## Publications

[Go to Proceedings Refereed] [Go to Theses]

Underlined names are links to recent or past GEG members

### REFEREED PUBLICATIONS IN JOURNALS

29.

Ezekiel, J., B.M. Adams, M.O. Saar, and A. Ebigbo, Numerical analysis and optimization of the performance of CO2-Plume
Geothermal (CPG) production wells and implications for electric power
generation, Geothermics, 98/102270, 2022. [Download PDF] [View Abstract]CO2-Plume Geothermal (CPG) power plants can produce heat and/or electric power. One of the most important parameters for the design of a CPG system is the CO2 mass flowrate. Firstly, the flowrate determines the power generated. Secondly, the flowrate has a significant effect on the fluid pressure drawdown in the geologic reservoir at the production well inlet. This pressure drawdown is important because it can lead to water flow in the reservoir towards and into the borehole. Thirdly, the CO2 flowrate directly affects the two-phase (CO2 and water) flow regime within the production well. An annular flow regime, dominated by the flow of the CO2 phase in the well, is favorable to increase CPG efficiency. Thus, flowrate optimizations of CPG systems need to honor all of the above processes. We investigate the effects of various operational parameters (maximum flowrate, ad- missible reservoir-pressure drawdown, borehole diameter) and reservoir parameters (permeability anisotropy and relative permeability curves) on the CO2 and water flow regime in the production well and on the power generation of a CPG system. We use a numerical modeling approach that couples the reservoir processes with the well and power plant systems. Our results show that water accumulation in the CPG vertical production well can occur. However, with proper CPG system design, it is possible to prevent such water accumulation in the pro- duction well and to maximize CPG electric power output.

28.

Ezekiel, J., D. Kumbhat, A. Ebigbo, B.M. Adams, and M.O. Saar, Sensitivity of Reservoir and Operational Parameters on the Energy Extraction Performance of Combined CO2-EGR–CPG Systems, Energies, 14/6122, 2021. [Download PDF] [View Abstract]There is a potential for synergy effects in utilizing CO2 for both enhanced gas recovery (EGR) and geothermal energy extraction (CO2-plume geothermal, CPG) from natural gas reservoirs. In this study, we carried out reservoir simulations using TOUGH2 to evaluate the sensitivity of natural gas recovery, pressure buildup, and geothermal power generation performance of the combined CO2-EGR–CPG system to key reservoir and operational parameters. The reservoir parameters included horizontal permeability, permeability anisotropy, reservoir temperature, and pore-size- distribution index; while the operational parameters included wellbore diameter and ambient surface temperature. Using an example of a natural gas reservoir model, we also investigated the effects of different strategies of transitioning from the CO2-EGR stage to the CPG stage on the energy-recovery performance metrics and on the two-phase fluid-flow regime in the production well. The simulation results showed that overlapping the CO2-EGR and CPG stages, and having a relatively brief period of CO2 injection, but no production (which we called the CO2-plume establishment stage) achieved the best overall energy (natural gas and geothermal) recovery performance. Permeability anisotropy and reservoir temperature were the parameters that the natural gas recovery performance of the combined system was most sensitive to. The geothermal power generation performance was most sensitive to the reservoir temperature and the production wellbore diameter. The results of this study pave the way for future CPG-based geothermal power-generation optimization studies. For a CO2-EGR–CPG project, the results can be a guide in terms of the required accuracy of the reservoir parameters during exploration and data acquisition.

27.

