Investigations in Geologic Carbon Sequestration: Multiphase Flow of CO2 and Water in Reservoir Rocks

Annual Report 2013

Sally M. Benson, Ferdinand Hingerl, Boxiao Li, Ronny Pini, Hamdi Tchelepi, and Lin Zuo

Department of Energy Resources Engineering School of Earth Sciences

Stanford University

May 2013 Contacts Sally M. Benson: smbenson@stanford.edu Ferdinand Hingerl: hingerl@stanford.edu Boxiao Li: boxiaoli@stanford.edu Ronny Pini: pini@stanford.edu Hamdi Tchelepi: Tchelepi@stanford.edu Lin Zuo: linzuo@stanford.edu

Abstract  

Understanding the multiphase flow properties of CO2 and water in porous media is essential for successful large-scale geologic CO2 storage. Optimizing the design and operation of injection projects will depend on knowledge of injectivity, trapping capacity, distribution of CO2 in the subsurface and overall areal extent of the subsurface plume. It is increasingly recognized that the capillarity, capillary heterogeneity, and accurate relative permeability curves of CO2-water systems are essential for accurate simulations ranging from the sub-core to the basin scale. Our research program aims at improving the fundamental understanding on the dynamics of multiphase flow of CO2 and brine in porous media. The research work integrates experimental investigations and numerical simulations, thus allowing for a direct link between observations in the lab and the physics of the multiphase displacement process. In this context, current available models can be validated and/or extended so as to include a more accurate description of the physical processes involved. Highlights of this year’s effort include the following:

• Publication of a new method for simultaneously measuring capillary pressure and relative permeability at pressures and temperatures representative of geological storage reservoirs. This method addresses many unresolved issues about the influence of factors such as interfacial tension and wettability on gas/brine relative permeability permeability curves (Pini et. al., 2013, Water Resources Research).

• Publication of a robust method for making sub-core permeability maps using multiphase displacement data and CT-scanning. This method has been demonstrated to accurately predict CO2 saturation distributions in spatially heterogeneous rocks over a wide range of flowrates and for different fluid pairs (Krause et al, 2013, Transport in Porous Media).

• An analytical solution for predicting the average CO2 saturation in core floods as a function of capillary and gravity numbers has been developed and published. This solution accurately accounts for buoyancy and capillary in 2 dimensional flow systems (Kuo and Benson, 2012, Society of Petroleum Engineers Journal).

• A paper has been accepted for publication that documents the influence of capillary entry pressure on the rate of solubility trapping. In particular, this paper shows that depending on the nature of the capillary pressure curve and how it is treated in the numerical simulator; solubility trapping can be significantly over or underestimated (Li et al., 2013, Journal of Greenhouse Gas Control).

• Micromodel investigations of exsolution of CO2 due to depressurization confirm our hypothesis that the low mobility to water and CO2 is caused the formation of a disconnected phase of exsolved CO2 bubbles. This observation is the basis for the development of a new concept for exsolution enhanced oil recovery (Zuo et al., 2013, Advances in Water Resources; Zuo and Benson, 2013, Energy Procedia, 11th International Conference on Greenhouse Gas Technology).

• Significant progress has been made to develop improved approaches for simulating flow of CO2 and brine in systems with strong capillary heterogeneity—such as is expected for many typical sequestration sites.

  1. Introduction

Carbon   dioxide   capture   and   sequestration   (CCS)   in   deep   geological  formations  has  emerged  over   the  past   fifteen  years  as  an   important  component  of  the  portfolio  of  options  for  reducing  greenhouse  emissions.  Our  research  focuses  on  the   fundamental   science   underpinning   sequestration   in   saline   aquifers   and  multiphase   flow  of   CO2,   brine   and   to   a   lesser   degree,   oil.   Saline   aquifers   have   the  largest   sequestration   capacity,   as   compared   to   oil   and   gas   reservoirs   or   deep  unmineable   coal  beds.   Saline  aquifers   are  also  more  broadly  distributed  and   thus,  closer   to   more   emission   sources.     However,   unlike   oil   and   gas   reservoirs   with  proven  seals  that  have  withstood  the  test  of  time,  saline  aquifers  must  be  carefully  characterized   to   assure   that   CO2   will   achieve   high   retention   rates.   Improved  fundamental  understanding  of  multi-­‐phase  flow  and  trapping  in  CO2-­‐brine  systems  will   be   needed   to   take   advantage   of   this   large   storage   capacity   of   saline   aquifers.    Important  questions  remain  to  be  answered,  such  as,  what  fraction  of  the  pore  space  will  be  filled  with  CO2,  what  will  be  the  spatial  extent  of  the  plume  of  injected  CO2,  how  much  and  how  quickly  will  CO2  dissolve   in  brine,   and  how  much  CO2  will   be  trapped  by   capillary   forces  when  water   imbibes  back   into   the  plume  and   to  what  extent   is  capillary  trapping  permanent?  Here  we  are  developing  new  experimental  data  and  carrying  out  simulations  to  improve  our  ability  to  answer  these  questions.  As  our  research  progresses,  we  will  assess  which,  if  any,  modifications  to  currently  accepted  multiphase  flow  theory  are  needed  and  to  develop  approaches  for  reliably  predicting  field-­‐scale  performance.  

