen of the injection well. At the well screen end of the domain, two basic injection scenarios were used:
(a) constant pressure injection; (b) injection at constant mass flow rate.
For both scenarios either pure CO2 was injected, or CO2 together with one of the following impurities: SO2, H2S, CH4, N2 and O2. For each binary gas couple, the composition was varied using CO2 mole fractions of 80, 90 and 95% and corresponding ‘impurity’ fractions of 20, 10 and 5%, respectively. In order to highlight JTC effects without contributions from other thermal processes, the temperature of the injected gas was generally set equal to the ambient the reservoir temperature. However, because in real cases the injected gas stream temperature may often be lower than the ambient reservoir temperature (Salimi et al., 2012), a few simulations were also performed with a lower injection temperature. It should be noted that the use of a constant injection temperature implies that potential thermal feedbacks from the reservoir to the wellbore are not considered (Pan et al., 2011).
At the distal end of the domain, open boundary conditions were applied for both heat and mass transport in order to minimize the influences of this boundary (infinitely-acting reservoir). Table 3.6 summarizes values of model parameters that were used in the simulations, unless otherwise stated.
Table 3.6: Default reservoir model parameters
Parameters Values
Wellbore radius (m) 0.05 ‘Reservoir’ radius (m) 1000
Permeability (m2) 5e-15 Porosity 0.3
Initial brine saturation (pore volume fraction) 0.2 Brine salinity (mole/kg water) 2
Rock/grain density (kg/m3) 2600 Rock/grain specific heat (J/kg K) 1000
Formation thermal conductivity (W/m K) 2.51 Initial reservoir pressure (bar) 60
Initial reservoir temperature (K) 323.15 Injection pressure (bar) 120 Injection rate (kg/s/m) 0.125
Sensitivity of Joule-Thomson cooling to impure CO2 injection in depleted gas reservoirs 56
Note that due to the 1D nature of the simulations a specific injection mass flow rate is provided in the
table. The value of 0.125 would, for instance, correspond to a total mass flow of 5
for a 40 m high well screen. These default parameter values represent relatively high pressure
and high-rate injection in a low-permeability reservoir and, therefore, are associated with relatively large JTC effects (Oldenburg, 2007; Mathias et al., 2010). This is useful since it renders the impacts of impurities clearly visible as well. Calculations were performed with a generic finite element code (FlexPDE version 5.1.4 3D;
1kg s m 1
1kg s
http://www.pdesolutions.com).
3.4. Results
3.4.1. Comparison with existing solutions for pure CO2 injection
Before presenting results which document the impact of impurities in the gas stream on JTC, in this section it is first shown how the present model performs relative to two previous studies which addressed the thermal response for the injection pure CO2 (Oldenburg, 2007; Mathias et al. 2010). Obviously, parameter values were chosen to match those used in these studies, and they can therefore be different from those listed in Table 3.6.
Figure 3.5 shows that the model is in perfect agreement with the analytical solution provided by Mathias et al. (2010). The symbols in figure 3.5 represent temperatures calculated with the analytical expressions provided by Mathias et al. (2010) and correspond to the graphical results displayed in figure 1c of that work. Note that in order to reproduce their results with our numerical model (solid lines), we had to enforce constant transport properties (also for CO2) and to nullify thermal conductivity, which are basic assumptions underlying the analytical solution. Minor numerical oscillations on the well-side of the sharp thermal front observed in our numerical results were produced by the absence of thermal diffusion in the model equation; these numerical features are not depicted in figure 3.5. The good correspondence with the analytical model provides a partial verification of the proper formulation and implementation of our model.
Fig. 3.5: Comparison between results for the model (solid lines) and analytical solution by Mathias et al. (2010) data (symbols) for pure CO2.
0 20 40 60 80 100 120 140 160295
300
305
310
315
320
r (m)
T (K
)
30 days1 year15 years30 years
Chapter 3 57
Fig. 3.6: Comparison between results for the model (solid lines) and numerical simulation by Oldenburg (2007) (symbols) for pure CO2.
0 20 40 60 80 100
320
318
316
314
312
310
308
306
120302
304
r (m)
T (K
)
90 days1 year15 days
In figure 3.6 predictions of the current model are compared with numerical predictions obtained by Oldenburg (2007) with the TOUGH2 code in combination with the EOS7C module. Results shown correspond to simulation results graphically depicted in figure 3.8 of the latter work. Apart from the appropriate CO2 injection, we also extracted 0.56 kg/s at the outer radial perimeter of the radial system (for 50 m reservoir thickness) as implemented by Oldenburg to mimic the influence of a gas production well as part of an enhanced gas recovery system.
Figure 3.6reveals that although overall behaviour of the two simulations is very similar, differences in the calculated response of up to several K after 15 years of injection occur, where our model tends to under-predict JTC (and over-predict temperature) relative to the predictions by Oldenburg. The reasons for these differences have not been ascertained. They may be related to the fact that the PR-EOS, which is implemented in EOS7C, over predicts the Joule-Thomson coefficient (Oldenburg, 2007), while our model equations for this parameter reproduce experimental data more accurately. However, other differences between the TOUGH2 simulations of Oldenburg and our model may also contribute to the simulation differences. For instance, contributions of evaporation of residual brine to the energy balance which may have been part of Oldenburg’s simulations might be responsible for the stronger cooling observed in his model predictions.
3.4.2. Sensitivity to impurity; constant pressure injection
Figure 3.7 displays predicted temperature and pressure responses for constant pressure injection, a suite of injected gas compositions, and default parameter values (Table 3.6). The curves depict the situation after 15 years of continuous injection. The right-hand side panels show that pressure conditions in the reservoir are hardly affected by the composition of the injected gas for constant pressure injection. By contrast, the left panels demonstrate that JTC is sensitive to the gas composition. Comparison with the pure CO2 injection curve shows that impurities can both enhance and suppress JTC depending on the specific gas species added to the gas stream. If the maximum reservoir cooling is considered for each simulation, systematic positive contributions to JTC (cooling enhancement) are inferred for O2, N2 and CH4 respectively, changes are small for H2S, and a marked negative impact (cooling suppression) is found for SO2.
Sensitivity of Joule-Thomson cooling to impure CO2 injection in depleted gas reservoirs 58
0 50 100 150 200 250 3006
7
8
9
10
11
12
x 106
b
r (m)
P (P
a)
CH
4
H2
S
N2
O2
SO2
Pure CO2
0 50 100 150 200 250 300290
295
300
305
310
315
320
325 a
r (m)
T (K
)
CH4
H2
S
N2
O2
SO2
Pure CO2
0 50 100 150 200 250 3006
7
8
9
10
11
12
x 106
d
r (m)P
(Pa)
CH
4
H2
S
N2
O2
SO2
Pure CO2
0 50 100 150 200 250 300290
295
300
305
310
315
320
325 c
r (m)
T (K
)
CH4
H2
S
N2
O2
SO2
Pure CO2
0 50 100 150 200 250 3006
7
8
9
10
11
12
x 106
f
r (m)
P (P
a)
CH
4
H2
S
N2
O2
SO2
Pure CO2
0 50 100 150 200 250 300290
295
300
305
310
315
320
325 e
r (m)
T (K
)
CH4
H2
S
N2
O2
SO2
Pure CO2
Fig. 3.7: Results for temperature and pressure profile for CO2 various impurities with composition in mole fraction (a and b) 95%, (c and d) 90% and (e and f) 80% at constant injection pressure.
However, figure 3.7 shows that the type of impurity also influences the location of the thermal front, which basically delimits the radial zone around the well in which significant reservoir cooling has been induced. Here also a systematic progression is observed where gases which enhance cooling (O2,N2 and CH4) cause a reduction in cooling extent while the gas which suppresses cooling (SO2) expands the zone of cooling. The total thermal impact of impurities therefore appears relatively complicated where an individual impurity can cause enhanced cooling relative to pure CO2 injection in the vicinity of the well bore, and strongly reduced cooling at larger distances (O2, N2 and CH4), and vice versa (SO2).
While the extent of the JTC zone can be of practical interest, the minimum temperatures attained during injection seem to be of greater practical concern in light of potential negative consequences for
well injectivity. Figure 3.8 shows the time history of both the minimum temperature, , in the
simulations (left panels) and the radial location at which the minimum temperature occurs, (right
panels). It is worth noting that for the present set of simulations the temporal progression of
provides a good indication of the temporal development of the thermal front as well.
miT
rn
minT
minTr
Chapter 3 59
0 5 10 150
50
100
150
200
250
b
Time (year)
r Tm
in (m
)
10−4
10−2
100
102
290
295
300
305
310
315
320
325a
Time (year)
Tm
in (K
)
CH4
H2
S
N2
O2
SO2
Pure CO2
0 5 10 150
50
100
150
200
250
d
Time (year)r T
min
(m)
10−4
10−2
100
102
290
295
300
305
310
315
320
325c
Time (year)
Tm
in (K
)
CH4
H2
S
N2
O2
SO2
Pure CO2
0 5 10 150
50
100
150
200
250
f
Time (year)
r Tm
in (m
)
10−4
10−2
100
102
290
295
300
305
310
315
320
325e
Time (year)
Tm
in (K
)
CH4
H2
S
N2
O2
SO2
Pure CO2
Fig. 3.8: Results for time history of both the minimum temperature, , in the simulations (left panels) and the
radial location at which the minimum temperature occurs, (right panels) for CO2 various impurities with
composition in mole fraction (a and b) 95%, (c and d) 90% and (e and f) 80% at constant injection pressure.
minT
minTr
An exception occurs at 20% SO2 (figure 3.8f) where considerably lags the advancement of the
thermal front. The results displayed in the left-hand side panels demonstrate that the cooling enhancement for O2, N2 and CH4 and the cooling suppression for SO2 observed in figure 3.7 are fully developed after a few weeks of injection; at earlier times these behaviours are more complex. The left-
hand side panels further illustrate that the difference of for an impurity relative to for pure
CO2 does not simply increase with the amount of impurity; the largest difference (impact) occurs for 10% rather than for 20% impurity (compare panels 3.8(d) and (f) for O2, N2 and CH4).
minTr
minT minT
Sensitivity of Joule-Thomson cooling to impure CO2 injection in depleted gas reservoirs 60
0 50 100 150 200 250 300
290
300
310
320
330
340
350 a
T= 353.15 KP= 100 bar
T (K
)
CH4
H2
S
N2
O2
SO2
Pure CO2
0 50 100 150 200 250 300
290
300
310
320
330
340
350 b
T= 353.15 KP= 120 bar
0 50 100 150 200 250 300
290
300
310
320
330
340
350 c
T= 353.15 KP= 150 bar
0 50 100 150 200 250 300
290
300
310
320
330
340
350 d
T= 338.15 KP= 100 bar
T (K
)
0 50 100 150 200 250 300
290
300
310
320
330
340
350 e
T= 338.15 KP= 120 bar
0 50 100 150 200 250 300
290
300
310
320
330
340
350 f
T= 338.15 KP= 150 bar
0 50 100 150 200 250 300
290
300
310
320
330
340
350 gT= 323.15 KP= 100 bar
r (m)
T (K
)
0 50 100 150 200 250 300
290
300
310
320
330
340
350 hT= 323.15 KP= 120 bar
r (m)0 50 100 150 200 250 300
290
300
310
320
330
340
350 iT= 323.15 KP= 150 bar
r (m)
Fig. 3.9: Results for predicted temperature profiles for various temperatures (both injection and initial reservoir temperature) and constant injection pressures and for 20% impurity.
In figure 3.9 illustrates predicted temperature profiles for various temperatures (both injection and initial reservoir temperature) and injection pressures and for 20% impurity. Figure 3.9h corresponds to the simulation with default parameters of figure 3.7e. Results show that the impact of the various gas species on the extent of the zone of cooling around the well-bore is fairly robust. That is, SO2 expands and O2, N2 and CH4 reduce the zone of cooling, irrespective of temperature and pressure conditions. By contrast, the influence of the gas species on JTC is highly dependent on pressure and temperature. For instance, while SO2 tends to suppress JTC under most conditions, for low injection pressure and high temperature (figure 3.9a) JTC enhancement occurs. Conversely, where O2, N2 and CH4 enhance JTC for relatively low temperatures and high pressures, JTC suppression occurs for high temperatures and low pressures. Presence of H2S in the CO2 stream has very little influence on JTC under all circumstances simulated.
3.4.3. Sensitivity to impurity; constant rate injection
Figures 3.10 and 3.11 show results analogous to those of figures 3.7 and 3.8 respectively, but for constant-rate injection. The right-hand side panels of figure 3.10 demonstrate that for constant rate injection, pressure conditions in the reservoir are mildly affected by the gas composition. Inspection of the left-hand side panels of figure 3.10 show that the impact of the impurities on the thermal front, or the extent of JTC, is very similar to that inferred for constant pressure injection (figure 3.7).
Chapter 3 61
0 50 100 150 2006
6.5
7
7.5
8
8.5
9
9.5
10x 10
6
b
r (m)
P (P
a)
CH
4
H2
S
N2
O2
SO2
Pure CO2
0 50 100 150 200300
305
310
315
320
325 a
r (m)
T (K
)
CH4
H2
S
N2
O2
SO2
Pure CO2
0 50 100 150 2006
6.5
7
7.5
8
8.5
9
9.5
10x 10
6
d
r (m)
P (P
a)
CH4
H2
S
N2
O2
SO2
Pure CO2
0 50 100 150 200300
305
310
315
320
325 c
r (m)
T (K
)
CH4
H2
S
N2
O2
SO2
Pure CO2
0 50 100 150 2006
6.5
7
7.5
8
8.5
9
9.5
10x 10
6
f
r (m)
P (P
a)
CH
4
H2
S
N2
O2
SO2
Pure CO2
0 50 100 150 200300
305
310
315
320
325 e
r (m)
T (K
)
CH4
H2
S
N2
O2
SO2
Pure CO2
Fig. 3.10: Results for temperature and pressure profile for CO2 various impurities with composition in mole fraction (a and b) 95%, (c and d) 90% and (e and f) 80% at constant injection rate.
The impact on, (figure 3.11), however, is quite different. For the suite of simulations with
constant-rate injection, hardly any enhancement of JTC relative to pure CO2 injection is predicted to occur after 15 years. Figure 3.12 displays results analogous to figure 3.9. These results suggest that for constant rate injection, risks of JTC enhancement are relatively small.
minT
The largest, albeit still relatively small, enhancement of JTC is found only at the high end of simulated temperature conditions for SO2. However, it is also apparent from the figure that for constant-rate injection, temperature has a rather large influence on the impact of the various gas species (e.g., compare bottom, middle and top panels for SO2).
Sensitivity of Joule-Thomson cooling to impure CO2 injection in depleted gas reservoirs 62
Fig. 3.11: Results for time history of both the minimum temperature, , in the simulations (left-hand side panels) and the radial location at which the minimum temperature occurs,
(right-hand side panels) for various impurities with composition in mole fraction (a and b) 95%, (c and d) 90% and (e and f) 80% of CO2 at constant injection rate.
minT
minTr
0 5 10 150
50
100
150
b
Time (year)
r Tm
in (m
)
10−4
10−2
100
102
300
305
310
315
320
325 a
Time (year)
Tm
in (K
)
CH4
H2
S
N2
O2
SO2
Pure CO2
0 5 10 150
50
100
150
d
Time (year)
r Tm
in (m
)
10−4
10−2
100
102
300
305
310
315
320
325 c
Time (year)
Tm
in (K
)
CH4
H2
S
N2
O2
SO2
Pure CO2
0 5 10 150
50
100
150
f
Time (year)
r Tm
in (m
)
10−4
10−2
100
102
300
305
310
315
320
325 e
Time (year)
Tm
in (K
)
CH4
H2
S
N2
O2
SO2
Pure CO2
0 50 100 150 200 250300
310
320
330
340
350 a
T= 353.15 Kq= 3 kg/s
T (K
)
CH4
H2
S
N2
O2
SO2
Pure CO2
0 50 100 150 200 250300
310
320
330
340
350 b
T= 353.15 Kq= 5 kg/s
0 50 100 150 200 250300
310
320
330
340
350 c
T= 353.15 Kq= 7 kg/s
0 50 100 150 200 250300
310
320
330
340
350 d
T= 338.15 Kq= 3 kg/s
T (K
)
0 50 100 150 200 250300
310
320
330
340
350 e
T= 338.15 Kq= 5 kg/s
0 50 100 150 200 250300
310
320
330
340
350 f
T= 338.15 Kq= 7 kg/s
0 50 100 150 200 250300
310
320
330
340
350 g
T= 323.15 Kq= 3 kg/s
r (m)
T (K
)
0 50 100 150 200 250300
310
320
330
340
350 h
T= 323.15 Kq= 5 kg/s
r (m)0 50 100 150 200 250
300
310
320
330
340
350 i
T= 323.15 Kq= 7 kg/s
r (m)
Fig. 3.12: Results for predicted temperature profiles for various temperatures (both injection and initial reservoir temperature) and constant injection rate and for 20% impurity.
Figure 3.13b shows calculated cooling effects when the injection temperature (50 C) is lower than the ambient reservoir temperature (80 C). Comparison with corresponding uniform high (figure 3.13a)
Chapter 3 63
and low (figure 3.13c) temperature responses demonstrate that the impact of the impurities is most strongly controlled by the injection temperature (differences relative to pure CO2 are more similar for the uniform low than for the high temperature simulation).
Fig. 2.13: Results for temperature profile for various injection and reservoir temperature with CO2 in mixture composition by the mole fraction 80% at constant injection rate (a) 80 C both injection and reservoir temperature (b) 50 C injection temperature and 80 C for reservoir temperature (c) 50 C for both injection and reservoir temperature.
0 20 40 60 80 100 120 140 160 180 200300
310
320
330
340
350 a
T (K
)
CH4
H2
S
N2
O2
SO2
Pure CO2
0 20 40 60 80 100 120 140 160 180 200300
310
320
330
340
350 b
T (K
)
0 20 40 60 80 100 120 140 160 180 200300
310
320
330
340
350 c
r (m)
T (K
)
3.4.4. The relative role of individual thermo-physical properties
The results presented in the previous sections brought to light that impurities tend to have a systematic, and hence, qualitatively predictable impact on the spatial extent of JTC in the reservoir. That is, SO2 expands the zone of JTC, H2S has little influence, and the light gases O2, N2 and CH4
reduce the radial zone of the reservoir cooling, and these behaviours appear to largely independent of initial reservoir and injection conditions. This relative simplicity and consistency in behaviour may indicate that but one of the five key transport parameters considered in our model exerts a dominant influence on the extent of JTC. By contrast, the impact of impurities on the magnitude of JTC is more complex and may indicate that the dependency on the transport parameters is less straightforward.
