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

g tx tw |yx a|yt

\t| | Zw v

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 Earths 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 CO2storage in an aquifer started in 1998 at the Sleipner field in the North Sea (Torp & Gale, 2003) followed in 2008 by storage at Snhvit, 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 Snhvit, Norway, K-12-B offshore gas field in the Dutch sector of the North Sea) and 19 projects are planned to start in 20152016 (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 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 EOSs.

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 PengRobinson EOS to calculate the fugacity of the gas phase. It is shown that the model performs favorably with respect to existing EOSs 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; Andr 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 SO2brine 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 EOSs 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( )NaqP NaqPT 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( )AqP AqPT P T P RT a , (3)

Equating the two chemical potentials gives

0 0( , ) ( , )lnAqP NaP

T P T P aRT 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 NaP

T 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 Henrys 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 Spychers 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 OH O H O

P P VK T P K T P

RT(11)

where T is temperature in K;2H O

V

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 OK7 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 OH O

H 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 EOSs 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 cc

R Ta T TP

(18)

0.07780 cc

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, Henrys 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 Henrys 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( , ) ln630

c 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

Mller et al. (1988) King et al. (1992) Drummond (1981)

Nighswander et al. (1989) Rumpf et al. (1994)

Prutton and Savage (1945)

WaterWaterWaterWaterWaterWater

3 23373

06. Cl 5 m Na00. aCl 17 m N

46 m NaCl 03.9 m CaCl2

285313 323623 323473 373473 288298 290673 353473 313433 348394

25710 25510

2 0035001 54 3 80

60250 35400 20100 1 100 10700

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 Na46 m NaCl

310.15443.15 283.15453.15 311.15-477.15 373.15-653.15 393.15-593.15 313.15398.15

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)

OSullivan and Smith (1970) Alvarez and Prini (1991)

Chapoy et al. (2004)

WaterWaterWaterWater

06. Cl 2 m Na04. Cl 6 m Na

WaterWater

273.15442.15 298.15

298.15373.15 338 15 .15513.

303.15 324.65398.15 33 6.3636.5

274.19363.02

101.3303.9 25.331013.25 25.331013.25

101.3304 1172.6

101.3616.1 5.34256

9.7170.43

CH4

Michels et al. (1936)

Dodson and Standing (1944) Culberson et al. (1950)

Culberson and Mcketta (1951) Duffy et al. (1961)

OSullivan and Smith (1970)

Water1.016.59 m aCl N2.912 aCl2.93 m C

0.00.6 m brine WaterWaterWater

0.5 aCl 6.1 m N07. Cl235 m Ca

Water

298.15423.15 298.15423.15

298.15 311.15394.15

298.15 298.2444.3

298 15.15303.303.15

298.15303.15 324 15

40.6469.1 41.8456.0 56.2209.9

35345 36.2667.4 2

.65398.

2.3689.13.1751.71 214.8957.5

3.274.8 101.3616.1

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)

1.014.4 m NaCl 1Water

1.0 m CaCl201. aCl 54 m N05.9 m NaCl

WaterWater

04. Cl 0 m Na04 Cl .0 m K

02.16 m MgCl202.0 m CaCl2

Water0.814.7 m NaCl

WaterWaterWaterWaterWaterWater

0.99- l 3.99 m KCWaterWater

324.65 8.15 39310.93 4.26 34298.2398.2

323623 372.15513.152 97.5518.3

298.15 298.15 298.15 298.15 298.15

27 7.2573.227 7.2573.2298.2338.2

298.15323.15298.15323.15273.2290.2

344 313473

313.5 3.19 1372 83.2303.2

275.11313.11

101.3 .1 61641.4 44.7 3

101608 295

751570 13.2 .51 76424.151.7 24.151.7 24.151.7 24.151.7 24.151.7 11132 19124 25125 3080

5 .6790.8234.5

2001000 3 .493

4.297.9 2 0400.39.7180

O2

Geng & Duan (2010) Water0-6 m Na l C

273.15-513 1-600

SO2

Rumpf & Maurer (1992) Xia et al. (1999)

Water2.9425.928 m NaCl

293.15413.15 0.125 313393 0.1-37

CO2+CH4+H2S

Huang et al. (1985) Water 37.8176.7 48.2173.1

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 Ox 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, , , , , , ,iii

yK i H O N O CO CH H S Sx 2

O (32)

According to Eq. (14) the K-value for water is

Chapter 2 25

2

2

2

2

00 exp H OH OH O

H 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 , Kis and zis, 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*10

0

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*10

0

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*10

0

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*10

0

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*10

0

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*10

0

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*10

0

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*10

0

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*10

0

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*10

0

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* 1

00

(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* 1

00

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 EOSs of Spycher et al. (2005) and Duan and Sun (2003) (symbols) for CO2 solubility as function of (a) pressures at 90C 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 76C 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* 1

00

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 (Sreide & 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 (Sreide & 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* 1

00

(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* 1

00

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*

100

0 (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* 1

000

(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*

100

0

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*

100

0

(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*

100

0

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*

100

0 (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*

100

0

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*

100

0

(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*

100

0

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*

100

0

(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* 1

000

(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 Henrys 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*10

0

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 EOSs 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 Shibues (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 SO2strongly 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 CO2during 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 CO2and 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; Andr 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 CO2storage 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 C) 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 C. 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 Darcys 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