 We  use  a  combination  of  laboratory  experiments,  numerical  methods  and  analytical  solutions   to   address   these   issues   as   shown   in   the   schematic   below   (Figure   1).  Interaction   and   iteration   between   these   four   approaches   improves   our   ability   to  quickly   identify  and  test  new  phenomena  and  approaches   for  accurately  capturing  them  in  quantitative  models.  

   Figure  1.  Illustration  of  the  4  interrelated  components  of  our  approach  to  study  multi-­‐phase  flow  and  trapping  of  CO2.  

2.  Nonlinear  Solver  for  Viscous,  Buoyancy,  and  Heterogeneous  Capillary  Pressure  Forces   The role of small-scale heterogeneities on multiphase flow has recently received increasing awareness and it finds support from a more extensive use of imaging techniques to characterize laboratory core-floods (Perrin and Benson, 2010). The impact of small-scale heterogeneities on large-scale CO2 migration can be studied via numerical simulations. Li et al. (2012) investigated the optimized numerical strategies in modeling multiphase flow of CO2 and brine with small-scale heterogeneities, using a standard reservoir simulator. An improvement in simulation speed in modeling CO2 core flood process was demonstrated in their work. However, in order to bridge the gap between core and aquifer scale, the simulator needs to handle much larger number of simulation grid-blocks, and more complicated heterogeneities. Current bottleneck of the computation speed lies in the convergence difficulties of nonlinear Newton solvers. One major reason of convergence failure is attributed to the ‘kink’ of the flux function. In the transport equation, the flux is a function of saturation, and the kink is a non-differentiable point with respect to saturation. The kink occurs when the flow directions of wetting and nonwetting fluids change from co-current to counter-current, or vice versa, if phase-based Single Point Upstream Weighting (SPU) – the industry standard – is used to discretize the flux. Wang and Tchelepi (2013) found that chopping the saturation to the kink value during the Newton iterations prevents saturation oscillations across the kink, thus facilitating convergence significantly. Here, we offer a deeper theoretical probe in the nonlinear space, and devise solution strategy that handles the kink in the presence of viscous, buoyancy, and heterogeneous capillarity forces. The flux across the interface of two neighboring simulation gridblocks is a function of the saturations of both gridblocks. Figure 2(a) illustrates such flux (expressed as the fractional flow of the wetting phase, Fw) in the presence of viscous and buoyancy forces (also see Kwok and Tchelepi, 2008). SwL is the wetting phase saturation in the upstream of total velocity (the sum of velocities of both phases), while SwR is the downstream saturation. When Fw < 1, the wetting and nonwetting phases flow co-currently, while counter-current flow occurs when Fw > 1. The kink is located at Fw = 1, which corresponds to the change of flow directions. Figure 2(b) shows the derivative of the flux with respect to SwL. Clearly a discontinuity can be seen, suggesting that the flux is non-differentiable at the location of the kink.

Figure 2 - (a) Flux under viscous and buoyancy forces; (b) derivative of flux w.r.t. SwL. It has been shown that the saturation chopping is very easy to manage when the kink location depends only on SwL (Li and Tchelepi, 2013), which is the case when only viscous and buoyancy forces are present. However, when SPU is used to discretize the capillary pressure term, two kinks occur, and both of them depend on SwL and SwR (see Figure 3). In addition, the kinks are curved, and their locations are hard to compute. This poses a significant difficulty in saturation chopping strategy (Li and Tchelepi, in preparation).