To evaluate the role of the transport parameters on the spatial extent of JTC, we first reorganized the heat transport equation (C14) in order to obtain an expression for the apparent thermal retardation factor (RF) which fundamentally controls the rate of migration of a thermal front:
Sensitivity of Joule-Thomson cooling to impure CO2 injection in depleted gas reservoirs 64
2 P JTTJT
P P
CKT PRF T P Tt C C t
(21a)
(1 ) 1AqPAqP AqP P AqP P r Pr
P
S C S C CRF
C(21b)
Note that in Eq. (21a), /v is the ‘pore velocity’, which is greater than Darcy’s velocity, and
which would determine the rate of ‘advection’ of a thermal front in the theoretical situation of zero retardation (that is, in case RF = 1).
Fig. 3.14: Results for RF (Retardation Factor) with CO2 composition in mixture by the mole fraction (a) 95%, (b) 90% and (c) 80% at constant injection rate.
0 50 100 150 200 2500
5
10
15
20
25
30
35
a
RF
CH4
H2
S
N2
O2
SO2
Pure CO2
0 50 100 150 200 2500
5
10
15
20
25
30
35
40
b
RF
CH4
H2
S
N2
O2
SO2
Pure CO2
0 50 100 150 200 2500
10
20
30
40
50
c
r (m)
RF
CH4
H2
S
N2
O2
SO2
Pure CO2
Figure 3.13 shows the retardation factor (RF), calculated with Eq. (21b), as a function of distance from the injection well after 15 years for the simulations of figure 3.14 (constant injection rate). The systematic relative differences in RF magnitudes that are revealed by this figure for the various gas compositions are fully consistent with the inferred thermal front migration behaviour described above; that is, high retardation for O2, N2 and CH4 and low for SO2. Eq. (21b) points out that the retardation factor fundamentally depends on the specific heat capacity and density of the NaqP (in addition to quantities that are little or not influenced by the gas composition). To evaluate the relative role of these
Chapter 3 65
quantities, we calculated thermal responses for simulations of the previous sections where only one transport parameter was impacted by the impurity, while the values of all other parameters were kept identical to the pure CO2 injection case.
Figure 3.14 shows results for the case of 20% SO2 and constant-rate injection (figure 3.10e).
Comparison of the thermal front locations in the three panels demonstrates that PC of the mixture
exerts a dominant control on the extent of JTC and that the JTC extent is hardly influenced by and
JT of the NaqP. At the same time, figure 3.15 shows that PC is largely inconsequential with regard
to the magnitude of JTC. As might be expected, the magnitude of JTC is strongly controlled by JT .
However, this is not the sole important property of the system. Also the impact of SO2 on the density of the NaqP (figure 3.15b) strongly suppresses the magnitude of JTC as observed for the simulation
with full parameterization. Similar relationships were found for other binary mixtures.
Fig. 3.15: Results for Retardation Factor (RF) for pure CO2 by adding 20% SO2 in mixture for (a) Joule-Thomson coefficient ( JT ) (b) density ( ) and (c) specific heat
capacity ( PC ). PC is more sensitive than others on RF.
0 50 100 150 200 250300
305
310
315
320
325
T (K
)
a
Pure CO2
Pure CO2
+JTC mixture
80% CO2
+ 20% SO2
0 50 100 150 200 250300
305
310
315
320
325
T (K
)
b
Pure CO2
Pure CO2
+density mixture
80% CO2
+ 20% SO2
0 50 100 150 200 250300
305
310
315
320
325
r (m)
T (K
)
c
Pure CO2
Pure CO2
+Cp mixture
80% CO2
+ 20% SO2
Sensitivity of Joule-Thomson cooling to impure CO2 injection in depleted gas reservoirs 66
3.5. Discussion and conclusions
The present study has shown that Joule-Thomson cooling (JTC) which accompanies CO2 storage in depleted gas reservoirs is sensitive to the composition of the injected gas. Presence of gases other than CO2 (impurities) affect both the spatial extent of the zone around the well bore in which cooling occurs and the magnitude of cooling. Both impacts are dependent on the type of impurity present in the gas stream. The influence of impurities on the spatial extent of cooling is found to be very consistent: SO2 expands the zone of JTC, O2, N2 and CH4 contract this zone, and H2S has but a very small influence on the spatial extent of cooling. This is found both for constant pressure and constant rate injection. These relative behaviours are primarily controlled by the impact the impurities have on the specific heat capacity of the gas mixture.
The influence of impurities on the magnitude of cooling is more complex and depends on operational conditions of gas injection. For the other gas species, both JTC enhancement and JTC suppression are predicted. Here SO2 on the one hand, and O2, N2 and CH4 on the other show contrasting behaviours. That is, SO2 tends to strongly suppress and enhance JTC for low and high injection temperatures, respectively, whereas O2, N2 and CH4 display opposite behaviours. Of the considered gases, H2S has a very small influence on the magnitude of JTC. Apart from the Joule-Thomson coefficient, the density of the gas mixture plays an important role in controlling these thermal responses.
Although these inferences from the model investigation are deemed fairly robust, the role of a number of processes, which were still simplified in the present analysis, would need further evaluation. Likely the most important of these is the progressive evaporation of the residual brine into the migrating gas (formation dry-out), which was neglected. This process should be expected to induce additional reservoir cooling. However, since the rate of evaporation is not expected to be highly sensitive to gas composition, it would seem unlikely that incorporation of this process would significantly change the relative impact behaviours gleaned from the present study.
Overall, it can be concluded that the thermal risks associated with impure gas injection appear to be rather small, especially for constant-rate injection. An extra temperature drop of 5 – 10 K relative to pure CO2 injection as predicted in the present set of simulations for constant pressure injection requires extreme conditions of high-pressure injection in a low permeability reservoir and presence of specific gases in the injected gas mixture. Results suggest that under most circumstances, cooling enhancement would be considerably smaller or even negative. In particular for low-temperature injection, co-injection of SO2 with the CO2 appears to have clear beneficial thermal consequences by suppressing JTC. Although these beneficial effects may be offset by potential negative impacts of SO2, for instance due to induced geochemical reactions, allowance of SO2 in the injected gas may represent a viable option to reduce the overall costs of reservoir storage of CO2 through savings in purification of source gases.
Chapter 3 67
Appendix 3-A
Enthalpy departure
The cubic form of PR-EOS is given by
2 2
( )2
RT a TPV b V bV b
(A1)
Enthalpy departure function
H U PV (A2)
By using differentiate Eq. (A1) with respect to volume at constant temperature
T T T
PVH UV V V
(A3)
We know that
dU TdS PdV (A4)
By differentiating Eq. (A4) with respect to volume at constant temperature
T T
U ST PV V
(A5)
From the Maxwell equations
T V
S PV T
(A6)
By combination of Eqs. (A3), (A5) and (A6) we obtain
( )
T V
H P PVT PV T V T
(A7)
By integrating Eq. (A1) and isothermal changes in enthalpy, we have
2
12 1
V
VV
PH H T P dV PVT
(A8)
Differentiating Eq. (A1) with respect to temperature at constant volume, we have
Sensitivity of Joule-Thomson cooling to impure CO2 injection in depleted gas reservoirs 68
2 2
1 (2V
P R da TT V b V bV b dT
)(A9)
Substituting Eq. (A1) and (A9) into (A8) and then simplify
2
12 1 2 2
( )2
V
V
da T dVH H a T PVdT V bV b
(A10)
Integrating Eq. (A10) gives
2
1
2 1 2 2 1( / ) 0.414ln
2.4142 2
V
V
a T da dT V bH H PV PVV bb 1 (A11)
By knowing that state 2 is the state of interest and state 1 is the ideal gas at zero pressure, Eq. (A11) becomes
0 ( / ) 0.4141 ln2.4142 2
a T da dT Z BH H RT ZZ Bb
(A12)
Where /B bP RT . Eq. (A12) is the enthalpy departure function for PR-EOS.
Specific heat capacity departure function
The constant pressure specific heat capacity departure function is given by the following thermodynamic relation
00
P P
P
H HC C
T. (A13)
Taking the derivative of Eq. (A12) with respect to temperature at constant pressure and simplifying the final relation for the specific heat capacity departure yields
2 20
2 2
0.414ln2 2 2.4142 2P P
R M N T d a Z BC C RM A Z B dT Z Bb
,
2 22Z BZ BMZ B
,B daNRb dT
.
(A14)
Chapter 3 69
Joule-Thomson Coefficient
The thermodynamic relation of the Joule-Thomson coefficient, JT , is as follows
1 VJT
PT
PT T VPC
V, (A15)
whereV
PT comes from Eq. (A9) and PC is calculated by Eq. (A13) and finally
TP
V is
differentiated Eq. (A1) with respect to volume at constant temperature as follow
2 22 2
( ) 2 2
2T
a T V bP RTV V b V bV b
. (A16)
Sensitivity of Joule-Thomson cooling to impure CO2 injection in depleted gas reservoirs 70
Appendix 3-B
F-theory
According to the Friction Theory Method (FTM), f-theory, (Quinones-Cisneros et al., 2001), the total viscosity of a fluid consists of a dilute gas term and a friction term
0 f , (B1)
where the dilute gas viscosity term in micro-poise ( P ) is given by
0 2/3 *40.785 cc
MwT FV
, (B2)
and by *
* 4 *0.14874*0.14874 * *
* 0.7683
1.16145 0.52487 2.16178 6.435 10exp 0.77320 exp 2.43787
sin 18.0323 7.27371
TT T T
T, (B3)
with
* 1.2593
c
TTT
. (B4)
In Eq. (B2) cV is the critical volume in cm3/mol, and the is obtained from cF
1 0.2756cF (B5)
where is the acentric factor. The friction term, f , is obtained from a reduced form of the friction
term
ff
c
(B6)
Where c is the characteristic critical viscosity which is given by
2/3
1/ 67.9483 cc
c
MwPT
(B7)
Chapter 3 71
Furthermore, the reduced friction viscosity is quantified through a reduced attractive
contribution, ,f a , and reduced repulsive contribution, ,f r , as follows
, ,f f r f a (B8)
where the attractive contribution term is
,a
af ac
PP
(B9)
and the repulsive contribution term
2
,r r
r rrf rc c
P PP P
(B10)
In Eqs. (B9) and (B10) and r are the attractive and repulsive term in an EOS. For the PR-EOS
these terms are respectively aP P
2 2
( )2aa TP
V bV b, Pr
RTV b
(B11)
The friction coefficients in Eqs. (B9) and (B10) are given by
ca a a
r
(B12)
cr r (B13)
and
crr rr rr (B14)
The temperature-dependency of the friction coefficients has been expressed by Quinones-Cisneros et al. (2001) as follows
,0,0 ,1,0 ,1,1
2,2,0 ,2,1 ,2,2
1 exp
exp 2 2 1 ,
a a a a
a a a
1 1(B15)
,0,0 ,1,0 ,1,1
2,2,0 ,2,1 ,2,2
1 exp
exp 2 2 1 ,
r r r r
r r r
1 1(B16)
Sensitivity of Joule-Thomson cooling to impure CO2 injection in depleted gas reservoirs 72
and
2,2,1 exp 2 1 1rr rr (B17)
where
cTT
, c
c
RTP (B18)
Eqs. (B12) to (B18) contain 16 model parameters which need to be constrained using viscosity data.
F-theory and gas mixtures
The viscosity of gas mixtures, as suggested by Quinones-Cisneros et al. (2001), is handled as follows
,1I cK II (B19)
where
20, , , ,I mix r I r a I a rr IP P rP (B20)
and
2, , ,II r II r a II a rr II rP P P (B21)
In Eq. (B20) the dilute gas viscosity and the friction coefficients of the mixture are
0, 0,1
exp lnn
mix i ii
x (B22)
,,,
1
m r ic ir I i
i ci
zP
(B23)
,,,
1
m a ic ia I i
i ci
zP
(B24)
,,,
1
m rr ic irr I i
i ci
zP
(B25)
where
Chapter 3 73
ii
i
xzMw Mw (B26)
with
1
ni
i i
xMwMw
and2/3
,2 1/ 6i ci
c cci
Mw PK
T(B27)
In Eqs (B22-B27), subscript i indicates a component of the mixture. For Eq. (B21) the fiction coefficients are expressed by
2/3,
, 1/ 61
nr ii ci
r II ii ci ci
Mw Pz
T P(B28)
2/3,
, 1/ 61
na ii ci
a II ii ci ci
Mw Pz
T P(B29)
And
2/3,
, 1/ 61
nrr ii ci
rr II ii ci ci
Mw Pz
T P(B30)
where , and K re the tuning parameter of the mixing model. ,1cK ,2c a
Sensitivity of Joule-Thomson cooling to impure CO2 injection in depleted gas reservoirs 74
Appendix 3-C
rmal model has been developed to solve the reservoir temperature distribution during The reservoir thethe transient flow test. The transient reservoir thermal model is derived from the general energy balance equation (Bird et al., 2002)
. . :U Uv p v vt
.q (C1)
With Fourier’s law, assuming the conductivity coefficient is constant in formation, the conduction
(C2)
Considering t e internal energy of both formation fluid and rock, we have the bulk internal energy
(C3)
For fluid flow in porous media, the term
TK
term can be calculated by
q K TT
hterm defined as
1U U r rU
: v can be replaced by .v P
21 . . .r r TU U Uv p v v p Kt
T (C4)
From the definition of enthalpy,
/H U p (C5)
The total derivative of enthalpy can be derived by using thermodynamic equilibrium relationships
P jT PdH C dT C dP (C6)
Where jT is Joule-Thomson coefficient and PC is specific heat capacity respectively, Substitution of
intoEq. C5 Eq. C4 and manipulation yields
21 r r TH P U Hv Kt
T (C7)
Assume the rock density is constant and the internal energy of rock can be approximated by specific
r (C8)
heat capacity and temperature change, we have
r r P rdU dH C dT
Chapter 3 75
Substitution of Eq. C8 into Eq. C7 and rearrangement result in
2
1
. . TH v v H K T
1 rr P r r r P r
TH PH C T Ct t t t t (C9)
From the mass balance equation of formation fluid,
. vt
(C10)
From the mass balance equation of formation rock,
1 0rt(C11)
Eq. C9 can be rewritten as
2.rT
T v H K Tt
(C12)
From Eq. C6 we have
1r P rH P Ct t
P jT PH TC Ct t
Pt
and P jT PH C T C P (C13)
Substitution of Eq. C13 int C12 and manipulation yields o Eq.
1P r P r P jT PT PC C C C vt t
2jT TT P K T (C14)
Sensitivity of Joule-Thomson cooling to impure CO2 injection in depleted gas reservoirs 76
Chapter 4
Sensitivity of the CO2 storage capacity of underground geological
structures to the presence of SO2 and other impurities
Part of this chapter is based on:
Ziabakhsh-Ganji, Z., Kooi, H., (2014). Sensitivity of the CO2 storage capacity of underground geological structures to the presence of SO2 and other impurities, Applied Energy, 135, 43-52.
Chapter 4 79
Abstract
Depleted hydrocarbon reservoirs and deep saline aquifers are key targets for geological storage of CO2
to reduce atmospheric CO2 emissions. Most studies in CCS investigate subsurface storage of pure CO2. In this chapter we investigate the impact of the presence of other gases (impurities) in the injected CO2 stream on solubility trapping (in the aqueous phase) and volumetric trapping (in the non-aqueous phase, for a wide range of pressure and temperature. Calculations for solubility trapping are based on an equation of state that accurately accounts for the pressure, temperature, gas-compositional (mixtures) and salinity influences on CO2 solubility and brine density. For volumetric trapping the Peng-Robinson equation of state is used, accounting for binary interaction for gas mixtures and density correction. In the analysis, special attention is paid to the impact of SO2, which exhibits anomalous storage effects when compared to other common impurities.
It is shown that while most impurities reduce the CO2 storage capacity (STC) in both the aqueous and non-aqueous phase, presence of SO2 enhances STC in both phases for a wide range of pressure and temperature conditions. However, for the realistic amounts of SO2 in flue gases, the effects are rather small; for an SO2 content of about 0.5 % the non-aqueous STC enhancement ranges up to about 4%.
For volumetric trapping, the greatest positive impact of SO2 occurs at relatively low pressures (74 – 100 bar) and temperatures (313 – 325 K). These are typical for shallow (< 1 km) aquifers or deeper depleted hydrocarbon reservoirs during the injection stage. For solubility trapping, the STC enhancement by SO2 increases with pressure and is relatively insensitive to temperature, implying that the greatest positive effect would be achieved for deep saline aquifers. These findings suggest that the positive effects of SO2 on the CO2 storage capacity could be of practical significance for CCS projects. The positive storage effects would have to be evaluated relative to possible negative effects due to induced geochemical reactions, corrosion of well casings, and health risks associated with potential leakage from transport or injection facilities or from the storage reservoir.
4.1. Introduction
Storage of CO2 in underground geological structures is considered an important methodology to reduce, and ultimately reverse, the trend of increasing carbon dioxide (CO2) concentrations in the atmosphere (IPCC, 2007). Carbon dioxide capture and storage (CCS) generally involves capture of CO2 at major stationary sources such as power plants and injection in underground geological structures such as saline aquifers, depleted hydrocarbon reservoirs, or producing hydrocarbon reservoirs to enhance oil or gas recovery. In general, captured CO2 contains additional gases - these are commonly referred to as co-contaminant gases or impurities - such as H2S, CH4, SO2, N2 and O2.The first two impurities (H2S, CH4) are common in acid gas that is produced in hydrocarbon production units. The other gases are common components of flue gas captured at power plants (Kather, 2009; Kather & Kownatzki, 2011).
Sensitivity of the CO2 storage capacity of underground geological Structures to the presence of SO2 and other impurities 80
Evaluating the CO2 storage capacity of underground storage structures is rather involved. Injected CO2
is generally trapped in different forms: (a) as a separate gas phase or supercritical fluid (called static, residual or volumetric gas trapping), (b) in an aqueous phase, often brines (solubility trapping), and (c) as a solid phase (mineral trapping) (IPCC, 2005). Moreover, the storage capacity of individual structures also depends on the reservoir geometry, its porosity structure and ambient pressure and temperature conditions (Bachu et al., 2005).
Several methods exist for the quantification of storage capacity. Some methods for hydrocarbon reservoirs use production parameters such as the oil/gas recovery factor and the original gas/oil in place (Bachu et al., 2005) to estimate how much CO2 can be stored. Tseng et al. (2012) developed an analytical method to account for the influence of water drive in gas reservoirs on CO2 storage capacity. Zhou et al. (2008) presented an approach to assess the storage capacity for saline aquifers. Deng et all. (2012) considered the impact of geologic heterogeneity on CO2 storage capacity. While all these studies considered storage of pure CO2, capabilities to investigate presence and impacts of other (gaseous) components than CO2 on the CO2 storage capacity are still limited. Evaluation of the impacts of the presence of such components is important because they modify fluid properties (e.g. density) of the gas/liquid streams. Moreover, knowledge of the consequences of impurities in the CO2
stream is of particular interest as high-level purification of CO2 is costly and injection of co-contaminants with the CO2 may therefore reduce the front-end processing costs of CCS. These costs of purification of CO2 are estimated represent about ¾ of the total costs of CCS (Metz et al., 2005).