Javanmard, H., A. Ebigbo, S.D.C. Walsh, M.O. Saar, and D. Vogler, No-Flow Fraction (NFF) permeability model for rough fractures under normal stress, Water Resources Research, 57/3, 2021. [Download PDF] [View Abstract]Flow through rock fractures is frequently represented using models that correct the cubic law to account for the effects of roughness and contact area. However, the scope of such models is often restricted to relatively smooth aperture fields under small confining stresses. This work studies the link between fracture permeability and fracture geometry under normal loads. Numerical experiments are performed to deform synthesized aperture fields of various correlation lengths and roughness values under normal stress. The results demonstrate that aperture roughness can more than triple for applied stresses up to 50 MPa – exceeding the valid range for roughness in most previously published models. Investigating the relationship between permeability and contact area indicates that the increase in flow obstructions due to the development of new contact points strongly depends on the correlation length of the unloaded aperture field. This study eliminates these dependencies by employing a parameter known as the No-Flow Fraction (NFF) to capture the effect of stagnation zones. With this concept, a new Cubic-law-based permeability model is proposed that significantly improves the accuracy of permeability estimations, compared to previous models. For cases, where the NFF is difficult to obtain, we introduce an empirical relationship to estimate the parameter from the aperture roughness. The new models yield permeability estimates accurate to within a factor of two of the simulated permeability in over three quarters of the 3000 deformed fractures studied. This compares with typical deviations of at least one order of magnitude for previously published permeability models.

26.

Hefny, M., C.-Z. Qin, M.O. Saar, and A. Ebigbo, Synchrotron-based pore-network modeling of two-phase flow in Nubian Sandstone and implications for capillary trapping of carbon dioxide, International Journal of Greenhouse Gas Control, 103/1031642, 2020. [Download PDF] [View Abstract]Depleted oil fields in the Gulf of Suez (Egypt) can serve as geothermal reservoirs for power production using a CO2-Plume Geothermal (CPG) system, while geologically sequestering CO2. This entails the injection of a substantial amount of CO2 into the highly permeable brine-saturated Nubian Sandstone. Numerical models of two-phase flow processes are indispensable for predicting the CO2-plume migration at a representative geological scale. Such models require reliable constitutive relationships, including relative permeability and capillary pressure curves. In this study, quasi-static pore-network modeling has been used to simulate the equilibrium positions of fluid-fluid interfaces, and thus determine the capillary pressure and relative permeability curves.
Three-dimensional images with a voxel size of 0.65 μm3 of a Nubian Sandstone rock sample have been obtained using Synchrotron Radiation X-ray Tomographic Microscopy. From the images, topological properties of pores/throats were constructed. Using a pore-network model, we performed a sequential primary drainage–main imbibition cycle of quasi-static invasion in order to quantify (1) the CO2 and brine relative permeability curves, (2) the effect of initial wetting-phase saturation (i.e. the saturation at the point of reversal from drainage to imbibition) on the residual–trapping potential, and (3) study the relative permeability–saturation hysteresis. The results illustrate the sensitivity of the pore-scale fluid-displacement and trapping processes on some key parameters (i.e. advancing contact angle, pore-body-to-throat aspect ratio, and initial wetting-phase saturation) and improve our understanding of the potential magnitude of capillary trapping in Nubian Sandstone.

25.

Ezekiel, J., A. Ebigbo, B. M. Adams, and M. O. Saar, Combining natural gas recovery and CO2-based geothermal energy
extraction for electric power generation, Applied Energy, 269/115012, 2020. [Download PDF] [View Abstract]We investigate the potential for extracting heat from produced natural gas and utilizing supercritical carbon dioxide (CO2) as a working uid for the dual purpose of enhancing gas recovery (EGR) and extracting geo- thermal energy (CO2-Plume Geothermal – CPG) from deep natural gas reservoirs for electric power generation, while ultimately storing all of the subsurface-injected CO2. Thus, the approach constitutes a CO2 capture double- utilization and storage (CCUUS) system. The synergies achieved by the above combinations include shared infrastructure and subsurface working uid. We integrate the reservoir processes with the wellbore and surface power-generation systems such that the combined system’s power output can be optimized. Using the subsurface uid ow and heat transport simulation code TOUGH2, coupled to a wellbore heat-transfer model, we set up an anticlinal natural gas reservoir model and assess the technical feasibility of the proposed system. The simulations show that the injection of CO2 for natural gas recovery and for the establishment of a CO2 plume (necessary for CPG) can be conveniently combined. During the CPG stage, following EGR, a CO2-circulation mass owrate of 110 kg/s results in a maximum net power output of 2 MWe for this initial, conceptual, small system, which is scalable. After a decade, the net power decreases when thermal breakthrough occurs at the production wells. The results con rm that the combined system can improve the gas eld’s overall energy production, enable CO2 sequestration, and extend the useful lifetime of the gas eld. Hence, deep (partially depleted) natural gas re- servoirs appear to constitute ideal sites for the deployment of not only geologic CO2 storage but also CPG.