Figure 3 - (a) Flux under viscous and capillary forces; (b) derivative of flux w.r.t. SwL. To resolve this issue, we propose a numerical scheme that discretizes the viscous and gravity flux using SPU, and the (heterogeneous) capillary flux using central difference. For each grid-block interface, two dummy saturation variables (S- and S+) are introduced (see Figure 4). The flux across the interface needs to be computed using the dummies, which can be obtained by solving a flux-continuity equation and a pressure-continuity equation:

Flux-continuity:

where

Pressure continuity: In the equations, f is the viscous and gravity flux, k is the permeability, uT is the total velocity, λ is the mobility, and Pc is the capillary pressure. Note that the scheme resembles the one in Cances (2009); however, the latter has been shown to have multiple kinks that depend on both SwL and SwR under heterogeneous Pc (Li and Tchelepi, 2013). The flux calculated from the scheme proposed here (see Figure 5) has only one kink, whose location depends purely on SwL. Hence, the saturation chopping for the kink becomes easy to manage even when viscous, buoyancy, and heterogeneous Pc exist simultaneously. It is worth highlighting, to fully resolve the convergence difficulty in Newton iterations, the other reason of convergence failure – inflection point – has to be handled efficiently in saturation chopping (Jenny et al., 2009; Wang and Tchelepi, 2013). This is our future research direction.

Figure 4 - Dummy saturation variables at the grid-block interface. Each grid-block has its own Pc curve.

Figure 5 - (a) Flux under viscous, buoyancy, and heterogeneous capillary forces; (b) derivative of flux w.r.t. SwL.

3. Investigations of CO2 Exsolution and the Effect on Water Mobility Previous core-flooding experiments suggest that gas liberation from CO2/water solution introduces significant mobility reduction to the water phase and the gas phase remains trapped by capillary forces even at high saturations. In this study, direct observations of carbon dioxide exsolution from carbonated water are acquired under reservoir conditions (9 MPa and 45°C). Fluorescence microscopy and image analysis are used to quantitatively characterize bubble formation, morphology, and mobility (see an example in Figure 6).

Figure 6 - Evolution of exsolved CO2 bubbles in porous media. Observations indicate the strong influence of interfacial tension and pore-geometry on bubble growth and evolution. Most of the gas exhibits little mobility during the course of depressurization and clogs water flow paths. However, a snap-off mechanism mobilizes a small portion of the trapped gas along the water flow paths. This feature contributes to the transport of the dispersed exsolved gas phase and the formation of intermittent gas flow. A new definition of critical gas saturation is proposed accordingly as the minimum saturation that snap-off starts to produce mobile bubbles. Low mobility of the water phase and CO2 phase in exsolution is explained by the formation of dispersed CO2 bubbles which block water flow and lack the connectivity to create a mobile gas phase. Understanding the multi-phase flow properties of this unconventional flow system with self-distributed gas saturation and local plugging effect would help develop applications such as leakage remediation in geological carbon sequestration and mobility control in CO2-EOR operations, which take advantage of this unique plugging effect of the exsolved gas phase. A series of core-flooding experiments were conducted to investigate the dependence of gas saturation profile and mobility on reservoir depletion rates. In contrast to solution gas drive, where dissolved gas evolves from hydrocarbons during oil reservoir depletion, saturation profiles and mobility of exsolved CO2 does not exhibit depletion rate dependency (see Figure 7). This indicates that CO2/water systems are significantly different from gas/oil systems in terms of gas phase formation and evolution. The high

interfacial tension and low liquid phase viscosity of CO2/water systems contribute to the unique characteristics of exsolved CO2 morphology and multiphase flow behavior.

Figure 7 - Carbon dioxide saturation profiles at different depletion rates in rock samples. A potential application of CO2 exsolution is related to water mobility control in oil production. Micromodel experiments have demonstrated the fundamental principles of the mobility control mechanism, i.e. the exsolved CO2 in water-filled pores blocked water flow in swept portions and displaced water into oil-filled pores, while trapped oil after carbonated water injection was mobilized by sequentially invading water. This method’s self-distributed mobility control and local clogging was tested in various sandstone samples under reservoir conditions. As compared to continuous carbonated water injection, core flooding experiments show that additional 5~15% OOIP can be recovered by CO2 exsolution and sequential carbonated water injection at a lowered reservoir pressure (Figure 8). Additionally, exsolved CO2 resides in the pores of the reservoir as an immobile phase with a high residual saturation after oil production, exhibiting a potential synergy opportunity between CO2 EOR and CO2 sequestration.