In this chapter, we explore the impacts of impurities on both volumetric trapping and solubility trapping of CO2 in underground storage reservoirs. For volumetric storage trapping, Wang et al. (2012) have recently evaluated the impact of co-contaminants which predominate in oxyfuel flue gas, notably N2, O2 and Ar by using the Peng-Robinson equation of state (PR-EOS). Rather than studying specific storage reservoirs and their geometries, these authors focused on the P, T-influences on the density of supercritical gas mixtures (CO2 trapping for the gas-available pore space). Wang et al. (2012) showed that the reduction of the storage capacity of CO2 due to the presence of the studied impurities is greater than the volume fractions of the impurities in the mixture. Therefore, the impurities are rather detrimental for the storage capacity of CO2. However, in a prior report, Wang et al. (2011) showed that SO2 exhibits opposite behavior, and can enhance the volumetric storage capacity. They showed that at 330 K and for 2.9 % SO2, the CO2 storage capacity can be up to 5% higher than for pure CO2 storage, and that the maximum storage capacity occurs at about 11 MPa. In this chapter, we expand on this finding and demonstrate the impact of SO2 on storage capacity for a more extensive range of temperature and pressure conditions that can occur at CCS sites, and for different amounts of SO2. Moreover, we use density corrections to the PR-EOS to achieve higher model accuracy. To our knowledge the impact of impurities on solubility trapping has not been analyzed before. Our approach uses our recently developed equation of state for gas mixtures and brine (Ziabakhsh-Ganji & Kooi, 2012) in combination with a model for aqueous phase density calculation.
Chapter 4 81
The chapter is organized as follows. First, we elucidate the storage capacity estimation method for both volumetric and solubility trapping. Then, the results of sensitivity analyses are presented which illustrate the impact of the various gases, and in particular SO2, on CO2 storage.
4.2. Method
4.2.1. Volumetric Storage Trapping Capacity (STCV)
For any given storage reservoir, the total mass mass of CO2 that can be stored in the form of a separate gas phase or supercritical fluid depends on the pore space that is available for this form of storage. For storage of pure CO2 for instance, Bachu et al. (2005) proposed that the total CO2 mass can be estimated using
2 2 Re (1 )CO CO s wrM V S (1)
where2CO is the (dry) CO2 density, Re sV is the total reservoir volume, and and are the
reservoir-averaged porosity and the (irreducible) water saturation, respectively. In our approach we use this conceptual model and assume that storage of impure CO2 does not change the available space for the non-aqueous phase storage. The method therefore does not account for mineral dissolution and precipitation processes that tend to accompany the storage of these gases. With these assumptions, for impure CO2 storage the total mass of CO2 stored is given by
wrS
2
Re (1 )1
mixs wr
i
i CO
M V Smm
(2)
where mix is the density of the gas mixture and 2i COm m is the ratio of the mass of impurity i to the
mass of CO2 in the mixture.
The ratio of Eqs. (2) and (1) now yields an intelligible measure to quantify the impact of impurities on volumetric CO2 storage:
2
2
2
1
mix
CO iCO
i CO
MSTCVM m
m(3)
When STCV< 1 the impurities reduce the CO2 storage capacity and vice versa for STCV > 1. The normalized volumetric CO2 storage capacity is identical to the quantity STC used by Wang et al. (2012). Our approach differs from Wang et al. (2012) in that we use slightly more accurate density calculations and consider additional/other gas species. For the calculation of densities, we use the corrected Peng Robinson Equation of State (PR-EOS) (Peng & Robinson, 1976) which is described in
STCV
Sensitivity of the CO2 storage capacity of underground geological Structures to the presence of SO2 and other impurities 82
section (3.2.2.2). For gas mixtures, we use standard simple mixing rules and binary interaction coefficients (Prausnitz et al., 1986)
1 1
( ) ( ) 1mix i j i j iji j
a T x x a T a T k ,1
n
mix i ii
b x b (4)
where x is the mole fraction of each component in the mixture. Table 1 lists the values of the binary
interaction coefficients ( ) that were used. Most values were adopted from Li and Yan (2009). The
listed value for CO2-SO2 was optimized using vapour liquid equilibrium experimental data from Cummings (1931), results of which will be shown in the results section.
ijk
Table 4.1: Binary interaction coefficient values for the PR EOS ( )ijk
Gas CH4 H2S O2 N2 SO2 Ar
CO2 0.1 0.099 0.114 0.07 0.047 0.163
Combining the relationships described in section (3.2.2.2) yields the following expression for the storage capacity.
2 2 2
,1
PRmix
i iPR
iCO CO CO
MwV cSTCV P T
x MwMwV c x Mw
(5)
The values of i for the pure gas species in this study, and for temperatures ranging from 1 to 170 C
and pressures up to 700 bar, are listed in Table 2. The values were obtained using the Weighted Nonlinear Least Squares (WNLS) method (Ziabakhsh-Ganji & Kooi 2014) and density data from the NISTa database.
Table 4.2: Density correction parameter values for the PR EOS
Gas CO2 CH4 H2S O2 N2 SO2 Ar
3.3894 6.4044 3.939 5.1749 6.8527 1.4431 5.2851
4.2.2. Solubility Storage Trapping Capacity (STCS)
As mentioned by Bachu et al. (2005) solubility trapping is a continuous, time-dependent process which, in particular for saline aquifers, tends to become more effective over longer time scales. The ultimate storage (capacity) of a finite size reservoir is reached when all the water in the reservoir has reached solubility saturation. Therefore, analogous to equation (1) for volumetric storage, the mass of
Chapter 4 83
CO2 that can be stored by solubility trapping can be determined using (Bachu & Adams, 2003; Bachu et al., 2005):
2 22
0 0ReCOs s wr AqP CO AqP CM V S X X O (6)
where AqP is the density of formation water, 2COX is the carbon dioxide content (mass fraction) in
formation water and the superscript 0 refers to the initial carbon dioxide content of the formation brine. Here, for simplicity we assume that initial carbon dioxide content is negligible. This seems very reasonable as our calculations for an initial partial CO2 pressure of 4.5 bar show that STCS is reduced by about 0.1 % only. If we further assume that the available water/brine volume for solubility trapping is not influenced by the presence of impurities in the CO2 stream, the impact of impurities on solubility storage capacity is defined by
2
22CO
AqP COs mix
s AqP CO
XMSTCSM X
(7)
where sM and represent the dissolved mass of CO2 for impure and for pure CO2 storage,
respectively. In Eq. (7),
2COsM
AqP is the density of brine as a function of temperature, pressure, dissolved
gases and brine salinity, is quantified by
2 2
1
10
nH O H O sa sa Aq
s AqP i ii
x Mw x MwMw V x (8)
where 0 is the pure brine (without dissolved gases) density, computed using a correlation proposed by
Rowe and Chou (1970) and AqV is the molar volume of each dissolved component in pure water, calculated from a correlation by Akinfiev and Diamond (2003) for various dissolved gases in pure water. The subscript refers to the salt and the x’s are the mole fractions of each component in the aqueous phase which are calculated with the equation of state (EOS) developed by Ziabakhsh-Ganji and Kooi (2012). The EOS describes the thermodynamic equilibrium between a non-aqueous phase (NaqP), basically a multi-component mixture (CO2, O2, H2S, CH4, Ar, N2 and SO2) that can be in gas, supercritical or condensed conditions, and an aqueous phase (AqP), that may include dissolved hydrocarbons and gases in addition to water and dissolved solids and does not include solid/minerals as a separate phase. This EOS predicts the water content in non-aqueous phase and composition of the various gas components in the aqueous and non-aqueous phase at moderate temperatures, a wide pressure range and various salinities (up to 6 mole per kilogram water).
sa
Sensitivity of the CO2 storage capacity of underground geological Structures to the presence of SO2 and other impurities 84
4.3. Results and Discussion
4.3.1. support for the applicability of the NaqP model
Figure 4.1 illustrates the performance of the model used for the NaqP calculations (for STCV) relative to data in the NISTa database (http://webbook.nist.gov/chemistry/fluid/) for pure (single component) gases. The figure shows that predicted densities compare favorably with the observational data.
0 100 200 300 400 500 600 700 800
200
400
600
800
1000
1200
CO2
a
P (bar)
dens
ity (k
g/m
3 )
T= 283.15 KT= 303.15 KT= 323.15 KT= 343.15 KT= 363.15 KT= 383.15 KT= 403.15 KT= 423.15 KT= 443.15 K
0 50 100 150 200 250 300
500
1000
1500
SO2
b
P (bar)
dens
ity (k
g/m
3 )
0 100 200 300 400 500 600 700 800
200
400
600
800
1000
H2S
c
P (bar)
dens
ity (k
g/m
3 )
0 100 200 300 400 500 600 700 800
200
400
600
800
O2
d
P (bar)
dens
ity (k
g/m
3 )
0 100 200 300 400 500 600 700 800
200
400
600
800
1000 Argon
e
P (bar)
dens
ity (k
g/m
3 )
0 100 200 300 400 500 600 700 800
200
400
600
N2
f
P (bar)
dens
ity (k
g/m
3 )
Fig. 4.1: Density of six component gases considered in this study. Solid lines: this work. Symbols: NISTa database.
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
100
x CO2
( % mole fraction)
P (b
ar)
313.15 K
373.15 K
403.15 K
Fig. 4.2: Comparison of vapour liquid equilibrium (VLE) conditions predicted by the model for a binary mixture of CO2-SO2 (solid lines) with experimental data (Cummings, 1931) (symbols). Red curves: dew line; blue curves: bubble line.
Chapter 4 85
For CO2-mixtures, lack of published experimental density data precludes similar direct validation of the density predictions of our model. In general the validity of density models for mixtures fundamentally depends on the accuracy/validity of the employed binary interaction coefficients (Table 4.1), which are generally constrained through fitting of experimental data on the vapour liquid equilibrium (VLE) conditions (boundary of the domain in which the two phases co-exist).
0 20 40 60 80 100
200
400
600
800
1000
1200
1400P= 75 barf
xSO2
(% mole fraction)
dens
ity (k
g/m
3 )
0 20 40 60 80 10050
100
150
200
250P= 75 barb
x Ar (% mole fraction)
dens
ity (k
g/m
3 )
0 20 40 60 80 10050
100
150
200
250P= 75 barc
x N2
(% mole fraction)
dens
ity (k
g/m
3 )
0 20 40 60 80 10050
100
150
200
250P= 75 bard
x O2
(% mole fraction)
dens
ity (k
g/m
3 )
0 20 40 60 80 1000
200
400
600
800P= 75 bare
x H2
S (% mole fraction)
dens
ity (k
g/m
3 )
0 20 40 60 80 10050
100
150
200
250P= 75 bara
x CH4
(% mole fraction)
dens
ity (k
g/m
3 )
T= 313.15 KT= 323.15 KT= 333.15 KT= 343.15 KT= 363.15 K
Fig. 4.3: Density of binary mixtures of CO2 and an impurity component for the six contaminant gases considered in this study, for 75 bar and various temperatures shown in the legend of (a). Solid lines: this work. Symbols: values obtained using the SUPERTRAPP software (2007).
Li and Yan (2009) reported that their binary interaction coefficient for CO2-SO2 (0.046) was based on limited VLE data. Therefore, we re-fitted our model to the comprehensive VLE data of Cummings (1931). Figure 2 shows the fit, and the inferred interaction coefficient (0.047) is listed in Table 4.1.
Figure 4.3 demonstrates that our model predictions for binary mixtures are similar to those of the SUPERTRAPP commercial software (NISTb, 2007; Battistelli & Marcolini, 2009), which methodology is not fully disclosed. Similar agreement was found for other pressures. Although this
Sensitivity of the CO2 storage capacity of underground geological Structures to the presence of SO2 and other impurities 86
model-model comparison does not provide formal validation of our model, it does provide confidence that our approach is well suited to evaluate the impact of these impurities on STCV.
0 200 400 600 800 1000 1200
100
200
300
400
500
600
700
800
900
1000
1100
1200a
P (bar)
dens
ity (k
g/m
3 )
T= 273.36 KT= 298.39T= 323.48 KT= 373.54 K
10 15 20 25 30 35 4010
20
30
40
50
60
70
80
90
100b
P (bar)
dens
ity (k
g/m
3 )
Fig. 4.4: Density behavior of a four-component gas mixture. Composition (89.83 mole% CO2, 5.05 % O2, 2.05 % Ar, 3.07 % N2) and experimental density data (symbols) from Chapoy et al. (2013). Solid lines: this work. Dashed lines: pure CO2.
Chapoy et al. (2013) conducted density measurements on a four-component synthetic gas mixture representative of oxyfuel flue gas containing CO2, O2, Ar, and N2. Figure 4 shows that our model accurately respoduces these multi-component gas density data.
4.3.2. Effect of impurities on the STCV
Figure 4.3 illustrates the contrasting influence of the contaminant-gases on mixture density. CH4, Ar, N2 and O2 decrease mixture density, while presence of H2S, and in particular SO2 increase mixture density. Note that for ideal gas mixtures, density would progress linearly between the two end-member (pure gases) densities. In that case STCV would equal the CO2 mole fraction of the mixture and impurities would reduce the CO2 storage capacity in a trivial way. The nonlinear nature of the curves of figure 4.3 therefore is of particular interest here. The concave nature of the curves of figure 4.3a to 4.3d show that CH4, Ar, N2 and O2 decrease mixture density more strongly than for ideal mixtures and, therefore, have a marked negative impact on the CO2 storage capacity. For H2S and SO2
the impact on volumetric storage capacity is less trivial.
A conspicuous and interesting feature of Figure 4.3f is that for a CO2-SO2 mixture at relatively low temperature density can double for SO2 mole fraction increases less than 10%. This indicates that CO2-SO2 mixtures may occupy a considerably smaller volume than pure CO2 at the same pressure and temperature conditions. The implications for the CO2 storage capacity is illustrated in detail below.
Chapter 4 87
280 290 300 310 320 330 340 350 360 3700
0.5
1
1.5
2
2.5a
P= 85 bar
T (K)
STCV
Pure CO
2
10% Ar10% CH
4
10% N2
10% O2
10% H2
S
10% SO2
0 50 100 150 200 250 3000
0.5
1
1.5
2
2.5b
T= 313.15 K
P (bar)
STC
V
Pure CO
2
10% Ar10% CH
4
10% N2
10% O2
10% H2
S
10% SO2
Fig. 4.5: Calculated STCV for binary gas mixtures containing 10% impurity. (a) Constant temperature. (b) Constant pressure.
Table 4.3: Typical major components of oxyfuel flue gas (Wang et al., 2012)
components CO2 O2 N2 Ar Total
low impurities (moles) 98 0.67 0.74 0.59 100
high impurities (moles) 85 4.73 5.8 4.47 100
Figure 4.5 illustrates, for impurity amounts up to 10%, that where other gases decrease STCV, SO2
can increase the CO2 storage capacity. Importantly, increased storage occurs within pressure and temperature ranges that are relevant to CCS. Comparison with calculations presented by Wang et al. (2011) for 2.9% SO2 and 330 K shows that our model, which includes density corrections to the PR EOS, yields a higher maximum value (STCV = 1.054 versus STCV = 1.064). Greater impacts than
Sensitivity of the CO2 storage capacity of underground geological Structures to the presence of SO2 and other impurities 88
predicted by Wang et al. (2012) (more negative STCV values) were also found for oxyfuel flue gas compositions (Tables 3).
280 290 300 310 320 330 340 350 360 3700.2
0.4
0.6
0.8
1
1.2c P= 80 bar
T (K)
STC
V
Pure CO2
5% Ar10% Ar15% Ar20% Ar
50 100 150 200 250 3000.2
0.4
0.6
0.8
1
1.2d T= 323.15 K
P (bar)
STC
V
Pure CO2
5% Ar10% Ar15% Ar20% Ar
280 290 300 310 320 330 340 350 360 3700.2
0.4
0.6
0.8
1
1.2e P= 80 bar
T (K)
STC
V
Pure CO2
10% H2
S
20% H2
S
40% H2
S
60% H2
S
50 100 150 200 250 3000.2
0.4
0.6
0.8
1
1.2f T= 323.15 K
P (bar)
STC
V
Pure CO2
10% H2
S
20% H2
S
40% H2
S
60% H2
S
280 290 300 310 320 330 340 350 360 370
0.5
1
1.5
2
2.5
3a P= 80 bar
T (K)
STC
V
Pure CO
2
5% SO2
10% SO2
15% SO2
20% SO2
50 100 150 200 250 300
0.5
1
1.5
2
2.5
3b T= 323.15 K
P (bar)
STC
V
Pure CO
2
5% SO2
10% SO2
15% SO2
20% SO2
Fig. 4.6: The impact of the amount of impurity on STCV for various binary gas mixtures. (a, b) CO2-SO2. (c, d) CO2-Ar. (e, f) CO2-H2S.
Figure 4.6 (top panels) shows that, for SO2 mole fractions up to 20%, the maximum CO2 storage capacity (for fixed temperature and variable pressure or vice versa shown in the panels) increases for increasing amounts of SO2 in the mixture. The amount of SO2 also influences the pressure and temperature for which maximum storage capacity occurs. However, the pressure and temperature window for which STC > 1 appears relatively insensitive to the amount of SO2. The other panels of figure 4.6 illustrate the analogous impacts of other contaminant gases. For Ar, the storage capacity consistently decreases for increasing Ar mole fractions. For H2S the behavior is more complex; low mole fractions cause a storage capacity decrease, but STCV values > 1 can occur when the H2Scontent is very high (e.g., 60% has been reported by (ExxonMobil)).
The different behaviors of the various contaminant gases is controlled primarily by the critical temperature (Tc for SO2 for instance is very high compared to the other gases) and to a lesser extent by the binary interaction coefficient and the critical pressure. Molecular weight does not play a role. This was inferred through simple sensitivity analyses where we recalculated STCV impacts for the various gases while changing one of the above parameters at a time. Contour plots of the CO2 storage capacity for CO2-SO2 mixtures are presented in figure 4.7 for a wide range of P-T conditions common in CCS. Results show that the greatest impact of SO2 occurs at relatively low pressures (74 – 100 bar) and temperatures (313 – 325 K). These pressures and temperatures are typical for relatively shallow saline aquifers like, for instance, the Utsira formation (~1 km depth) which is currently used to store CO2
Chapter 4 89
obtained from the Sleipner gas field in the North Sea. For such storage sites, presence of SO2 would clearly be favorable. However, figure 4.7 also shows that for deeper aquifers where pressure and temperatures are usually higher (e.g., 180 bar and 340 K at 2 km depth), the CO2 storage capacity is enhanced only very little or is even reduced due to the presence of SO2. For depleted oil and gas reservoirs where pore pressures are relatively low, injection of CO2 at about 80 bar and at low temperatures appears quite realistic, and these conditions can to a large extent be controlled. Therefore, the positive effects of SO2 on the CO2 storage capacity can, in principle, also be exploited for storage in depleted hydrocarbon reservoirs. However, following the injection phase in deep reservoirs, the temperature of the stored CO2-rich gas should be expected to gradually rise to the pre-injection reservoir temperature, which typically is higher than 350 K. Our results show that this warming would be accompanied by expansion of the gas (reduction of STC), which would give rise to a gradual – probably on time scales of thousands of years - post-injection increase of the pore pressure. Although evaluation of the magnitudes of such long-term pressure increases would require further study, they should be of interest for assessments of the long-term reservoir integrity of CCS sites.
1
1
1.00
5
1.01
P (bar)
T (K
)
x SO2
= 0.5% (mole fraction)
a
*Sleipner aquifer
80 100 120 140 160 180 200
320
330
340
350
360
1
1.005
1.01
1.015
1.02
1.025
1.03
1.035
1.04
0.92102
1.01
61.11
09
1.20
59
1.30
09
1.39
58
1.49
08
1.58
58
1.68
08
P (bar)
T (K
)
x SO2
= 20% (mole fraction)
b
*Sleipner aquifer
80 100 120 140 160 180 200
320
330
340
350
360
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
10 20 30 40 50 60 70 80 90
0.5
1
1.5
2
2.5
3
3.5c T= 313.15 K
xSO2
(% mole fraction)
STC
V
Pure CO
2
P= 75 barP= 80 barP= 100 barP= 120 barP= 140 bar
10 20 30 40 50 60 70 80 90
0.5
1
1.5
2
2.5
3
3.5d P= 80 bar
xSO2
(% mole fraction)
STC
V
Pure CO
2
T= 313.15KT= 323.15KT= 333.15KT= 343.15KT= 363.15K
Fig. 4.7: STCV behavior of SO2-CO2 for a wide range of P-T conditions. (a), 0.5 % SO2 mole fraction (b), 20 % SO2 mole fraction (c), variable composition and constant temperature (d), variable composition and constant pressure.
Figures 4.7c and d show that for given pressure and temperature conditions an optimum amount of SO2 exists for which the CO2 storage capacity is greatest. For increasing temperature this optimum rapidly becomes exceedingly high. Even for low temperatures the mole fraction of SO2 required to obtain the greatest positive impact on CO2 storage is larger than 10%, the feasibility of which is discussed in paragraph 3.4 below.
Sensitivity of the CO2 storage capacity of underground geological Structures to the presence of SO2 and other impurities 90
4.3.4. Effect of impurities on STCS
Figure 4.8 (panels c and d) shows that presence of N2 decreases the solubility storage capacity of CO2,STCS. Decreases of STCS are also predicted for H2S (panels e and f) and most other gases (Ar, O2,CH4). SO2 again shows deviating behavior; it enhances CO2 solubility and increases STCS (panels a and b). The STCS enhancement increases with pressure, and (at 100 bar) shows a relatively complex temperature dependency with largest impacts occurring between approximately 320 and 350 K.
320 330 340 350 360 3700.995
1
1.005
1.01
1.015
1.02a P= 100 bar , S= 2 M
T (K)
STC
S
Pure CO
2
1 % SO2
2 % SO2
3 % SO2
4 % SO2
5 % SO2
100 150 200 250 300 350 400
1
1.02
1.04
1.06
1.08
1.1b T= 323.15 K , S= 2 M
P (bar)
STC
S
Pure CO
2
1 % SO2
2 % SO2
3 % SO2
4 % SO2
5 % SO2
320 330 340 350 360 3700.85
0.9
0.95
1c P= 100 bar , S= 2 M
T (K)
STC
S
Pure CO
2
3 % N2
6 % N2
9 % N2
12 % N2
15 % N2
100 150 200 250 300 350 4000.85
0.9
0.95
1d T= 323.15 K , S= 2 M
P (bar)
STC
S
Pure CO
2
3 % N2
6 % N2
9 % N2
12 % N2
15 % N2
320 330 340 350 360 3700.94
0.96
0.98
1
1.02e P= 100 bar , S= 2 M
T (K)
STC
S
Pure CO
2
1 % H2
S
2 % H2
S
3 % H2
S
4 % H2
S
5 % H2
S
100 150 200 250 300 350 4000.94
0.96
0.98
1
1.02f T= 323.15 K , S= 2 M
P (bar)
STC
S
Pure CO
2
1 % H2
S
2 % H2
S
3 % H2
S
4 % H2
S
5 % H2
S
Fig. 4.8: The impact of the amount of impurity on STCS for various binary gas mixtures. (a, b) CO2-SO2. (c, d) CO2-Ar. (e, f) CO2-H2S.
As shown in figure 4.9a presence of SO2 in the CO2 stream leads to marked density enhancement of the aqueous phase. This is of particular interest for storage in saline aquifers where dissolution of the free gas that has migrated on top of the groundwater can cause an instable density stratification and free convection in the top of the aquifer. The convection continuously moves the layer of saturated water downward, replacing it with unsaturated water, thus enhancing the dissolution process (Ennis-King & Paterson, 2003; Bachu et al., 2005; Meybodi & Hassanzadeh, 2013; Li & Jiang, 2014). The results, therefore, suggest that presence of SO2 not only enhances the ultimate storage of CO2, but also the dissolution process or dissolution rates.
Figure 9b shows model-calculated solubility of SO2 in comparison with available experimental data. Because experimental data are very scarce for SO2, model predictions are associated with relatively large uncertainty, in particular for pressures beyond about 10 bar.
Chapter 4 91
0.86
0.865
0.87
0.875
0.88
0.8850.890.895
P (bar)
T (K
)
x N2
= 15 % (mole fraction)
d
100 150 200 250 300
320
330
340
350
360
370
0.86
0.865
0.87
0.875
0.88
0.885
0.89
0.895
0.9
1.01
5
1.02
1.02
5
1.03
1.03
5
1.04
1.04
5
P (bar)
T (K
)
x SO2
= 3 % (mole fraction)
c
100 150 200 250 300
320
330
340
350
360
370
1.005
1.01
1.015
1.02
1.025
1.03
1.035
1.04
0 5 10 15 200
5
10
15
P (bar)
Slou
bility
of S
O2 *
100
T= 363.15 K, m= 0
T= 333.15 K, m= 5.928
T= 313.15 K, m= 2.942
b
150 200 250 300 350 4001060
1080
1100
1120
1140
1160
1180
P (bar)
dens
ity (k
g/m
3 )
a
5 % SO2
4 % SO2
3 % SO2
2 % SO2
1 % SO2
Pure CO2
Fig. 4.9: (a) Solubility of SO2 for a range of values for temperature, pressure and salinity. Solid line: Ziabakhsh and Kooi’s EOS (2012). Symbols: experimental data (Rumpf & Maurer, 1992; Xia et al, 1999). (b) Aqueous phase density in the presence of SO2 from the present work. (c) STCS-behavior for a wide range of P-T conditions of SO2-CO2. (d) STCS-behavior for a wide range of P-T conditions of N2-CO2.
Contour plots of STCS for CO2-SO2 mixtures and CO2-N2 are presented in figures 9c and 9d for a wide range of P-T conditions common in CCS. Results show that at pressures beyond 100 bar, the positive impact of SO2 on CO2 storage is rather insensitive to temperature. By contrast, the negative impact of N2 is rather sensitive to both pressure and temperature and least negative effects occur for relatively low pressure and temperature.
Finally, Table 4.4 lists calculated STCS values for oxyfuel flue gas with low and high impurity contents (compositions shown in Table 4.3). The chosen values for depth, pressure and temperature in Table 4.4 are representative for the large range of conditions (cases) in saline aquifers that are considered for CO2 storage, and that have been determined from a global assessment in the framework of the International Energy Agency’s Greenhouse Gas Programme (IEA GHG) (2004). The salinity of the saline aquifer has been assumed 2 mole per kilogram water in all cases. Inferred STCS values are about 0.98 for low impurity oxyfuel flue gas and the values is rather insensitive to pressure and temperature conditions.
For high-impurity flue gas, values range from about 0.86 to 0.90 where STCS is most strongly affected by aquifer depth/pressure. These dependencies are also apparent in the left panels of figure 4.10 (a, d). The other panels of figure 4.10 (b,c,e,f) illustrate, as an example, how addition of SO2 to the oxyfuel flue gas (high and low impurities) can compensate for the negative storage impacts of the dominant O2, N2 and Ar co-contaminants for storage capacity in solubility trapping.
Sensitivity of the CO2 storage capacity of underground geological Structures to the presence of SO2 and other impurities 92
Table 4.4: effect of oxyfuel flue gasa on STCV and STCS
Cases Depth (m) P(bar) T (K)
Low impurities
STCS
Highimpurities
STCS
Low impurities
STCV
Highimpurities
STCV
Highimpurities
STCV[10]
Shallow-Low Temp 895 92 306.15 0.982 0.898 0.902 0.361 0.392
Shallow-Mid Temp 895 92 311.15 0.980 0.881 0.825 0.389 0.427
Shallow-High Temp 895 92 318.15 0.981 0.867 0.873 0.538 0.573
Median-Low Temp 2336 240 335.15 0.981 0.870 0.961 0.721 0.734
Median-Mid Temp 2336 240 348.15 0.981 0.868 0.959 0.715 0.731
Median-High Temp 2336 240 365.15 0.981 0.865 0.958 0.721 0.739
Deep-LowTemp 3802 388 365.15 0.981 0.863 0.969 0.776 0.786
Deep-MidTemp 3802 388 386.15 0.981 0.862 0.968 0.775 0.787
Deep-HighTemp 3802 388 414.15 0.981 0.862 0.969 0.782 0.794
a compositions listed in Table 4.3
0.9804
0.98
06
0.98
06
0.9808
P (bar)
T (K
)
low impurities
(a)
100 200 300 400
320
330
340
350
360
370
0.98
4
0.98
6
0.98
8
0.99
0.99
2
0.99
4
0.99
6
P (bar)
T (K
)
low impurities + 1 mole SO2
(b)
100 150 200 250 300
320
330
340
350
360
3701
1.01
1.02
1.03
1.04
1.05
P (bar)
T (K
)
low impurities + 5 mole SO2
(c)
100 150 200 250 300
320
330
340
350
360
370
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
0.86
0.86
5
0.87
0.8750.88
P (bar)
T (K
)
high impurities
(d)
100 150 200 250 300
320
330
340
350
360
370
0.87
0.88
0.89 0.
9
0.91
P (bar)
T (K
)
high impurities + 5 mole SO2
(e)
100 150 200 250 300
320
330
340
350
360
370
0.87
0.88
0.89 0.
90.
91
0.92
0.93
0.94
0.95
P (bar)
T (K
)
high impurities + 10 mole SO2
(f)
100 150 200 250 300
320
330
340
350
360
370
0.86
0.88
0.9
0.92
0.94
0.96
Fig. 4.10: The impact on STCS of SO2 addition to oxyfuel flue gas. Top panels: low impurity oxyfuel. Lower panels: high impurity oxyfuel. Oxyfuel compositions are listed in Table 3.
4.3.5. Potential use of the positive effect of SO2
Reported SO2 contents of potential CCS source gases usually do not exceed 1.5% mole fraction (Jakobsen et al., 2011). IEA GHG (2004) reported a very high mole fraction of 2.9% (Table 4.5),
Chapter 4 93
although Wang et al., (2011), who used the same value in calculations, also state that values in excess of 0.5 %, are considered unlikely and only report values less than 0.005 %.
Table 4.5: Range of mole fractions of impurities in CCS source gases (Jakobsen et al., 2011; IEA GHG, 2004; ExxonMobil; Renard et al., 2014)
component SO2 H2S CO2 N2 O2 Ar CH4
min mole% <0.0001 0.01 40 0.02 0.04 0.005 0.7
max mole% 4 60 99 10 5 3.5 4
Although optimum conditions can therefore not be achieved by using these SO2 contents directly, the present study does show that the SO2 can have a positive impact on the CO2 storage capacity and that it may be worthwhile considering retaining the SO2 in the gas stream. At coal and oil-fired power plants this might imply considerable savings on the costs of flue gas desulfurization (FGD) by techniques such as scrubbing that are widely used to remove SO2 due to stringent environmental regulations regarding SO2 emission. Our model shows that, for a SO2 content of about 0.5 % the STCV enhancement can range up to about 4% (figure 4.7). Given the large positive effect on CO2
storage capacity, it may even be an option to utilize SO2 from other sources to enhance the SO2
content of CO2-streams to be stored in subsurface reservoirs, although these amounts would likely have to be less than 0.5% because of the strongly negative health impacts of SO2 and associated strict requirements imposed in HSE (Health, Safety and Environment) regulations. In spite of such restrictions to practical SO2 amounts, the results presented (including much higher percentages of SO2)are still useful and relevant to our general understanding of the impact of this gas. As SO2 contents of flue gases can be exceedingly low (e.g., Table 4.5), the possibility of addition of SO2 before subsurface storage seems particularly interesting for storage in depleted hydrocarbon reservoirs, where presence of SO2 also suppresses Joule Thomson cooling in the vicinity of the well bore during injection of relatively cold gas, thereby limiting potential clogging problems due to freezing of residual pore water or hydrate formation (Ziabakhsh-Ganji & Kooi, 2014). In comprehensive assessments, these positive effects of SO2 would also have to be evaluated relative to potential negative effects such as corrosion of steel well casing (Dugstad et al., 2013; Ruhl & Kranzmann, 2013) – this can be greatly suppressed by using dry gas injection –, geochemical reactions in the storage reservoir that may reduce well injectivity due to the strong acidification of the reservoir or aquifer brine (Knauss et al., 2005; Xu et al., 2007), and health and environmental risks associated with potential leakage of SO2 from the storage reservoir or from transport and injection facilities. Future work may also have to look into the way in which presence of SO2 would affect the CO2 storage potential though its effects on mineral dissolution and mineral trapping, which alter the pore space of storage reservoirs.
Sensitivity of the CO2 storage capacity of underground geological Structures to the presence of SO2 and other impurities 94
4.4. Conclusion
The present study has assessed sensitivity of CO2 storage capacity (STC) in both solubility trapping (in the aqueous phase) and volumetric trapping (in the non-aqueous phase) induced by presence of impurities (H2S, CH4, O2, N2, Ar and SO2) in the stored CO2. For both forms of trapping STC is shown to be sensitive to the type(s) of impurity present in the gas stream.
For binary mixtures, presence of SO2 causes anomalous STC behavior compared with other gas species; while other gases reduce the storage capacity for both solubility trapping (STCS) and volumetric trapping (STCV) of CO2, SO2 can increase STC for realistic pressure and temperature conditions. The greatest impact of SO2 on STCV occurs at relatively low pressures (74 – 100 bar) and temperatures (313 – 325 K) that are typical for shallow (< 1 km) aquifers, or for deeper depleted hydrocarbon reservoirs during the injection stage. STCS enhancement by SO2 increases with pressure, and at pressures larger than 100 bar STCS is relatively insensitive to temperature. Presence of SO2 is also expected to enhance the dissolution process or dissolution rates.
For multi-component impurity mixtures such as oxyfuel flue gas, addition of SO2 can compensate for the negative impact of other impurities.
In particular for low-temperature injection, co-injection of SO2 with the CO2 appears to have clear beneficial CO2 storing consequences by enhancing STC. However, for the relatively low amounts of SO2 in flue gases, the beneficial effects are rather small. In comprehensive assessments, these positive effects of SO2 would have to be evaluated relative to possible negative effects due to induced geochemical reactions, corrosion of steel well casings, and risks associated with potential leakage from the storage reservoir. Allowance of SO2 in the injected gas may nonetheless represent a viable option to reduce the overall costs of reservoir storage of CO2 through savings in purification of source gases.
PART II CHEMICAL EFFECTS
Chapter 5
Sensitivity of the geochemical response of a saline aquifer to the
presence of impurities in the stored CO2
Chapter 5 99
Abstract
In this chapter, the EOS presented in Chapter 2 is used in conjunction with the geochemical modelling code PHREEQC to address the long-term, geochemical impacts of impure CO2 storage in a saline aquifer. The impurities considered represent component gases which predominate in flue gases (O2, N2,
and Ar), in acid gas (H2S and SO2), and in in-situ gas (CH4). The 1-D model simulates the dissolution of the component gases of an impure CO2 store at a gas-brine interface, and subsequent diffusive transport of the gases into the brine together with the associated aqueous and water-rock interactions. This system provides an approximate representation of post-injection conditions where flows of the non-aqueous phase and the brine have become small and diffusive transport predominates. The adopted aquifer mineralogy corresponds to that of the Triassic Hardegsen Formation (sandstone/claystone) at the P-18 field in the Dutch offshore.
After 10,000 yr, irrespective of the gas composition, a very large porosity reduction is predicted up to about 10 m from the gas-brine interface and a slight porosity increase at larger distances. For pure CO2, the original reservoir porosity (0.11) is reduced to virtually zero (0.0002) at the interface by precipitation of quartz and large amounts of dawsonite (it may be important to emphasize that such porosity reduction would not be expected for injection in a depleted gas reservoir). Presence of O2, N2, Ar or combinations thereof, such as in oxyfuel flue gas, and presence of CH4 have very little effect on the geochemical response. Presence of SO2 induces complex changes, including a strong reduction or absence of dawsonite precipitation near the interface, precipitation of kaolinite and anhydrite near the interface, and anhydrite and dawsonite precipitation some distance (~5m) from the interface. Porosity is enhanced near the interface (to 0.03 for 4% SO2), but strongly reduced away from the interface mainly due to anhydrite precipitation. The geochemical effect of H2S shows similarities with that of SO2, but with smaller magnitude and impacts only become significant for large mass fractions > 3%. The possible significance of these impacts are discussed.
5.1. Introduction
Fluid-mineral chemical reactions constitute a fundamental component of the chain of processes that are induced by CO2 storage in subsurface reservoirs. The associated mineral dissolution and precipitation reactions are of particular practical relevance to CCS for their potential to alter the porosity and permeability structure of the host rock, and for their role in (long-term) mineral trapping of the CO2 (Czernichowski-Lauriol et al., 1996; Gunter et al., 1997; Gaus et al., 2010).