Figure 8 - Oil recovery with CO2 exsolution. 4. Determination of Capillary Pressure and Relative Permeability Curves from Core-Flooding Experiments with Various Fluid Pairs Capillary pressure and relative permeability curves are traditionally obtained from experimental measurements. The petroleum literature provides many examples for water/oil, water/gas and oil/gas systems on a variety of rocks and that have in turn allowed for the identification of useful trends regarding the general character of these functions; while the shape of the capillary pressure function can be directly related to the pore size distribution of a given rock, the landmarks of a relative permeability curve (curvature, end-point values and residual saturations) are indicators of the difference in wettability for the two fluids. In comparison, the currently available dataset of the same properties for the CO2/water system at pressure and temperature conditions representative of a deep reservoir is still very limited. Interestingly enough, some of these initial observations suggest that the scCO2/Brine system doesn't follow some of these general rules and can be summarized as follows:

- While CO2/water capillary pressure curves do show the expected strong dependency on the interfacial tension (as related to variations in pressure, temperature and salinity conditions), a change in wettability (from water- to intermediate-wet) with increasing pressure was observed in the experiments with sand-packs (Plug and Bruining 2007) and during contact angle measurements in two-dimensional transparent silica micromodels (Kim et al., 2012).

- Maximum gas saturations observed during relative permeability experiment with scCO2 and brine are generally less than 0.5 and the measured relative permeabilities are low (kr,nw < 0.2) for both sandstone and carbonate samples (Bachu and Bennion 2008, Krevor et al. 2012, Akbarabadi and Piri 2013).

- As compared to other gas/liquid fluid pairs, the CO2/water system show a

particularly strong effect of the interfacial tension on the shape of the relative permeability curves across the range of 20 to 56 mN/m (Bachu and Bennion 2008).

It is unclear whether these observations are due to the peculiar properties of supercritical CO2 (large density and low viscosity), to the experimental challenges associated with the use of this fluid pair and/or to its complex interactions with the rock minerals (wetting behavior). With the purpose of explain and reconcile some of these inconsistencies, an experimental campaign was designed that includes measurements on a single Berea Sandstone core by using three different fluid pairs, namely gCO2/Water, gN2/Water and scCO2/Brine. To this aim, a novel technique has been developed that allows measuring drainage capillary pressure and relative permeability curves simultaneously during a core-flooding experiment. Experimental conditions have been chosen so as to cover a relatively wide range of interfacial tension values (γ = 40-65 mN/m), while maintaining a constant viscosity ratio µw/µnw = 30.

Figure 9a shows the measured capillary pressure curves for the three systems described above; full symbols represent results from the core flooding experiments and are compared to data (empty symbols) from an independent mercury intrusion experiment carried out on a small plug drilled from a section adjacent to the inlet face of the core sample. For the comparison, the contact angle was used as a fitting parameter, while interfacial tension values for each fluid pair have been obtained from the literature for similar pressure, temperature and salinity conditions. The agreement between the two techniques data is generally very good and the obtained contact angle takes a value of 39.9° ± 1°, thus suggesting that in all cases water-wet conditions prevail. Interestingly, this value corresponds to the one assumed for the mercury/vacuum pair, thus implying that the contact angle can be neglected in the conversion from one fluid-pair to the other. In other words, when a capillary pressure curve is measured on a uniformly wetted core (i.e. with a contact angle <50°) by mercury intrusion instead of using the actual reservoir fluids, the contact angle should not be used for the conversion. Brooks-Corey curves are shown in the same figure; it can be seen that this model allows for a very good description of the capillary pressure data. Importantly, very similar values are obtained among the three experiments for both the irreducible water saturation and the so-called pore-size distribution index, with average estimates of Sw,irr = 0.33 and λ = 2.6, respectively. Additionally, three distinct entry capillary pressure values are observed for gN2/Water (8.13 kPa), gCO2/Water (6.80 kPa) and scCO2/Brine (4.94 kPa), thus reflecting the expected influence of the latter on the capillary pressure curve.    