Over the last two decades many studies have addressed the fluid-rock interactions in the presence of CO2 as a single component gas species through reactive (transport) modelling (Gunter et al., 1993, 1997, 2000; Johnson et al., 2004; Xu et al., 2004; Gaus et al., 2005; Lagneau et al., 2005; White et al., 2005; Xu et al., 2005; Zwingmann et al., 2005; Andre et al., 2007; Bickle et al., 2007; Gherardi et al., 2007; Xu et al., 2007, 2010; Okuyama et al. 2013; Tambach et al., 2015) and via laboratory
Sensitivity of the geochemical response of a saline aquifer to the presence of impurities in the stored CO2 100
experiments at pressure and temperature conditions relevant for CO2 storage (Ueda et al, 2005; Hangx et al, 2009; Fischer et al., 2010; Huq et al, 2012). These studies have found that injected CO2 is trapped geochemically by precipitation of carbonate minerals in host rocks. The carbonate minerals are formed using cations present in the formation brine, and additional cations that are released by the dissolution of primary reservoir minerals stimulated by the presence of carbonic acid (formed by dissolution of CO2 in the formation brine).
Experimental studies have also provided essential constraints on thermodynamic and kinetic parameters for some of the important geochemical reactions (Gunter et al., (1997), Shiraki and Dunn, 2000, Kaszuba et al., 2003, Kirste et al., 2004, Brosse et al., 2005, Kaszuba et al., 2005; Wigand et al., 2008). Apart from these modelling and experimental studies, some studies have also gleaned information about geochemical reactions by investigating water-rock interaction at natural CO2-rich gas fields such as the Werkendam, Barendrecht-Ziedewij gas field in The Netherlands (Koenen et al., 2013), the Madison of Wyoming gas field in the USA (Kaszuba et al., 2011), the Miller gas field (Lu et al., 2011) and the Fizzy and Orwell field (Heinemann et al., 2013) in the UK sector of the North Sea.
Over the last decade, increasing attention is starting to be paid to the impact of potential other gas species than CO2 (e.g., CH4, O2, SO2, H2S, N2, and NOx) in the CO2-rich phase, and how such impurities can alter brine mineral reactions (Jacquemet et al., 2009; Gaus, 2010). Laboratory experimental work and numerical modeling studies have found that injection of impurities can drastically affect reservoir minerals through dissolution and precipitation.
Wilke et al., (2012) recently presented batch experiments using relatively pure minerals (mono-mineral) that showed that presence of traces of SO2 or NO2, and the resulting formation of H2SO4 and HNO3, intensifies the dissolution of anhydrite and calcite minerals. Furthermore, even for the relatively short time scale of their experiments (42 days), a higher amount of cations was released during experiments with silicates and impure supercritical CO2. Experiments conducted by Jung et al. (2013) showed that co-injection of O2 can drive significant water-rock interactions when sulfide minerals are present in the host rock. In their experiments on Gothic shale caprock, oxidation of pyrite produces sulfuric acid which reduces the brine pH and causes ensuing dissolution and precipitation of minerals. Such impact of O2 in the presence of sulfides was also found by Renard et al. (2014). For their experiments with carbonate rocks and injection of an oxyfuel combustion stream (CO2= 0.82, SO2= 0.04, O2= 0.04, N2=0.04 and Ar= 0.06) they reported anhydrite and quartz precipitation and dolomite and chlorite dissolution. Fracture porosity of their samples was found to be reduced. Schaef et al. (2014) showed experimentally that gypsum can precipitate in basalts when injected with a mixture of SO2, O2 and CO2.
Through batch-type modeling (without transport) Gunter et al. (2000) inferred dissolution of carbonate minerals and precipitation of anhydrite for brine containing dissolved H2S and H2SO4 (latter can be considered to be derived from SO2–brine system). Knauss et al. (2005) used a more comprehensive approach involving 1D radial transport modeling, simulating the response of an aquifer to injection of a brine pre-equilibrated with imposed fugacities of CO2, H2S and SO2. They found that in contrast to
Chapter 5 101
H2S, which had little effect on the brine-mineral reactions, SO2 caused dissolution of primary calcite, and suppressed precipitation of secondary carbonates (and hence C sequestration). However, they expected that C sequestration would be enhanced by SO2 on long time scales (not modeled). Xu et al. (2007) performed numerical simulations using TOUGHREACT (Xu et al., 2004) simulating injection of pure CO2 together with an H2S and SO2 equilibrated brine. They predicted precipitation of sulfate minerals such as alunite and pyrite. André et al., (2014) used the same approach to investigate the impact of a CO2 and SO2-O2 mixture in a saline aquifer. They showed that the high reactivity, observed around the well zone when ancillary gases (SO2 and O2) are co-injected with CO2, leads to the dissolution of carbonates and the precipitation of sulfate minerals. Recently Amin et al. (2014) suggested through modeling that the presence of CH4 in injected CO2 inhibits dissolution of carbonate minerals in the cap rock of the Sleipner field and helps maintain the sealing capacity of the cap rock.
In this chapter we add to these existing modelling studies. Here we assess the geochemical effect of impurities on mineralogy of the P-18 depleted gas reservoir in the Netherlands offshore. We include sensitivity analyses for an extensive set of impurities, and for different impurity amounts. In contrast to previous studies, the solubility of specific amounts of co-contaminants such as CH4, O2, H2S and SO2 with CO2-in the brine were calculated using an accurate EOS for gas mixtures (Chapter 2). P-18 is an important target for CO2 storage since the ROAD project mentioned in Chapter 1 presently (November 2014) is one of the few remaining candidate European demonstration projects for industrial-scale CO2 storage under the European Energy Programme for Recovery (EEPR). The chosen mineral assemblage is based on the Hardegsen Formation, a Triassic sandstone unit which is located at approximately 3500 m depth below sea level, and the youngest member of the main Bundsandstein Subgroup.
5.2. Methods
5.2.1. General modelling approach
The model includes the following set of general processes and conditions: (1) equilibrium dissolution of the component gases of a specified impure CO2 store at a gas-brine interface; (2) diffusive transport of the gases into the brine; (3) aqueous chemistry and water-rock interactions. This system may be taken to provide an approximate representation of post-injection conditions in saline aquifers where flows of the non-aqueous phase, which tends to migrate to the top of the aquifer, and of the underlying brine, have become small and diffusive transport predominates (figure 5-1). The use of molecular diffusion as the sole transport process implies that possible free convection due to unstable density stratification of the brine as it acquires the gases (Hassanzadeh et al., 2007) is ignored. This is reasonable as long as the permeability of the aquifer is sufficiently low such that the critical Rayleigh number of the diffusive boundary layer, which determines transition to unstable conditions (Wooding et al., 1997; Post & Kooi, 2003; Slim, 2014), is not exceeded. This appears to be the case for the Hardegsen Formation, where the reported vertical permeability and formation thickness (for the P-18 field) are about 15.1 mD and 25 m, respectively (Arts et al., 2012; Tambach et al., 2015), and where
Sensitivity of the geochemical response of a saline aquifer to the presence of impurities in the stored CO2 102
the Rayleigh number is subcritical (about 7.6) when the diffusive front extends over the total thickness of the formation.
The Equation of State (EOS) presented in Chapter 2 was used for the solubility calculations of the gases. The transport and chemical reactions were modelled using PHREEQC v.2.18.0 (Parkhurst & Appelo, 1999).
Apart from the employed EOS, our approach is similar to that used in several studies of geochemical impacts of CO2 on caprock (Koenen et al., 2011; Amin et al., 2014), albeit in our application diffusive transport is considered downward instead of upward. In contrast to Knauss et al. (2005) who also used single-phase (aqueous) reactive transport modelling, we refrained from including advection (inflow) of the gases-charged brine because, apart from small-scale sinking brine plumes (Meybodi & Hassanzadeh, 2011) such conditions are unlikely to occur in actual aquifer storage projects.
Fig. 5.1: Schematic of the conceptual model; modified after Steefel et al. (2005)
5.2.2. Mineral composition and initial formation water chemistry
The mineral composition of the Hardegsen Formation at the P-18 field was adopted from Tambach et al. (2015) and is listed in Table 5.1. Anhydrite and dawsonite were defined as secondary minerals. Other carbonate and sulfur-containing minerals such as alunite, calcite and magnesite were tested as well as secondary minerals in addition to the above two, but found not to precipitate.
Table 2 lists the initial formation water chemical composition used in the modelling. This brine composition is (approximately) in thermodynamic equilibrium with the reservoir minerals and was obtained by equilibrating a 1.60 M NaCl (93.5 g/L) and pH=7 brine with the reservoir minerals over a period of 10 ky in a batch calculation with PHREEQC.
Chapter 5 103
Table 5.1: Adopted mineralogy of the Hardegsen formation and employed secondary minerals (s.m.)
Minerals volume percentage in solid
Density (gr/cm3) Molar volume (cm3/mol)
Quartz 81.8 2.65 22.690 Kaolinite 0.3 2.59 99.520 K-feldspar 6.0 2.56 108.870 Dolomite-dis 3.7 2.87 64.390 Albite 2.0 2.62 100.250 Clinochlore-14a 0.7 2.68 20.980 Illite 5.5 2.76 59.890 Dawsonite s.m. 2.43 59.300 Anhydrite s.m. 2.96 46.103
Predicted dissolution/precipitation amounts in the batch calculation were very small. Therefore, the volume fractions of the minerals shown in Table 5.2 were not modified for these changes. More details about the reactions and kinetic parameters are provided in the next section. The H+ content of the equilibrated brine (Table 5.2) corresponds to a pH of 6.126.
Table 5.2: Brine initial compositions
Components Concentrations(mol/kg water)
Cl 1.595e+00
Na 1.536e+00 2Ca 4.595e-03 2Mg 2.263e-02 24SO 3.878e-06
K 1.028e-02
2SiO (aq) 7.142e-04
3HCO 4.263e-03 3Al 8.940e-14
H 9.097e-07 23SO 1.383e-17
5.2.3. Reactions
PHREEQC is supplemented with a number of thermodynamic databases that provide equilibrium constants (Parkhurst & Appelo, 1999). Here we have used the llnl.dat thermodynamic database which has an extensive list of minerals and species. Table 5.3 lists the inhomogeneous reactions (dissolution-precipitation) that were included in the calculations.
Sensitivity of the geochemical response of a saline aquifer to the presence of impurities in the stored CO2 104
Table 5.3: The chemical kinetic reactions considered in this study
Reaction 1: Albite dissolution: + + 3
3 8 2 2NaAlSi O +4H = Na Al 2H O 3SiO (aq)
Reaction 2: K-feldspar dissolution: + +
3 8 2 2KAlSi O + 4H = K + 2H O+3SiO (aq) +Al3+
Reaction 3: Dolomite-dis dissolution 2 2
3 32CaMg CO 2H Ca Mg 2HCO
Reaction 4: Kaolinite dissolution + 3
2 2 5 4 2 2Al Si O (OH) +6 H = 5H O + 2Al +2SiO (aq)
Reaction 5: Quartz dissolution
2Quartz = SiO (aq)
Reaction 6: Illite dissolution + + 2+ 3+
2 2Illite+ 8H = 0.6K + 5H O+0.25Mg +2.3Al 3.5SiO aq
Reaction 7: Clinochlore-14A dissolution + 3 2+
5 2 3 10 2 28Mg Al Si O OH + 16H = 2 Al 12 H O +5 Mg 3SiO aq
Reaction 8: Anhydrite precipitation 2 2
4 4Ca SO CaSO
Reaction 9: Dawsonite precipitation: 3 +
3 2 3 2Al HCO Na 2H O NaAlCO (OH) +3H
The following kinetic rate law for mineral dissolution/precipitation was adopted (Lasaga et al., 1994).
1 nn n n
n
QR k T AK
(3)
where is the temperature-dependent reaction rate constant of minerals (mole/(m2s)), is the
reactive surface area (m2/kgw), Qn is the reaction quotient and Kn the equilibrium constant for the mineral-water reaction. Ideally,
nk nA
and should be determined experimentally, but since such data
are generally lacking, we take them to be unity similar to the approach in related studies (Xu et al.,
2007; Zheng et al., 2009; Xu et al., 2011). is calculated from multiplication of the specific surface
area (m2/gr), molar mass (gr/mole) and the molality (mole/kgw) for each mineral. This approach nA
Chapter 5 105
accounts for changes in reactive surface area due to changes in mineral contents during dissolution and precipitation. The Van ‘t Hoff equation was used to account for temperature dependency of the rate constants and potential pressure effects on reaction equilibria and rates were not considered. Moreover, following Palandri and Kharaka (2004) for instance, the kinetic rate constant was determined via addition of acid, base and neutral mechanisms:
25 25
25
1 1 1 1exp exp298.15 298.15
1 1exp298.15
nHnu Hn nu H
nOHOHOH OH
E Ek T k k aR T R T
Ek aR T
H
(4)
where the subscripts and OH stand for acid, neutral and base mechanisms respectively. E is
activation energy (J/mol), is the rate constant (mol/(m2 s)) at 25 ºC, R is the gas constant
(J/(mol K)), T is temperature (K), a is activity of the species and n is the power constant for the mineral (
,H nu
k 25
Xu et al., 2012).
Table 5.4: kinetic rate parameter for minerals of Hardegsen formation
(Palandri & Kharaka, 2004; Tambach et al., 2014)
K25 (mol/(m2 s)) E (kJ/mol) nminerals
Surfacearea
(cm2/gr) Acid Neutral Base Acid Neutral Base Acid Base
Quartz 9.8 - 1.2E-14 - - 87.7 - - -
Albite 9.8 6.91E 11 2.75E 13 2.51E 16 65 69.8 71 0.457 -0.572
K-feldspar 9.8 8.71E 11 3.89E 13 6.31E 22 51.7 38 94.1 0.5 -0.823
Dolomite-dis 9.8 6.46E 04 2.95E 08 - 36.1 52.2 - 0.5 -
Kaolinite 151.6 4.90E 12 6.61E 14 8.91E 18 65.9 22.2 17.9 0.777 -0.472
Illite 151.6 1.05E 11 1.66E 13 3.20E 17 23.6 35 58.9 0.34 -0.40
Clinochlore-14A 151.6 7.76E-12 3.02E-13 - 88 88 - 0.5 -
Dawsonite 9.8 6.457E-4 1.26E-9 - 36.1 62.76 - 0.5 -
Anhydrite 9.8 - 6.46e-4 - - 14.3 - - -
The kinetic parameters for the minerals were adopted from Tambach et al. (2014) and are listed in Table 5.4. In PHREEQC the activity coefficients of the aqueous species are calculated from the concentrations via the Debye–Hückel equation (Appelo & Postma, 2005). This probably overestimates the activity coefficients (e.g., Amin et al., 2014).
5.2.4. Further assumptions and model discretization
The 1-dimensional reactive transport calculations were done on a 25 m long domain. Pressure and temperature were assumed constant: 90 ºC and 250 bar, respectively. This would be reasonable ambient conditions for a saline aquifer at 2 – 2.5 km depth. Note that pressure is solely relevant for the
Sensitivity of the geochemical response of a saline aquifer to the presence of impurities in the stored CO2 106
gases solubility calculations, whereas temperature also influences the geochemical reactions. The
adopted effective diffusion coefficient for CO2 (aq), = 2.192e-9 m2/s (includes reduction of pure-
water diffusion by a factor of 3 (tortuosity of the porous medium)) was taken constant in space and time, and its value was based on an empirical relationship developed by Hassanzadeh et al. (2008) which accounts for temperature dependency. This diffusion coefficient was used for all solute species. Reduction or enhancement of diffusive transport through porosity changes by precipitation or dissolution of the solid phase was neglected. Figure 5.2 shows the computational domain was divided into 25 cells (grid spacing of 1 m). A small-size (0.1 m) ‘ghost cell’ was used to simulate the brine-gas exchange at the top boundary. This ghost cell contains brine and the dissolved gases, no minerals.
eD
Fig. 5.2: Key design aspects of the 1D-Phreeqc simulations.
This approach limits back-diffusion of ionic species from the first nominal model cell where cation concentrations can become very high due to dissolution of mineral species. Back-diffusion does occur towards the narrow ghost cell, but mass loss beyond the top boundary of that cell is prevented. The basal boundary at end of the domain is also closed to solute transport (gradients of concentrations are zero). The initial condition was assumed homogeneous for all dependent and independent variables. An initial porosity of 0.11 was used.
5.2.5. Model experiments
Table 5.5 summarizes the runs/experiments that were conducted. A pure CO2 simulation was conducted as a reference case to allow evaluation of the impact of impurities. Other runs include both binary gas mixtures with a single impurity component and multi-impurity runs with compositions that
Chapter 5 107
are representative of oxyfuel flue gas (Table 3 in Chapter 4) as well as runs with artificially enhanced amounts of SO2. Focus of the impact assessment is precipitation/dissolution of minerals and the associated change in porosity.
Table 5.5: summary of the runs/experiments that were executed in this study
Run No. CO2 SO2 H2S Ar O2 N2 CH4
1 (Pure CO2)
100% 0 0 0 0 0 0
Single mixture 2 97% 0 0 3% 0 0 0 3 97% 0 0 0 3% 0 0 4 97% 0 0 0 0 3% 0 5 97% 0 0 0 0 0 3% 6 99% 1% 0 0 0 0 0 7 98% 2% 0 0 0 0 0 8 97% 3% 0 0 0 0 0 9 96% 4% 0 0 0 0 0
10 99% 0 1% 0 0 0 0 11 97% 0 3% 0 0 0 0 12 95% 0 5% 0 0 0 0 13 93% 0 7% 0 0 0 0 14 91% 0 9% 0 0 0 0 15 90% 0 10% 0 0 0 0
Multiple Mixtures 16
(High Oxyfuel ) 90% 0 0 4.3% 1.8% 3.9% 0
17 90% +1 %a 0 4.3% 1.8% 3.9% 0 18 90% +2 % 0 4.3% 1.8% 3.9% 0 19 90% +3 % 0 4.3% 1.8% 3.9% 0 20 90% +4 % 0 4.3% 1.8% 3.9% 0 21
(Low Oxyfuel ) 98.% 0 0 0.54% 0.25% 0.47% 0
22 98.% +1% 0 0.54% 0.25% 0.47% 0 23 98.% +2% 0 0.54% 0.25% 0.47% 0 24 98.% +3% 0 0.54% 0.25% 0.47% 0 25 98.% +4% 0 0.54% 0.25% 0.47% 0
a plus symbol indicates the adding of SO2 to the Oxyfuel flue gas mixtures.
5.2.6. Porosity changes
Momentary porosity values for the PHREEQC model cells were calculated by post-processing output
values of the moles, , of all primary and secondary minerals for each cell as follows, ,i tn
Sensitivity of the geochemical response of a saline aquifer to the presence of impurities in the stored CO2 108
,11
N
i t ii
ttotal
n V
V (5)
where t is reservoir porosity at every time t. iV denotes the molar volume of mineral , N is the
number of minerals and is the volume of the cell.
i
totalV
5.3. Results
In this section, first results are presented for the default 1 m grid size simulations. Subsequently, the impact of finer discretization, time step size, and domain length influences are illustrated.