 Figure  9  –  Capillary  pressure  (a)  and  relative  permeability  (b)  curves  on  Berea  Sandstone  for  three  gas-­‐liquid  fluid  pairs  investigated  here.  Solid  lines  are  Brooks-­‐Corey  curves.      

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Measured drainage relative permeability curves are shown as symbols in Figure 9b for the three fluid pairs considered in this study. No discernible difference can be seen in the three relative permeability curves, despite the different interfacial tension levels among the three fluid pair systems. Additionally, curves are shown in the figure that have been obtained by the Brooks-Corey relationship for relative permeability in a fully predictive way, i.e. by using the parameter dataset obtained upon fitting a Brooks-Corey model to the capillary pressure data presented above. The two curves are representative for the experiments carried out at low pressure (γ = 57-65 mN/m, dashed line) and at high pressure (γ = 41 mN/m, solid line), respectively. Similarly to the experimental observations, the Brooks-Corey model suggests that interfacial tension effects are absent; however, the agreement between model and experiments is rather poor. Interestingly enough, a very similar discrepancy was reported in the original publication by Brooks and Corey (1964), also for a Berea Sandstone core; the latter was attributed to anisotropy, thus highlighting the limits of the model for describing relative permeability curves in consolidated rocks. As a matter of fact, empirical functions are often used, where both the curvature and the end-point values of the relative permeability curves can be properly captured upon fitting a given number of parameters.    

 Figure 10 - Comparison with relative permeability data from the literature on Berea Sandstone; (A) all data from present study are compared to data with N2/brine by Oak et al. (1990) and with scCO2/brine by Perrin et al. 2010, Krevor et al. 2012 and Akbarabadi and Piri 2013. (B) scCO2/brine data from the present study are compared to drainage relative permeability curves from two previous studies from the same laboratory, but using the steady-state technique (Perrin et al. 2010 and Krevor et al. 2012).    The reliability of the measured relative permeability curves is supported by the very good agreement with data from the literature, as shown in Figure 10a and 10b. The

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measurements from the present study overlap with those reported in Perrin et al. (2010), Krevor et al. (2012) and Akbarabadi and Piri (2013) for the Berea/scCO2/Brine system, and they further extend to higher relative permeability values by closely following the data by Oak et al. (1990) for the Berea/N2/Brine system. Most importantly, the different fluid pairs yield essentially the same drainage relative permeability curve, thus suggesting that under these experimental conditions interfacial effects are negligible, as often reported for water/oil,oil/gas and water/gas systems. With respect to the scCO2/Brine system, this further confirms that as long as the same wetting preference is maintained, the use of analogue fluids is justified for the characterization of relative permeability curves. A complete set of scCO2/brine drainage relative permeability curves on Berea Sandstone is shown in Figure 10b, where the data from this study are combined with results from two previous studies from the same laboratory, but using the (traditional) steady-state technique. Again, the agreement among the three data sets is good and considering that it is used in a fully predictive way, the BC model (solid lines) provides a satisfactory description of both wetting and nonwetting relative permeability curves. With respect to the maximum relative permeability to the nonwetting phase kr,nw, a value of about 0.9 has been measured in his study at an irreducible water saturation of about 40 %; this end-point value and related irreducible water saturation levels provide another confirmation that the system is strongly water-wet.

5. Development of a new method for assessing sub-core scale permeability distributions using MRI measured fluid velocities The motivation for this work is two-fold. First, we seek an independent method of measuring sub-core scale permeabilities to compare to the method we developed in Krause et al (2013). Such measurements are needed to assess sub-core scale permeability and capillary heterogeneity. Second, heterogeneities in rocks have a strong influence on fluid flow properties such as fluid velocities, saturation distributions, and fluid residence times. The latter in turn determine the degree of thermodynamic (non-) equilibrium between rock and fluid and therefore also influence the formation of stable mineral assemblages. Parts of the rock that are in contact with a stagnant fluid can reach thermodynamic equilibrium with the fluid, and will precipitate/dissolve entirely different minerals, as compared to those parts of the rock that are in contact with a fast moving fluid phase. Depending on the minerals involved, such precipitation/dissolution reactions can in turn have a strong feedback on the fluid flow properties due to associated porosity and permeability changes. An understanding of mechanisms controlling fluid velocities as well as their relation to other flow properties, such as permeabilities and capillary pressure curves, is therefore crucial for successfully predicting the flow behavior in heterogeneous rocks as well as their impact on geochemical fluid-rock interactions. Using a new MRI technique developed at the MRI Center at the University of New Brunswick (Romanenko and Balcom, 2011) we created 3D maps of porosity distributions as well as single-phase fluid velocity distributions of a heterogeneous sandstone rock (permeability 1160 mD). The rock sample comes from a potential Carbon Sequestration site in Israel (Arqov site). Water was injected into the saturated core at a flow rate of 4 ml/min under ambient conditions while the MRI scans were performed. To evaluate the accuracy of the scans, we summed up the voxel-based volumetric flow rates in flow direction of each slice. Slice averaged flow rates varied between 3.9 and 4.4 ml/min (largest errors occur close to the inlet and outlet), with a computed core average of 4.1 ml/min; an error of 2.5% can be considered very low and clearly speaks for the usability of the MRI technique for the investigation of fluid flow properties in heterogeneous sandstone rock samples. Using the porosity and velocity maps from the MRI measurements we investigated two approaches two create permeability fields that, upon using them in the Darcy representation of the single phase flow equation, reproduced the measured velocities with different degrees of fidelity. The fluid flow simulations were performed with the Stanford code GPRS. In the first method, we generated a permeability map of the core by applying the Kozeny-Carman relationship to the measured porosities. Figure 11 shows that the computed velocity field poorly represents features shown in the measured velocity map and the Kozeny-Carman relationship seems therefore unsuitable for producing velocity maps at this scale.

Figure 11 - Velocities computed using Kozeny-Carman permeabilities (left graph) significantly differ from measured velocities (middle graph), while permeabilities generated by the iterative updating approach (right map) result in velocities that reproduce the measured velocities very well. For the second method, we introduced an iterative scheme, which combined the generated pressure drops with MRI measured velocities and porosities to generate a new permeability distribution. We started the iterative procedure with a set of Kozeny-Carman permeabilities; a new pressure map was generated from GPRS that was used to update the permeability field. After three iterations the measured velocity field could be represented with over 99% accuracy. Figure 11 (comparison between middle and right images) clearly illustrates the quality of the velocities resulting from the updated permeability field. The significant difference between permeabilities from Kozeny-Carman versus iterative updating can be seen in Figure 12. Kozeny-Carman clearly overestimates the dependence of permeability on porosity and therefore results in velocities that do not match the measured values. Provided the new set of permeabilities is correct, Figure 13 indicates that no single interpolative function can represent the spread of data in a permeability-porosity plot. Even though the permeabilities follow a broad trend with respect to porosity, the large scatter of permeabilities shows that rock properties other than porosity strongly contribute to their value (e.g. pore size distribution, pore-body to pore-throat aspect ratio). This result is consistent with our earlier studies, based on multiphase flows, which demonstrated that at the sub-core scale, the Kozeny-Carman relationship does not provide accurate permeability distributions (Krause, 2009).

Figure 12 - Permeabilities calculated from the Kozeny-Carman relationship differ significantly from those generated by using the iterative updating approach.

Figure 13 – Comparison between the permeability values calculated with the iterative procedure and their respective porosities measured using the MRI method. Even though the modeled permeabilities follow a broad trend with respect to porosity, their scatter is too large to be represented by a single linear (red line) or quadratic (blue line) fitting function.

References Akbarabadi, M., and M. Piri (2013), Relative permeability hysteresis and capillary

trapping characteristics of supercritical CO2/brine systems: An experimental study at reservoir conditions, Adv. Water Resour. 52, 190–206.

Bachu, S., and B. Bennion (2008), Effects of in-situ conditions on relative permeability characteristics of CO2-brine systems, Environ. Geol., 54(8), 1707–1722.

Brooks, R. H., and A. T. Corey (1964), Hydraulic properties of porous media, Hydrology Paper No. 3, Colorado State University, 1–27.

Cances, C. (2009), Finite volume scheme for two-phase flows in heterogeneous porous media involving capillary pressure discontinuities. Math. Model. Numer. Anal., 43, 973-1001.

Jenny, P., Tchelepi, H.A., and Lee, S.H. (2009), Unconditionally convergent nonlinear solver for hyperbolic conservation laws with S-shaped flux functions. J. Comp. Phys., 228, 7497-7512.