5.3.1. Impacts on pH
Brine acidification or pH reduction induced by CO2 storage is known to be an important driver of water-fluid interaction. Figure 5.2 and Table 5.6 document predicted development of pH for selected runs.
5 10 15 20 250
1
2
3
4
5
6
7
z(m)
pH
(a)
Pure CO21% SO22% SO23% SO24% SO2
5 10 15 20 250
1
2
3
4
5
6
7
z(m)
pH
(b)
Pure CO21% SO22% SO23% SO24% SO2
5 10 15 20 250
1
2
3
4
5
6
7
z(m)
pH
(c)
Pure CO21% SO22% SO23% SO24% SO2
5 10 15 20 250
1
2
3
4
5
6
7
z(m)
pH
(d)
Pure CO21% SO22% SO23% SO24% SO2
Fig. 5.2: Predicted pH distribution for pure CO2 and binary mixtures containing SO2 at (a) 100 years (b) 1,000 yrs (c) 5,000 yrs (d) 10,000 yrs.
Chapter 5 109
As may be anticipated, pH is most sensitive to presence of SO2 (figure 5.2) which produces sulfurous
acid ( ) and sulfuric acid ( ), which are involved in the following equilibria (Goldberg
1985; Knauss et al., 2005; Xu et al., 2007): 2H SO3 42H SO
2 2 3SO (aq) H O HSO H (6)
23 3HSO SO H (7)
2 2 2 4 24SO 4H O 3H SO H S (8)
The figure illustrates how the acidified zone expands into the brine. The abscissa of the x-axis (x=0) corresponds to the top of the ghost cell, so the value for the ghost cell is shown explicitly. Figure 5.2b (t = 500 yrs) indicates that the distal zone of relatively low pH reduction expands more rapidly than the more proximal zone where the diffusive transport appears inhibited by reactions.
Table 5.6: Effect of various gas compositions on pH level at t = 10,000 yrs.
x Pure CO2 10% H2S Low Oxyfuel High Oxyfuel 1% SO2
0.05 3.72683 1.78179 3.73422 3.78254 0.733263 0.5 5.34462 4.28559 5.34373 5.33927 4.60415 1.5 5.41379 4.88857 5.41525 5.42737 4.84374 2.5 5.42153 5.15607 5.42184 5.42979 5.06522 3.5 5.42062 5.5621 5.42091 5.42914 5.28648 4.5 5.41984 5.55853 5.42029 5.42973 5.4158 5.5 5.41956 5.55954 5.42024 5.43142 5.41587 6.5 5.41975 5.56361 5.4207 5.43400 5.41556 7.5 5.42036 5.56959 5.42164 5.43735 5.41624 8.5 5.42138 5.57676 5.42302 5.44138 5.41766 9.5 5.42279 5.58468 5.4248 5.44602 5.41967
10.5 5.42454 5.59304 5.42695 5.45119 5.42213 11.5 5.42661 5.60161 5.42944 5.45681 5.42493 12.5 5.42896 5.61024 5.4322 5.46282 5.42799 13.5 5.43152 5.61876 5.43519 5.4691 5.43122 14.5 5.43425 5.62705 5.43834 5.47557 5.43453 15.5 5.43707 5.63499 5.44158 5.4821 5.43784 16.5 5.43991 5.64246 5.44482 5.48858 5.44108 17.5 5.4427 5.64932 5.44799 5.49487 5.44418 18.5 5.44536 5.65547 5.451 5.50083 5.44706 19.5 5.44782 5.66081 5.45377 5.50631 5.44966 20.5 5.44999 5.66529 5.45622 5.51115 5.45192 21.5 5.45182 5.66887 5.45827 5.51521 5.45379 22.5 5.45324 5.67155 5.45987 5.51836 5.45523 23.5 5.45421 5.67334 5.46096 5.5205 5.45621 24.5 5.4547 5.67423 5.46151 5.52158 5.45671
Sensitivity of the geochemical response of a saline aquifer to the presence of impurities in the stored CO2 110
Table 5.6 shows how pH is also significantly reduced by presence of H2S and that the gases that are dominant in oxyfuel flue gas hardly affect pH. Results show that acidity is even slightly reduced by the latter impurities, which is most likely caused by the corresponding lower CO2 contents of the non-aqueous phase.
5.3.2. Impacts on mineral dissolution and precipitation
Figures 5.3, 5.5, 5.6, 5.7 and 5.8 illustrate how the initially uniform contents of the seven primary (panels a-g) and the two secondary minerals (panels h-i) are altered for the various model runs at t = 10,000 yr. For pure CO2 (black lines in the figures), the predicted geochemical response is dominated by dissolution of clinochlore and Illite and precipitation of K-feldspar and quartz. Dawsonite precipitates as a secondary mineral, thereby sequestering CO2 in carbonate, with the highest concentration (14.5 mole/kgw) occurring at or near the gas-brine interface (first model cell). Calcite is not formed (not shown), but some small precipitation of Dolomite is predicted.
5 10 15 20 250
2
4
6
8x 10 4
z(m)
M (m
ol/k
gW)
(a)Albite
Pure CO2
1% SO2
2% SO2
3% SO2
4% SO2
5 10 15 20 250
5
10
15
z(m)
M (m
ol/k
gW)
(b)Kaolinite
5 10 15 20 250
5
10
15
z(m)
M (m
ol/k
gW)
(c)K feldspar
5 10 15 20 250
2
4
6
8
z(m)
M (m
ol/k
gW)
(d)Dolomite dis
5 10 15 20 250
1
2
3
4
z(m)
M (m
ol/k
gW)
(e)Clinochlore 14A
5 10 15 20 250
5
10
15
z(m)
M (m
ol/k
gW)
(f)Illite
5 10 15 20 25
295
300
305
310
315
z(m)
M (m
ol/k
gW)
(g)Quartz
5 10 15 20 250
5
10
15
z(m)
M (m
ol/k
gW)
(h)Dawsonite
5 10 15 20 250
2
4
6
z(m)
M (m
ol/k
gW)
(i)Anhydrite
Fig. 5.3: Mineral dissolution and precipitation for mixtures containing various amounts of SO2 for 10,000 yrs.
Sulfur-dioxide. Figure 5.3 shows that presence of SO2 dissolves all of the available illite, dolomite and clinochlore near the interface, and albite further into the domain (note the small scale range for the latter mineral; the initial albite content was 1.6 mole/kgw). Where pure CO2 induces precipitation of K-feldspar near the interface, presence of SO2 causes dissolution of K-feldspar there, but precipitation of this mineral further away from the interface. Similarly, precipitation of dawsonite is suppressed near, but enhanced further away from the interface. Quartz precipitation, by contrast, is slightly enhanced.
Chapter 5 111
Relatively large amounts of kaolinite and anhydrite precipitate. A few tests have shown that the peak concentration of the precipitated K-feldspar continues to grow and moves away from the interface for longer simulation times. Analogous behavior also has been observed for dawsonite.
Figure 5.4 displays the concentrations of main cations for the runs of figure 5.3. The dissolution of illite and clinochlore-14A contributes Al3+ to the solution, which reacts with Na+ in the initial brine and dissolved CO2 to form dawsonite. For pure CO2, this is an efficient mechanism which keeps Al3+ concentrations low. With SO2, the low pH near the interface suppresses dawsonite precipitation and Al3+ is to a large extent, but not completely, removed by precipitation of kaolinite instead. The Mg2+ from dolomite and clinochlore dissolution by contrast, is retained in solution and is transported to more distal parts of the domain by diffusion (figure 5.4d). The reduced sequestration of CO2 by dawsonite appears to result in a more efficient advance of CO2 (total C) into the brine (figure 5.4f). The Ca2+ delivered by dolomite dissolution is largely removed by anhydrite precipitation and sequesters SO2.
5 10 15 20 250
1
2
3
4
5x 10 5
z(m)
M (m
ol/k
gW)
(a)Al3+
Pure CO21% SO22% SO23% SO24% SO2
5 10 15 20 250
0.1
0.2
0.3
0.4
z(m)
M (m
ol/k
gW)
(b)K+
0 5 10 15 20 250
1
2
3
4
5
6x 10 3
z(m)
M (m
ol/k
gW)
(c)Ca2+
0 5 10 15 20 250
1
2
3
4
5
6
z(m)
M (m
ol/k
gW)
(d)Mg2+
5 10 15 20 250
0.2
0.4
0.6
0.8
x(m)
M (m
ol/k
gW)
(e)Na+
5 10 15 20 250
1
2
3
4
x(m)
M (m
ol/k
gW)
(f)tot(C)
Fig. 5.4: Evolution of cations in the brine during reactions (10,000 yrs).
Hydrous-sulfide. Figure 5.5 illustrates the effect of H2S in the mixture. Comparison with Figure 3 shows that the geochemical effect of H2S is somewhat similar to that of SO2. However, smaller amounts of anhydrite, kaolinite and in particular of quartz precipitate in the H2S runs. Furthermore, albite dissolution is less than for pure CO2 and CO2-SO2 mixtures. Cation contents (not shown) also show great similarity relative to that of SO2.
Sensitivity of the geochemical response of a saline aquifer to the presence of impurities in the stored CO2 112
Oxygen, nitrogen and methane: Figure 6 shows the geochemical effect of CO2-O2, CO2-N2 and CO2-CH4 mixtures for 3% mass fraction of each impurity. Results show that these impurities have very little effect in that the predicted mineral contents hardly differ from that of pure CO2.
5 10 15 20 250
0.05
0.1
0.15
0.2
z(m)
M (m
ol/k
gW)
(a)AlbitePure CO2
1% H2S
3% H2S
5% H2S
7% H2S
9% H2S
5 10 15 20 250
2
4
6
8
z(m)
M (m
ol/k
gW)
(b)Kaolinite
0 5 10 15 20 252
4
6
8
z(m)
M (m
ol/k
gW)
(c)K feldspar
5 10 15 20 250
2
4
6
z(m)
M (m
ol/k
gW)
(d)Dolomite dis
5 10 15 20 250
1
2
3
4
z(m)
M (m
ol/k
gW)
(e)Clinochlore 14A
5 10 15 20 254
5
6
7
8
9
z(m)
M (m
ol/k
gW)
(f)Illite
5 10 15 20 25290
295
300
305
310
z(m)
M (m
ol/k
gW)
(g)Quartz
5 10 15 20 250
5
10
z(m)
M (m
ol/k
gW)
(h)Dawsonite
5 10 15 20 250
1
2
3
4
z(m)
M (m
ol/k
gW)
(i)Anhydrite
Fig. 5.5: mineral dissolution and precipitation with various values of H2S at 10,000 yrs.
0 5 10 15 20 250
0.005
0.01
0.015
z(m)
M (m
ol/k
gW)
(a)Albite
Pure CO2CH4
N2
O2
0 5 10 15 20 25
0.2
0.25
0.3
z(m)
M (m
ol/k
gW)
(b)Kaolinite
0 5 10 15 20 254
5
6
7
8
z(m)
M (m
ol/k
gW)
(c)K feldspar
0 5 10 15 20 25
4.65
4.655
4.66
4.665
z(m)
M (m
ol/k
gW)
(d)Dolomite dis
5 10 15 20 250
1
2
3
4
z(m)
M (m
ol/k
gW)
(e)Clinochlore 14A
0 5 10 15 20 252
4
6
8
10
z(m)
M (m
ol/k
gW)
(f)Illite
0 5 10 15 20 25290
300
310
320
z(m)
M (m
ol/k
gW)
(g)Quartz
0 5 10 15 20 250
5
10
15
z(m)
M (m
ol/k
gW)
(h)Dawsonite
5 10 15 20 251
0.5
0
0.5
1
z(m)
M (m
ol/k
gW)
(i)Anhydrite
Fig. 5.6: comparison of geochemical effect of impurities on minerals for 3% (mass fraction) and 10,000 yrs simulation with pure CO2
Chapter 5 113
0 5 10 15 20 250
0.005
0.01
0.015
x(m)
M (m
ol/k
gW)
(a)Albite
Pure CO2Low OxyfuelHigh Oxyfuel
0 5 10 15 20 25
0.2
0.25
0.3
x(m)
M (m
ol/k
gW)
(b)Kaolinite
Pure CO2Low OxyfuelHigh Oxyfuel
0 5 10 15 20 254
5
6
7
8
x(m)
M (m
ol/k
gW)
(c)K feldspar
Pure CO2Low OxyfuelHigh Oxyfuel
0 5 10 15 20 25
4.65
4.655
4.66
4.665
x(m)
M (m
ol/k
gW) (d) Dolomite dis
Pure CO2Low OxyfuelHigh Oxyfuel
5 10 15 20 250
1
2
3
4
x(m)
M (m
ol/k
gW)
(e)Clinochlore 14A
Pure CO2Low OxyfuelHigh Oxyfuel
0 5 10 15 20 252
4
6
8
10
x(m)
M (m
ol/k
gW)
(f)Illite
Pure CO2Low OxyfuelHigh Oxyfuel
0 5 10 15 20 25290
300
310
320
x(m)
M (m
ol/k
gW)
(g)Quartz
Pure CO2Low OxyfuelHigh Oxyfuel
0 5 10 15 20 250
5
10
15
x(m)
M (m
ol/k
gW)
(h)Dawsonite
Pure CO2Low OxyfuelHigh Oxyfuel
5 10 15 20 251
0.5
0
0.5
1
x(m)
M (m
ol/k
gW)
(i)Anhydrite
Pure CO2Low OxyfuelHigh Oxyfuel
Fig. 5.7: geochemical effects of oxyfuel flue gas on minerals in comparison with pure CO2 effect for 10,000 yrs.
0 5 10 15 20 250
0.005
0.01
0.015
x(m)
M (m
ol/k
gW)
(a)Albite
High Oxyfuel+1% SO2
+2% SO2
+3% SO2
+4% SO2
0 5 10 15 20 250
5
10
15
x(m)
M (m
ol/k
gW)
(b)Kaolinite
High Oxyfuel+1% SO2+2% SO2+3% SO2+4% SO2
0 5 10 15 20 250
5
10
15
x(m)
M (m
ol/k
gW)
(c)K feldspar
High Oxyfuel+1% SO2+2% SO2+3% SO2+4% SO2
0 5 10 15 20 250
2
4
6
8
x(m)
M (m
ol/k
gW)
(d)Dolomite dis
High Oxyfuel+1% SO2+2% SO2+3% SO2+4% SO2
5 10 15 20 250
1
2
3
4
x(m)
M (m
ol/k
gW)
(e)Clinochlore 14A
High Oxyfuel+1% SO2+2% SO2+3% SO2+4% SO2
0 5 10 15 20 250
5
10
x(m)
M (m
ol/k
gW)
(f)Illite
High Oxyfuel+1% SO2+2% SO2+3% SO2+4% SO2
0 5 10 15 20 25290
300
310
320
x(m)
M (m
ol/k
gW)
(g)Quartz
High Oxyfuel+1% SO2+2% SO2+3% SO2+4% SO2
0 5 10 15 20 250
5
10
15
x(m)
M (m
ol/k
gW)
(h)Dawsonite
High Oxyfuel+1% SO2+2% SO2+3% SO2+4% SO2
0 5 10 15 20 250
2
4
6
x(m)
M (m
ol/k
gW)
(i)Anhydrite
High Oxyfuel+1% SO2+2% SO2+3% SO2+4% SO2
Fig. 5.8: The impact of high oxyfuel flue gas with added SO2 on minerals after 10,000 yrs.
Sensitivity of the geochemical response of a saline aquifer to the presence of impurities in the stored CO2 114
Oxyfuel flue gas: Figure 5.7 displays results for the high and low impurity oxyfuel flue gas compositions (Table 4.3). Similar to nitrogen, oxygen and methane, geochemical impacts are minor relative to pure CO2. The greater impact for the high impurity run is consistent with the inferred pH behaviour illustrated in Table 5.4; that is, the brine acidity is suppressed by increasing amounts of the impurities.
Oxyfuel flue gas with artificially enhanced sulfur-dioxide: In the Chapter 4 it was found that addition of SO2 to oxyfuel flue gas can compensate for the negative storage capacity impacts of the dominant O2, N2 and Ar co-contaminants. Figure 8 shows that admixed SO2 dictates the geochemical response; even 1% SO2 yields a response that is virtually indistinguishable from that of binary CO2-SO2 mixture with this sulfur-dioxide content.
5.3.3. Impacts on porosity
The predicted porosity distribution at t = 10,000 yrs for several model runs is presented in Figure 5.9. For pure CO2, the reservoir porosity is reduced dramatically near the interface by quartz and dawsonite precipitation to a minimum porosity of about 0.0002. The relatively inert impurities (O2, N2, CH4) evidently hardly change this pattern (figure 5.9d).
5 10 15 20 250
0.05
0.1
0.15
x(m)
φ
(a)
φiPure CO21% SO22% SO23% SO24% SO2
5 10 15 20 250
0.05
0.1
0.15
x(m)
φ
(b)
φiPure CO21% H2S3% H2S5% H2S7% H2S9% H2S
5 10 15 20 250
0.05
0.1
0.15
x(m)
φ
(c)
φiHigh oxyfuel+1% SO2+2% SO2+3% SO2+4% SO2
5 10 15 20 250
0.05
0.1
0.15
x(m)
φ
(d)
φiPure CO23% N23% O23% CH43% H2S3% SO2
Fig. 5.9: porosity changes comparison of impure CO2 with pure CO2 at 10,000 yrs.
Figure 5.9b shows that presence of H2S, can partly compensate for the porosity reduction caused by CO2 and that this effect increases with increasing impurity content. SO2 alters the available pore space by enhancing porosity near, and reducing porosity some distance away from the gas-brine interface
Chapter 5 115
(figure 5.9a, c). The porosity reduction is primarily caused by the precipitation of anhydrite. Where porosity reduction may be a desirable impact for caprocks where it can improve sealing security, it should be considered a negative influence on reservoirs as it would slow down both the gas dissolution and the mineral trapping of the CO2 and the associated gases. For all runs, a porosity increase is predicted at relatively large distance from the gas-brine interface. Theoretically, this might reduce the mechanical strength of the rock framework and cause compaction. However, the predicted porosity increase by dissolution of minerals is rather small in the simulations.
5.3.4. Grid convergence and domain size influences
For pure CO2, the model was also run for a finer spatial and temporal discretization; both the grid size and time step were halved (0.5 m and 50 yrs), and results compared to that of the original run. Essentially identical results were obtained (figure 5.10). This provides some assurance that potential inaccuracies associated with discretization are relatively small (Appelo & Postma, 2005).