Kim, Y., J. Wan, T. J. Kneafsey, and T. Tokunaga (2012), Dewetting of silica surfaces upon reactions with supercritical CO2 and brine: pore-scale studies in micromodels, Environ. Sci. Technol., 46(7), 4228–4235.

Krause (2009). Modeling Sub-Core Scale Permeability in Sandstone for Use in Studying Multiphase Flow of CO2 and Brine in Core Flooding Experiments. M.S. Thesis, Department of Energy Resources Engineering, Stanford University.

Krause, M. S.C. Krevor, and S.M. Benson, 2013. A Procedure for the Accurate Determination of Sub-Core Scale Permeability Distributions with Error Quantification, Transport in Porous Media, DOI 10.1007/s11242-013-0161-y.

Krevor, S., R. Pini, L. Zuo, and S. Benson (2012), Relative permeability and trapping of CO2 and water in sandstone rocks at reservoir conditions, Water Resour. Res., 48 (W02532).

Kwok, F. and Tchelepi, H.A. (2008), Convergence of implicit monotone schemes with applications in multiphase flow in porous media. SIAM J. Numer. Anal., 46, 2662-2687.

Oak, M., L. Baker, and D. Thomas (1990), Three-phase relative permeability of Berea Sandstone, J. Petrol. Technol., 42(8), 1054–1061.

Perrin, J.C. and Benson, S.M. (2009), An experimental study on the influence of sub-core scale heterogeneities on CO2 distribution in reservoir rocks. Transp. Porous Med. 82, 93-109.

Plug, W.-J., and J. Bruining (2007), Capillary pressure for the sand-CO2-water system under various pressure conditions. Application to CO2 sequestration, Adv. Water Resour., 30 (11), 2339–2353.

Romanenko, K. V., Balcom, B. J. (2011). Permeability mapping in porous media by magnetization prepared centric-scan SPRITE. Experiments in Fluids, 50 (2), 301-312.

Wang, X. and Tchelepi, H.A. (2013), Trust-region Newton solver for multiphase flow and transport in heterogeneous porous media. Paper SPE 163600, 2013.

Journal articles (published and submitted) Pini R. and S.M. Benson (2013), Simultaneous determination of capillary pressure and

relative permeability curves from core-flooding experiments with various fluid pairs. Water Resour. Res., in press.

M.  Krause,  S.C.  Krevor,  and  S.M.  Benson,  2013.  A  Procedure  for  the  Accurate  Determination  of  Sub-­‐Core  Scale  Permeability  Distributions  with  Error  Quantification,  Transport  in  Porous  Media,  DOI  10.1007/s11242-­‐013-­‐0161-­‐y.  

C.-­‐W.  Kuo  and  S.  M.  Benson,  2013.  Analytical  Study  of  Effects  of  Flow  Rate,  Capillarity  and  Gravity  on  CO2/Brine  Multiphase  Flow  System  in  Horizontal  Corefloods,    SPEJ.  SPE-­‐153954-­‐PA  (in  press;  posted  18  April  2013).  

B.  Li.,  H.  Tchelepi,  and  S.  M.  Benson,  2013.  The  Influence  of  Capillary  Entry-­‐Pressure  Representation  on  the  Rate  of  CO2  Solubility  Trapping.  Water  Resources  Research,  accepted  pending  minor  revisions.  

Zuo L., C. Zhang, R.W. Falta, S.M. Benson (2013), Micromodel Investigations of CO2 Exsolution from Carbonated Water in Sedimentary Rocks, Adv. Water Resour., 53, 188–197.

Conference papers Li, B., Benson, S.M., Tchelepi, H.A. (2012) Modeling fine-scale capillary heterogeneity

in multiphase flow of CO2 and brine in sedimentary rocks. Proceedings of the XIX International Conference on Computational Methods in Water Resources, University of Illinois at Urbana-Champaign, USA, June 17-21.

Li, B., H.A .Tchelepi, S. Benson (2012), Sensitivity of long-term CO2 sequestration simulation result to the treatment of capillary entry pressure, 11th International Conference on Greenhouse Gas Control Technologies (GHGT-11), Kyoto (Japan), November 18-22.

Pini, R., S. Krevor, M. Krause, S.M. Benson (2013). Capillary heterogeneity in sandstones rocks during CO2/water core-flooding experiments, Proceedings of the 11th International Conference on Greenhouse Gas Control Technologies (GHGT-11), Kyoto, Japan, November 18-22.