5 10 15 20 255.2
5.4pHfine grid
coarse grid
0 5 10 15 20 25
3.54
4.5
x 10 8
Al3+
0 5 10 15 20 250
2
4x 10 5
Ca2+
0 5 10 15 20 250.5
1
1.5Mg2+
0 5 10 15 20 250
0.5
1Na+
0 5 10 15 20 250.04
0.05
0.06K+
0 5 10 15 20 250
1
2C
5 10 15 20 25
0.2
0.4 Kaolinite
0 5 10 15 20 254
6
8K feldspar
0 5 10 15 20 250
0.5
1x 10 3
Albite
M (m
ol/k
gw)
5 10 15 20 250
5
10 Illite
0 5 10 15 20 254.6
4.65
4.7Dolomite dis
5 10 15 20 250
5Clinochlore 14A
z(m)0 5 10 15 20 25
0
10
20Dawsonite
z(m)0 5 10 15 20 25
280
300
320Quartz
z(m)
Fig. 5.10: comparison between fine grid and coarse grid affects on minerals and cations after 10,000 yrs for pure CO2.
Figure 5.11 demonstrates how a larger domain (50 m) affects the predicted aqueous cation concentrations and mineral contents. It shows that the location of the adopted zero diffusion boundary at the base of reservoir model has very little effect on the mineral contents, but does change the cation amounts. The concentrations of most cations (Na+, Ca2+ and Al3+) are enhanced at the base of the formation (~25 m) for the larger domain. This is probably due to back diffusion from depths >25 m. Conversely, the concentration of Mg2+ and K+ are reduced because these species can diffuse down to
Sensitivity of the geochemical response of a saline aquifer to the presence of impurities in the stored CO2 116
greater depths. Perhaps more importantly however, the domain size has very little influence on predicted porosity (maximum difference is 1.42E-3).
0 10 20 30 40 505
6
7pH50 m
25 m
0 10 20 30 40 500
1
2x 10
Al3+
0 10 20 30 40 500
2
4x 10
Ca2+
0 10 20 30 40 500
1
2Mg2+
M (m
ol/k
gw) 0 10 20 30 40 50
0
1
2Na+
0 10 20 30 40 500
0.05
0.1K+
0 10 20 30 40 500
1
2C
0 10 20 30 40 500
0.2
0.4Kaolinite
0 10 20 30 40 504
6
8K feldspar
0 10 20 30 40 500
1
2Albite
10 20 30 40 500
5
10 Illite
0 10 20 30 40 504.6
4.65
4.7Dolomite dis
0 10 20 30 40 500
2
4Clinochlore 14A
z(m)0 10 20 30 40 50
0
10
20Dawsonite
z(m)0 10 20 30 40 50
280
300
320Quartz
z(m)
Fig. 5.11: comparison between large domain (50 m) and small domain (25 m) after 10,000 yrs for pure CO2.
5.4. Discussion and Conclusions
5.4.1. Summary of the geochemical impacts
The geochemical response to impure CO2 storage was studied for a fictitious aquifer with a porosity and mineral composition representative of the Triassic Hardegsen Formation in the Dutch offshore at the P18 gas field. The following was found (mainly referring to conditions after 10,000 yr):
Irrespective of the gas composition, a very large porosity reduction is predicted up to about 10 m from the presumed stable gas-brine interface and a slight porosity increase at larger distances.
For pure CO2, the geochemical response is dominated by dissolution of clinochlore and illite and precipitation of K-feldspar and quartz. Dawsonite precipitates as a secondary mineral, thereby sequestering CO2 in carbonate, with the strongest precipitation occurring at or near the presumed stationary gas-brine interface. Minor precipitation of dolomite is predicted. The large amounts of precipitated quartz and dawsonite reduce the original reservoir porosity (0.11) to virtually zero (0.0002) at the interface after 10,000 yrs.
Presence of O2, N2, Ar or combinations thereof, such as in oxyfuel flue gas, and presence of CH4 have very little effect on the geochemical response.
Presence of SO2 induces complex changes: 1. Comprehensive dissolution of illite, dolomite, K-feldspar, clinochlore, and albite near the interface. 2. Dissolution of albite further from the interface. 3.
Chapter 5 117
Suppression of dawsonite precipitation and mild reinforcement of quartz precipitation near the interface. 4. Precipitation of kaolinite and anhydrite near, and anhydrite and dawsonite some distance from the interface. SO2 enhances porosity near (to 0.03 for 4% SO2), and reduces porosity dramatically some distance away from the interface, where the porosity reduction is primarily caused by precipitation of anhydrite.
The geochemical effect of H2S shows similarities with that of SO2, but with smaller magnitude and impacts only become significant for large mass fractions > 3%.
5.4.2. Possible significance of the predicted impacts
The large porosity reduction (clogging) predicted for the present set of models in a zone up to about 5 m from the gas-brine interface should be expected to reduce the diffusive mobility of the aqueous species in that zone. This might hinder the dissolution of the gases and their transfer further into the aquifer. Although significant mineral trapping by carbonate and sulfate precipitation clearly occurs near the gas-brine interface, the reduced rate of gas transfer through the aquifer may have important implications for the time scale of overall solubility and mineral trapping of the total volume of gas stored. The model results suggest that small amounts of H2S and SO2 could be favorable to prevent total clogging of pore space for the studied mineral assemblage. For all runs, a porosity increase is predicted at relatively large distance from the gas-brine interface. Theoretically, this might reduce the mechanical strength of the rock framework and cause compaction. However, the predicted porosity increase by dissolution of minerals is rather small in the simulations.
Overall, it can be concluded that co-injection of O2, N2, CH4 and small amounts of H2S and SO2 with CO2 does not have significant negative consequences and could be of interest to reduce CO2 purification costs.
It is important to note, however, that it cannot be ruled out that these findings are sensitive to uncertainties or errors in the values of the very large set of parameters in the employed llnl.dat thermodynamic database, or that some relevant chemical processes were not included in the present simulations. Experimental studies would be required to gain confidence in the validity of the inferred impacts. And finally, the predicted behaviors are expected to be rather sensitive to the primary mineral assemblage and their individual contents. For example, as shown by Jung et al. (2013) and Renard et al. (2014), presence of sulfide minerals may cause a markedly different response to presence of O2.
Sensitivity of the geochemical response of a saline aquifer to the presence of impurities in the stored CO2 118
Chapter 6
Summary
Chapter 6 121
6.1 Summary and conclusions
Source gases that are used in subsurface CO2 sequestration such as flue gas of power plants and acid gas as a waste product of oil production, do not consist of pure CO2, but contain additional gases. Removal of these ‘impurities’ is a rather costly element in the chain of steps that are required to store CO2 in the subsurface. Apart from these impurities, the CO2 that is injected in subsurface also encounters ambient (non-CO2) gases that exist in the storage reservoir.
In this thesis research is presented that addresses the impacts of impure gas compositions for the storage of CO2 in depleted hydrocarbon reservoirs and saline aquifers. In general these impacts can be divided into two main categories: physical and chemical. Physical effects concern conditions and processes such as phase behaviour, storage capacity, wellbore injectivity, permeation flux, buoyancy, etc. Chemical effects include rock-water (geochemical) reactions, caprock integrity, corrosion of well materials, hazardousness in the event of leakage, etc. Although the work presented in this thesis is far from exhaustive on all of these potential impacts, results include both novel tools to address such impacts and new insights into a number of physical and chemical effects of impurities.
Chapter 1 introduces the principle of Carbon Capture, transport and Storage (CCS) as one of the methods to reduce the CO2 of industrial sources to the atmosphere that are invoked to mitigate climate warming associated with the ‘greenhouse effect’ of this gas. Additionally, the present use of CCS for storage in depleted hydrocarbon reservoirs and saline aquifers around the globe and in the Netherlands is elucidated in this chapter, and the aims and foci of the present research are specified.
The conclusions of each chapter are summarized as follows:
In chapter 2 a new non-iterative and accurate EOS has been presented (fully documented) for gas mixtures in equilibrium with brine. The EOS allows calculation of the composition of the gas mixtures in both the aqueous and the non-aqueous phase for a large range of pressure (1-600 bar), temperature (1- 110 ºC) and salinity conditions (up to 6 M). The gas mixtures can include CO2, SO2, H2S, CH4, O2 and N2 (gases that occur in flue gases, in acid gas, or in-situ in a gas reservoir). In the model, the Peng–Robinson EOS is used to calculate the fugacity of the gas phase, but it can be easily modified to include another cubic EOS such as SRK. The model has been shown to perform favorably with respect to existing EOS’s and experimental data for single gas systems, and it accurately reproduces available data sets for gas mixtures. Predictions with this model show that the amount of dissolved CO2 is most sensitive (negatively) to CH4. Presence of SO2, by contrast, can enhance the amount of dissolved CO2.
In chapter 3, first methods were developed to calculate transport properties such as density, heat capacity and viscosity of both aqueous and non-aqueous phases for single gases and gas mixtures. Then, as one of the physical effects of impurities, the Joule-Thomson Cooling (JTC) effect in depleted hydrocarbon reservoirs was studied by using coupled heat and mass transport modeling with accurate pressure-, temperature-, and gas-compositional dependency of the thermo-physical transport properties. Injection of pure CO2 causes JTC-cooling (due to expansion of the gas) as it spreads into the reservoir. It was found that presence of gases other
Summary 122
than CO2 (impurities) affect both the spatial extent of the zone around the well bore in which this cooling occurs and the magnitude of cooling. These two effects are predominantly controlled by the specific heat capacity and the density of the gas mixture, respectively. SO2
can expand the zone of cooling, O2, N2, and CH4 can contract this zone, and H2S has a very small influence on the spatial extent of cooling. However, the operational conditions of gas injection can play an important role in these behaviours. Enhanced cooling (up to 5 ºC) is caused by O2, N2, and CH4 in combination with constant pressure injection, while for constant rate injection cooling enhancement is minimal or absent. However, the thermal risks associated with co-injection of these impurities for hydrate formation (this might clog pores and potentially impair injectivity) appear small. Co-injection of SO2 has beneficial thermal consequences by suppressing JTC.
In chapter 4, the sensitivity of the CO2 storage capacity (STC) to the presence of impurities (H2S, CH4, O2, N2, Ar and SO2) was investigated for both solubility trapping (in the aqueous phase) (STCS) and volumetric trapping (in the non-aqueous phase) (STCV). It was found that binary mixtures of CO2-SO2 exhibit anomalous storage effects when compared to other common impurities; while other gases reduce CO2 storage in the aqueous and non-aqueous phase, SO2 can increase both forms of CO2 storage. SO2 enhances CO2 volumetric trapping significantly for relatively low temperatures that are representative for shallow (< 1 km) aquifers, and in deeper depleted hydrocarbon reservoirs during the injection stage. Solubility trapping, by contrast, is mostly enhanced by SO2 for relatively high pressures (deep aquifers), while at pressures larger than 100 bar it is relatively insensitive to temperature. Presence of SO2 is further expected to enhance the gas dissolution rates (transfer from non-aqueous to the aqueous phase) due to its marked influence on brine density and free convection. For multi-component impurity mixtures such as oxyfuel flue gas, addition of SO2 can compensate for the negative impact of the other impurities. These findings suggest that the positive effects of SO2
on the CO2 storage capacity could be of practical significance for CCS projects.
In chapter 5, the new EOS (Chapter 2) was used in conjunction with the geochemical modelling code PHREEQC to study the long-term geochemical impacts of impure CO2
storage in a saline aquifer. The 1D model simulates the dissolution of the component gases of an impure CO2 store at a gas-brine interface, and subsequent diffusive transport of the gases into the brine together with the associated aqueous and water-rock interactions. This system provides an approximate representation of post-injection conditions where flows of the non-aqueous phase and the brine have become small and diffusive transport predominates. The mineralogy of the Triassic Hardegsen Formation at the P-18 gas-field in the Dutch offshore was used for the mineralogy of the aquifer storage simulations (it is important to emphasize that these simulations are not representative for CO2 storage in depleted gas fields like P-18). After 10,000 yr, irrespective of the gas composition, very large porosity reduction is predicted up to about 10 m from the gas-brine interface and a slight porosity increase at larger distances. For pure CO2, the original reservoir porosity (0.11) is reduced to virtually zero (0.0002) at the interface by precipitation of quartz and large amounts of dawsonite. Presence of O2, N2, Ar or
Chapter 6 123
combinations thereof, such as in oxyfuel flue gas, and presence of CH4 have very little effect on the geochemical response. Presence of SO2 induces complex changes, including a strong reduction or absence of dawsonite precipitation near the interface, precipitation of kaolinite and anhydrite near the interface, and anhydrite and dawsonite precipitation some distance (~5m) from the interface. Porosity is enhanced near (to 0.03 for 4% SO2), but strongly reduced away from the interface mainly due to anhydrite precipitation. The geochemical effect of H2Sshows similarities with that of SO2, but with smaller magnitude and impacts only become significant for large mass fractions > 3%. However, the predicted behaviors are expected to be rather sensitive to the primary mineral assemblage and their individual contents and, therefore, do not have broad applicability to aquifers with other geochemical compositions.
6.2. Recommendations
A recurring feature in the chapters of this thesis is the paucity of experimental data for gas mixtures and for some of the impurity gases. In Chapter 2 for instance, the lack of solubility data of SO2 in water and brine and for the water-content of the SO2-rich phase for relevant pressures and temperatures was highlighted. Similarly, limited data for H2S at pressures in excess of 200 bar and the overall paucity of experimental data on solubility and water content of gas mixtures was documented. This implies that EOS’s that are essential for impurity-impact assessments, such as the one developed in this work, remain relatively poorly constrained for important ranges of PT-conditions. Additionally, more experimental data for transport properties (density, heat capacity, viscosity) of both aqueous and non-aqueous phase gas mixtures are needed (Chapter 3) to improve the accuracy and reliability of predictions of reservoir behavior and of related parameters such as the CO2 storage capacity of aquifers and depleted hydrocarbon reservoirs (Chapter 4). The fact that the methods/models developed in this thesis are fully documented allows for efficient updates of the models when relative new data become available in the coming years.
For CO2 storage in very deep aquifers or hydrocarbon reservoirs with ambient temperatures in excess of 110 ºC the EOS developed in this thesis may not be sufficiently accurate. This is due to model parameterization rather than lack of data. It would, therefore, be worthwhile to adjust the EOS to also allow usage at these higher temperatures.
Since reliable EOS’s for the extensive set of gas mixtures and brine considered in this study were not available through conventional, advanced reservoir simulators, and coupling of the newly developed EOS to such simulators is a laborious task, analyses involving transport processes have remained relatively simple in the work presented in this thesis (Chapters 3 and 5) and many opportunities remain to expand modeling capabilities and impact assessment. An obvious advance would be to allow multi-dimensional (2D/3D) simulations. This would be particularly relevant for coupling with buoyancy-driven flows in aquifer storage and to assess the role of reservoir heterogeneity. Important therein is accurate compositional simulation; that is, multi-phase transport of multi-component mixtures. This requires a great deal of attention to ensure consistent partitioning of the multiple gas species and water among the aqueous and non-aqueous phases during transport. Preferential transfer of individual
Summary 124
component gases between aqueous and non-aqueous phase due to the different solubilities of the component gases should allow continuous adjustment of the gas composition of both phases which, in turn, feeds back to transport. The simulations of Joule-Thomson cooling presented in Chapter 3, for instance, were conducted for an invariant gas composition and absence of water. It would be of great value to know to what extent compositional simulation, including development of a dry-out zone around the well bore, would modify the predicted reservoir thermal response.
In recent years there has been considerable attention for the role of free convection as a factor which enhances the rate at which CO2 stored in aquifers is dissolved in the brine. In Chapter 4 it was shown that the density of brine at the gas-brine interface in aquifers is very sensitive to the presence of some impurities, and in particular SO2. This shows that impurities may have an important effect on the timescale at which the injected gas becomes trapped in the aquifer brine and subsequently in secondary minerals.
In closing, the work presented in this thesis has highlighted that impurities can have both positive and negative consequences for CO2 storage. Most impurities (N2, O2, CH4 and Ar) have a number of negative physical impacts. They tend to enhance Joule-Thomson cooling and reduce the CO2 storage capacity. H2S can have variable physical consequences depending on the impurity amount, and reservoir and operational conditions. Sulfur dioxide (SO2), by contrast, was generally found to have positive consequences both for Joule-Thomson cooling and CO2 storage. For the aquifer mineralogy adopted in the geochemical impact investigation in this thesis (Chapter 5), no clear negative impacts of presence of impurities were deduced. Overall, these results show that under favorable conditions, storage of impure CO2 may be a viable option to reduce the overall costs of reservoir storage of CO2
through savings in purification of source gases.
Chapter 7
Samenvatting
Chapter 7 127
Fysische en chemische gevolgen van onzuiverheid van de gassamenstelling voor de berging van CO2 in uitgeputte olie- en gas-reservoirs en in zoute watervoerende lagen.
7.1 Conclusies
Afvalgassen die worden aangewend als bron voor het ondergronds bergen van CO2, zoals rookgas van energiecentrales en ‘acid gas’ als bijproduct van oliewinning, bevatten naast CO2 ook andere gassen. Het verwijderen deze ‘onzuiverheden’ is een bijzonder grote kostenpost in de keten van stappen die nodig is om CO2 ondergronds te bergen. Daarnaast komt het geïnjecteerde CO2 in de ondergrond in aanraking met reeds aanwezige (niet-CO2) gassen.
In dit proefschrift wordt onderzoek gepresenteerd naar de gevolgen van onzuiverheid van de gassamenstelling voor de CO2 berging in uitgeputte olie- en gas-reservoirs en in zoute watervoerende lagen. In het algemeen kunnen fysische en chemische consequenties worden onderscheiden. Fysische gevolgen hebben betrekking op condities en processen als de bergingscapaciteit van het opslagreservoir, het fase gedrag en de injecteerbaarheid van het gas, en het opdrijvend vermogen ervan. Chemische effecten omvatten gesteente-water (geochemische) reacties en corrosie van putmaterialen, effecten die bijzonder relevant zijn voor de veiligheid van opslag. De resultaten die worden gepresenteerd in dit proefschrift behelzen zowel nieuwe gereedschappen die het mogelijk maken om fysische en chemische gevolgen van onzuiver CO2 te onderzoeken via computersimulatie als nieuwe inzichten in een aantal geselecteerde specifieke gevolgen.
In hoofdstuk 1 wordt het principe van CO2 afvang, transport en berging (Eng.: Carbon Capture and Storage; afgekort: CCS) kort beschreven als één van de methoden om de CO2 uitstoot van industriële bronnen naar de atmosfeer te reduceren in het kader van het tegengaan of verminderen van klimaatverandering door het broeikaseffect. Ook wordt het huidige gebruik van ondergrondse CO2
berging in uitgeputte olie- en gas-reservoirs en in zoute watervoerende pakketten, wereldwijd en in Nederland, kort toegelicht. Verder worden de doelstellingen van het onderzoek gespecificeerd.
De bevindingen van het onderzoek kunnen als volgt worden samengevat:
In hoofdstuk 2 wordt een nieuw ontwikkelde, non-iteratieve toestandsvergelijking (Eng: EOS) gepresenteerd voor de beschrijving van het evenwicht tussen gas mengsels en brijn. De EOS kwantificeert de verdeling van de gascomponenten over de water fase (brijn) en de gas fase (Eng: non-aqueous phase) voor een groot bereik van druk (1-600 bar), temperatuur (1- 110 ºC) en zoutgehalte (tot 6 M). De gas mengsels kunnen bestaan uit CO2, SO2, H2S, CH4, O2
en N2 (componenten die voorkomen in rookgassen, ‘acid gas’ en in-situ in het reservoir). In het model wordt de Peng–Robinson EOS gebruikt voor de berekening van de ‘fugacity’ van de gas fase. Het model kan echter makkelijk worden aangepast voor gebruik met een andere kubische EOS als SRK. Er wordt getoond dat het model goede overeenstemming vertoont met bestaande modellen en experimentele data voor enkelvoudige (pure) gas-brijn systemen, en dat het beschikbare datasets voor gas mengsels nauwkeurig reproduceert. Het model laat zien dat de hoeveelheid opgelost CO2 het meest gevoelig is (in negatieve zin) voor de
Samenvatting 128
aanwezigheid van CH4. SO2 daarentegen kan de hoeveelheid opgelost CO2 juist doen toenemen.
In hoofdstuk 3 worden eerst methoden beschreven die werden ontwikkeld voor de berekening van transporteigenschappen (zowel voor enkelvoudige gassen als voor gas mengsels) van de water- en de gas fase, zoals dichtheid, warmte capaciteit en viscositeit. Vervolgens worden resultaten gepresenteerd van een studie naar de invloed van onzuiverheid van het CO2 op het Joule-Thomson (JT) effect in uitgeputte olie- of gasreservoirs middels simulatie van gekoppeld stof- en warmtetransport met nauwkeurige druk-, temperatuur-, en gas-compositie-afhankelijkheid van de thermofysische transporteigenschappen. Injectie van pure CO2
veroorzaakt JT-afkoeling door expansie van het gas tijdens het verspreiden ervan in het reservoir. Aanwezigheid van andere gassen (onzuiverheden) beïnvloeden zowel de breedte van de zone rond de injectieput waarbinnen de afkoeling optreedt als de mate van afkoeling. Deze twee effecten worden hoofdzakelijk bepaald door respectievelijk de soortelijke warmte en de dichtheid van het gas mengsel. SO2 kan de zone van afkoeling verbreden, O2, N2, en CH4
kunnen deze versmallen, en H2S heeft weinig invloed op de breedte van de afkoelingszone. De operationele condities van gasinjectie spelen echter ook een belangrijke rol bij deze effecten. Bij opslag onder constante injectiedruk wordt versterkte afkoeling (tot 5 ºC) geïnduceerd door aanwezigheid van O2, N2, and CH4, terwijl bij constant injectiedebiet niet of nauwelijks versterking van afkoeling optreedt door deze gassen. De thermische risico’s van co-injectie van deze onzuiverheden op gashydraat vorming (dit zou poriën kunnen verstoppen en de injecteerbaarheid negatief kunnen beïnvloeden) lijken klein. Co-injectie van SO2 heeft positieve thermische effecten doordat het JT-afkoeling onderdrukt.
In hoofdstuk 4 wordt de gevoeligheid van de CO2 bergingscapaciteit (STC) voor aanwezigheid van onzuiverheden (H2S, CH4, O2, N2, Ar and SO2) onderzocht. De invloed op oplosbaarheidsberging (Eng: solubility trapping; STCS) en volumetrische berging (Eng: volumetric trapping; STCV) zijn daarbij apart gekwantificeerd. Resultaten laten zien dat binaire mengsels van CO2-SO2 afwijkend gedrag vertonen in vergelijking met binaire mengsels met andere onzuiverheden; waar die andere onzuiverheden STCS en STCV verlagen, kan SO2 beide vormen van CO2-berging juist verhogen. SO2 versterkt de volumetrische berging van CO2 in sterke mate bij relatief lage temperaturen die representatief zijn voor ondiepe (< 1 km) watervoerende lagen, en voor dieper gelegen koolwaterstofreservoirs gedurende de injectie fase. Oplosbaarheidsberging van CO2
daarentegen wordt vooral versterkt door SO2 bij relief hoge druk (diepe watervoerende pakketten), waarbij het voor drukken hoger dan 100 bar de gevoeligheid voor temperatuur gering is. Vermoed wordt dat SO2 tevens de snelheid van gasoverdracht naar de water fase (het oplossen van het gas) positief beïnvloedt door de sterke invloed van dit gas op de dichtheid van het aanwezige brijn, wat vrij convectie kan induceren. Voor meervoudig onzuivere mengsels zoals oxyfuel rookgas, kan toevoeging van SO2 compenseren voor de negatieve bergingsinvloeden van de aanwezige onzuiverheden. Deze bevindingen suggereren
Chapter 7 129
dat de positieve effecten SO2 op de CO2 bergingscapaciteit van praktisch nut kunnen zijn voor CCS projecten.
In hoofdstuk 5 is de nieuwe toestandsvergelijking (EOS hoofdstuk 2) toegepast in combinatie met het geochemische simulatiepakket PHREEQC om geochemische gevolgen van berging van onzuiver CO2 in een zout watervoerend pakket te bestuderen. De 1D modelberekeningen simuleren het oplossen van de gascomponenten van een onzuivere CO2 voorraad op een gas-brijn grensvlak, en het daaropvolgende transport van deze opgeloste gassen via diffusie, terwijl tegelijkertijd aquatische en water-gesteente reacties plaatsvinden. Dit systeem wordt verondersteld bij benadering de post-injectie omstandigheden te representeren waarin transport van zowel de gas fase als het brijn gering is en diffusief transport de overhand heeft. In de simulaties is de mineraalsamenstelling van de Triassische Hardegsen Formatie van het P-18 gas-veld in het Nederlandse deel van de Noordzee gebruikt (het is belangrijk om te benadrukken dat de resultaten van de simulaties daarmee niet van toepassing zijn op CO2
berging in gasvelden zoals P-18). Na 10.000 jaar gesimuleerde tijd tonen de berekeningen een zeer sterke porositeitsafname tot zo’n 10 m afstand van het gas-brijn grensvlak en een geringe porositeitstoename op grotere afstand, ongeacht de gassamenstelling. Voor zuiver CO2 wordt de oorspronkelijke reservoir porositeit (0.11) gereduceerd tot vrijwel nul (0.0002) bij het grensvlak door neerslag van kwarts en grote hoeveelheden dawsoniet. Aanwezigheid van O2,N2, Ar, of combinaties daarvan, zoals in oxyfuel rookgas, en aanwezigheid van CH4, hebben een bijzonder geringe invloed op dit geochemische systeem. Aanwezigheid van SO2 induceert complexe veranderingen, waaronder een sterke afname of afwezigheid van dawsoniet neerslag bij het grensvlak, neerslag van kaoliniet en anhydriet bij het grensvlak, en anhydriet en dawsoniet neerslag wat verder (~5m) van het grensvlak. In vergelijking met zuiver CO2 is de porositeit iets hoger (tot 0.03 voor 4% SO2), maar daarentegen sterk verminderd verder weg van het grensvlak door anhydriet neerslag. De geochemische effecten van H2S tonen overeenkomsten met die van SO2, maar met kleinere magnitude; de gevolgen zijn alleen significant bij grote massa fracties van dit gas (> 3%). De voorspelde gevolgen zijn waarschijnlijk erg gevoelig voor de samenstelling van de primaire mineralen en de individuele hoeveelheden van deze mineralen en zullen daarom niet breed toepasbaar zijn op watervoerende pakketten met een ander geochemische samenstelling.
7.2. Aanbevelingen
Een thema dat regelmatig terugkomt in de hoofdstukken van dit proefschrift is gebrek aan experimentele data voor gas mengsels and voor sommige individuele gassen. In hoofdstuk 2 bijvoorbeeld, wordt het gebrek aan data voor de oplosbaarheid van SO2 in water and brijn, en voor het watergehalte van de SO2-rijke gas fase voor relevante drukken en temperaturen naar voren gebracht. Daarnaast wordt de beperktheid van data voor H2S voor drukken hoger dan 200 bar en de algemene schaarste van experimentele gegevens over de oplosbaarheid van en het watergehalte van gas mengels gedocumenteerd. Dat heeft tot gevolg dat toestandsvergelijkingen die essentieel zijn voor
Samenvatting 130
gevoeligheidsstudies van de gevolgen van bijgemengde gassen, zoals de EOS die is ontwikkeld in het huidige onderzoek, op dit moment relatief slecht getoetst/afgepaald zijn voor een belangrijk bereik van PT-condities. Daarnaast zijn meer experimentele data nodig voor transporteigenschappen (dichtheid, warmtecapaciteit, viscositeit) van zowel de water fase en de gas fase voor gas mengsels in conact met brijn (hoofdstuk 3) om de nauwkeurigheid en betrouwbaarheid te verbeteren van voorspellingen van de processen bergingsreservoirs en van gerelateerde parameters zoals de CO2-bergingscapaciteit van aquifers en uitgeputte olie- en gasreservoirs (hoofdstuk 4). Het feit dat de methodes/modellen die zijn ontwikkeld in dit proefschrift volledig zijn beschreven maakt het mogelijk om efficiënt aanpassingen te plegen wanneer nieuwe gegevens beschikbaar worden in de komende jaren.
De EOS die is gepresenteerd in dit proefschrift is mogelijk niet voldoende nauwkeurig voor berekeningen aan CO2 berging in erg diepe watervoerende lagen of koolwaterstofreservoirs met temperaturen die hoger zijn dan 110 ºC. Dit wordt niet zozeer veroorzaakt door gebrek aan data als door de manier waarop het model is geparameteriseerd/opgezet. Het zou derhalve de moeite waard zijn om de huidige EOS aan te passen om gebruik voor deze hoger temperaturen mogelijk te maken.
Omdat nauwkeurige toestandsvergelijkingen voor de uitgebreide set van gas mengsels en brijn die in beschouwing zijn genomen in deze studie niet beschikbaar waren via conventionele, geavanceerde reservoir simulatoren, en het koppelen van de nieuw ontwikkelde EOS met zulke simulatoren een erg arbeidsintensieve taak is, zijn de analyses waarin transportprocessen zijn opgenomen in dit proefschrift relatief simpel gebleven (hoofdstukken 3 en 5) en zijn er uitgebreide mogelijkheden om op het huidige onderzoek voort te bouwen. Een evidente uitbreidingsmogelijkheid betreft meer-dimensionale (2D/3D) simulaties. Dit zou met name relevant en nodig zijn voor de koppeling met dichtheidsgedreven bij de berging in aquifers en voor onderzoek naar de betekenis van de heterogeniteit van het opslagreservoir. Belangrijk daarbij is nauwkeurige simulatie van de (veranderende) samenstelling van de multi-component mengsels gedurende het meer-fase transport. Dit vergt speciale aandacht voor consistente herverdeling van de verschillende gas componenten en van het water over de water fase en de gas fase gedurende het transport. Preferente overdracht van individuele gas componenten tussen de verschillende fases door de verschillen in oplosbaarheid van de gas componenten moet de continue aanpassing van de gassamenstelling van beide fases bewerkstelligen, wat op zijn beurt weer terugkoppelt naar het transport. De simulaties van Joule-Thomson afkoeling gepresenteerd in hoofdstuk 3 bijvoorbeeld, betreffen berekeningen voor een invariante gassamenstelling en een afwezigheid van water. Het zou van grote waarde zijn om te weten in hoeverre ‘compositionele simulatie’, inclusief de ontwikkeling van een uitdrogingszone rond de injectieput, de gesimuleerde thermische respons zou veranderen.
Recentelijk is er ruim aandacht geweest voor de rol van vrije convectie als factor die de snelheid vergroot waarmee CO2 dat wordt ingebracht in aquifers oplost in het aanwezige brijn. In hoofdstuk 4 is getoond dat de dichtheid van brijn op het brijn-gas grensvlak in watervoerende pakketten erg gevoelig is voor de aanwezigheid van sommige gassen, met name SO2. Dit geeft aan dat deze onzuiverheden van het CO2 van grote invloed zouden kunnen zijn voor de tijdschaal waarop het geïnjecteerde gas wordt gevangen in de water fase en vervolgens in secundaire mineralen.
Chapter 7 131
Het werk gepresenteerd in dit proefschrift heeft, tot slot, voor het voetlicht gebracht dat onzuiverheden van het ingebrachte gas zowel negatieve als positieve consequenties kunnen hebben voor ondergrondse CO2 berging. De meeste onzuiverheden (N2, O2, CH4 and Ar) hebben een aantal negatieve implicaties. Ze hebben de tendens om Joule-Thomson afkoeling te versterken en de CO2-bergingscapaciteit te reduceren. H2S heeft meer wisselende fysische gevolgen afhankelijk van de onzuiverheidsfractie, van reservoir condities, en van operationele condities waaronder het gas wordt ingebracht. Voor zwaveldioxide (SO2), daarentegen, zijn over het algemeen positieve effecten gevonden, zowel voor wat betreft het Joule-Thomson effect als voor de CO2-opslagcapaciteit. Voor de mineraalsamenstelling van het aquifer die is gebruikt in de geochemische impact studie (hoofdstuk 5) zijn geen duidelijke negatieve gevolgen van onzuiverheden gevonden. Samengenomen geven deze bevindingen aan dat, onder gunstige omstandigheden, berging van on(ge)zuiver(d) CO2 een nuttige optie zou kunnen zijn om de algehele kosten van ondergrondse CO2 opslag te drukken door besparing op de kosten van purificatie van de oorspronkelijke CO2-rijke afvalgassen.
Samenvatting 132
Chapter 8
Bibliography
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Acknowledgment
Acknowledgment 153
Doing doctoral research is a long journey with many other travelers who contribute to its course and to how it is experienced. I express my sincere thanks to those who have given me support and encouragement during the four years of my PhD. Undoubtedly, completing a PhD is a challenging task that one can not do alone without proper support and guidance of many individuals.
First and foremost, I would like to express my sincere gratitude to my promotor, Professor Dr. Pieter Stuijfzand who gave me the opportunity to being my PhD study in the Critical Zone Hydrology Group in department of Dynamic Earth and Resources of VU University and guided and support me through my work.
I would like to express my cordial thanks and appreciation to my lovely daily supervisor Dr. Henk Kooi, for his excellent guidance. Many thanks for the time, knowledge and energy you shared with me, I cannot tell you how much I appreciated and enjoyed working with you, and it was very inspiring, never tiring and an extremely valuable experience. Dear Henk, from you I learned how to read and speak the language of science. You will always have something to teach me. It was a great joy and pride for me to work with you. Also you were always able to read my mind from my imperfect English sentences and better express my thoughts than I could. Henk, you not only scientifically guided me but also helped and supported me for adapting to the new situation in the Netherlands. Henk thank you for facilitating my stay at the department and for the critical questions you always pose and without your arrangements, valuable comments and revisions, I would never have reached this goal.
In addition, I would like to thank the members of the Ph.D. review committee for their time and interest in my thesis.
I was lucky to meet Prof. Dr. Davood Doumiriganji during my life’s research. He taught me a lot and provided many ideas for future research and you learned me how I tackle problems in new research field. Davood, I am grateful to you and your warmly support and I can not satisfy your kindness and your help during my life. We have fruitful collaboration and research projects with the nonlinear dynamic group. Various projects are still running and the results will come out in the future. Thank you for all of your support and your efforts are highly appreciated.
Dear Dr. Gholamhossein Montazeri, I would like to repay my deepest gratitude you. I learned so many valuable things, not only for my future career but also because of the companionship and communication with the friendly people who work in the National Iranian Oil Company. You are great colleagues and friends to me; thanks a lot for your comments and help.
I acknowledge the sponsors of CATO2 for their financial support and positive feedback. They provided me a nice opportunity to meet great researchers and find cool colleagues. I would like to particularly thank Jan Brouwer, Jan Hopman, Sander van Egmond, Marlies Verlinde, Mirjam van Deutekom and Dr. Patrick van Hemert.
I would like to thank the staff of the Dynamic Earth and Resources cluster, my entire colleague, who collaborated with me for performing these studies, especially Dr. Mariene Gutierrez-Neri and Dr. Martaan Waterloo. Stefanie, Hylke, Lintao, Yanjiao, Jun, Artem, Heloise, Liang, Diego, I am
Acknowledgment 154
incredibly thankful for all the support, discussions and good times I had with you at the VU. I would especially like to thank our kindly secretary of the department, Edith and Yvonne who are always very helpful for solving our bureaucracy issues.
I would also like to thank my Iranian friends here in Amsterdam, Saeed Eslami, Zhila Taherzadeh, Mohammad Sahragard, Hamidreza Abassi, Mahmoud Botshekan, Pouria Eslami, Mohammad Haddad, Mohammad Rafiei, Mahsa Vahabi, Mehran Aflakparast, Seyed Amin Tababtabaei, Hamid Bazoobandi, Hossein Rezazadeh, Seyed Esmaeil Mousavi, Amirhossein Habibian, Masoud Mazlom, Mehdi Sargolzaei, Naser Ayat, Ahmad Mohtadi, Naser Jamali, Ramin Sarrami, Jazayeri, Jaghori, Soleimani, Shafahi, Moradi, Karamifard and their families as well as and specially thanks to Amin Joneidi, Mohammad Mozaffari, Amir Raoof, Rozbeh khosrokhavar, Narjes Shojaei, Mojtaba Talebian, Hamidreza Salimi and many others. You provided many memorable moments for me.
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Father and mother you support, you give, and you ask nothing in return. You taught us that one achieves goals through persistence and hard work. It is difficult to express my feeling in words. Thank you for your tireless efforts. I love you all and I never forget your everlasting love and support.
I have a great wife. I sincerely appreciate my beloved wife, Niloufar, I was a busy husband all the time but you make my life full of happiness and successes. Niloufar, thank you for your understanding of my busy situation and as a token of appreciation for your love, your loyalty, and your support, I want to tell you: Thank and Love You. May we grow old together. Also I would like to thank my family and my lovely and cute nephew, Seyed Javad has brought happiness to my life.
I really enjoyed my time in the Netherlands. Although it is a cold land, the open-minded friendly Dutch people were warm to us. It became like a second homeland for us alongside Iran, a land with thousands years of history and civilization in which I grew and which I love.
Zaman Ziabakhsh-Ganji February - 2015
Amsterdam, The Netherlands
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