Zuo L., S.M. Benson (2013). Exsolution Enhanced Oil Recovery with Concurrent CO2 Sequestration, Proceedings of the 11th International Conference on Greenhouse Gas Control Technologies (GHGT-11), Kyoto, Japan, November 18-22.

Presentations and posters S. M. Benson (2013), “Mesoscale Investigations of the Influence of Capillary

Heterogeneity on Multiphase Flow of Fluids in Rocks,” Imperial College, London, U.K.

S. M. Benson (2013), “Research Needs and Opportunities in CO2 Storage,” Uppsala University, Stockholm, Sweden

S. M. Benson (2013), “Mesoscale Investigations of the Influence of Capillary Heterogeneity on Multiphase Flow of Fluids in Rocks”, SIAM Conference, Boston,

Massachusetts. S.M. Benson (2013), “CCS:When will it Be Ready?” UC Berkeley, BERC Energy

Symposium. S.M. Benson (2012), Prospects and Challenges for CO2 Storage, Brigham Young

University, Utah. S.M. Benson (2012), Invited Speaker, Mesoscale Science Workshop, SLAC National

Laboratory, Mesoscale Investigations of Multiphase Flow. S.  M.  Benson  (2012),  “Carbon  Capture  and  Storage,”  UKERC  Energy  Summer  School,  Warrick  University,  U.K.

Li, B. and , H.A., Tchelepi (2013), Nonlinearity of viscous, buoyancy, and heterogeneous capillary forces in porous media. 30th SUPRI-B Affiliate Meeting, Stanford University, Stanford (USA), May 6-7.

Li, B., H.A .Tchelepi, S. Benson (2012), Sensitivity of long-term CO2 sequestration simulation result to the treatment of capillary entry pressure, 11th International Conference on Greenhouse Gas Control Technologies (GHGT-11), Kyoto (Japan), November 18-22.

Li, B., H.A .Tchelepi, S. Benson (2012), The Influence of Capillary Entry-Pressure Representation on the Rate of CO2 Solubility Trapping. GCEP Symposium, Stanford University, Stanford (USA), October 10-11.

Hingerl F., K. Romanenko, R. Pini, B. Balcom and S. Benson (2013), Modeling and comparative study of fluid velocities in heterogeneous rocks, EGU General Assembly, Vienna (Austria), April 7-12.

Hingerl, F., R. Pini, S. Benson (2012), Petrological heterogeneities and their impact on multiphase flow properties in the framework of CCS, GCEP Symposium, Stanford University, Stanford (USA), October 10-11.

Pini R., S. Krevor, S. Benson (2012), Capillary heterogeneity in sandstones rocks during CO2/water core-flooding experiments, GCEP Symposium, Stanford University, Stanford (USA), October 10-11.

Pini R., S. Krevor, M. Krause, S. Benson (2012), Capillary heterogeneity in sandstones rocks during CO2/water core-flooding experiments, Gordon Research Conference - Flow & Transport in Permeable Media, Les Diablerets (Switzerland), June 24-29.

Pini R., S. Krevor, M. Krause, S. Benson (2012), Capillary heterogeneity in sandstones rocks during CO2/water core-flooding experiments, 11th International Conference on Greenhouse Gas Control Technologies (GHGT-11), Kyoto (Japan), November 18-22.

Pini R. and S. Benson (2012), The effect of small- and core-scale heterogeneity on the multiphase flow properties of CO2 and water in sandstones, AGU Fall Meeting, San Francisco (USA), December 3-7.

Pini R., F. Hingerl and S. Benson (2013), Simultaneous Determination of Capillary Pressure and Relative Permeability Curves from Core-Flooding Experiments with Various Fluid Pairs, EGU General Assembly, Vienna (Austria), April 7-12.

Zuo, L., S. Benson (2013), CO2 Exsolution – A New Way to Control Mobility in Waterflooding, Stanford Center for Carbon Storage EOR workshop, Stanford University, Stanford (USA), January 23-24.

Zuo, L., S. Benson (2013). Mobility Control by CO2 Exsolution – Micromodel and Coreflooding Experiments, Permian Basin CCUS Forum: CO2 Enhanced Oil Recovery - Operations in the Permian Basin, Odessa, TX (USA), March 25-26.