24.

Cunningham, A. B., H. Class, A. Ebigbo, R. Gerlach, A. J. Phillips, and J. Hommel, Field-scale modeling of microbially induced calcite precipitation, Computational Geosciences, 23/2, pp. 399-414, 2019. [Download PDF] [View Abstract]The biogeochemical process known as microbially induced calcite precipitation (MICP) is being investigated for engineering and material science applications. To model MICP process behavior in porous media, computational simulators must couple flow, transport, and relevant biogeochemical reactions. Changes in media porosity and permeability due to biomass growth and calcite precipitation, as well as their effects on one another must be considered. A comprehensive Darcy-scale model has been developed by Ebigbo et al. (Water Resour. Res. 48(7), W07519, 2012) and Hommel et al. (Water Resour. Res. 51, 3695–3715, 2015) and validated at different scales of observation using laboratory experimental systems at the Center for Biofilm Engineering (CBE), Montana State University (MSU). This investigation clearly demonstrates that a close synergy between laboratory experimentation at different scales and corresponding simulation model development is necessary to advance MICP application to the field scale. Ultimately, model predictions of MICP sealing of a fractured sandstone formation, located 340.8 m below ground surface, were made and compared with corresponding field observations. Modeling MICP at the field scale poses special challenges, including choosing a reasonable model-domain size, initial and boundary conditions, and determining the initial distribution of porosity and permeability. In the presented study, model predictions of deposited calcite volume agree favorably with corresponding field observations of increased injection pressure during the MICP fracture sealing test in the field. Results indicate that the current status of our MICP model now allows its use for further subsurface engineering applications, including well-bore cement sealing and certain fracture-related applications in unconventional oil and gas production.

23.

Schädle, P., P. Zulian, D. Vogler, S. Bhopalam R., M.G.C. Nestola, A. Ebigbo, R. Krause, and M.O. Saar, 3D non-conforming mesh model for flow in fractured porous media using Lagrange multipliers, Computers & Geosciences, 132, pp. 42-55, 2019. [Download PDF] [View Abstract]This work presents a modeling approach for single-phase flow in 3D fractured porous media with non-conforming meshes. To this end, a Lagrange multiplier method is combined with a parallel variational transfer approach. This Lagrange multiplier method enables the use of non-conforming meshes and depicts the variable coupling between fracture and matrix domain. The variational transfer allows general, accurate, and parallel projection of variables between non-conforming meshes (i.e. between fracture and matrix domain). Comparisons of simulations with 2D benchmarks show good agreement, and the applied finite element Lagrange multiplier spaces show good performance. The method is further evaluated on 3D fracture networks by comparing it to results from conforming mesh simulations which were used as a reference. Application to realistic fracture networks with hundreds of fractures is demonstrated. Mesh size and mesh convergence are investigated for benchmark cases and 3D fracture network applications. Results demonstrate that the Lagrange multiplier method, in combination with the variational transfer approach, is capable of modeling single-phase flow through realistic 3D fracture networks.

22.

Hobé, A., D. Vogler, M.P. Seybold, A. Ebigbo, R.R. Settgast, and M.O. Saar, Estimating Fluid Flow Rates through Fracture Networks using Combinatorial Optimization, Advances in Water Resources, 122, pp. 85-97, 2018. [Download PDF] [View Abstract]To enable fast uncertainty quantification of fluid flow in a discrete fracture network (DFN), we present two approaches to quickly compute fluid flow in DFNs using combinatorial optimization algorithms. Specifically, the presented Hanan Shortest Path Maxflow (HSPM) and Intersection Shortest Path Maxflow (ISPM) methods translate DFN geometries and properties to a graph on which a max flow algorithm computes a combinatorial flow, from which an overall fluid flow rate is estimated using a shortest path decomposition of this flow. The two approaches are assessed by comparing their predictions with results from explicit numerical simulations of simple test cases as well as stochastic DFN realizations covering a range of fracture densities. Both methods have a high accuracy and very low computational cost, which can facilitate much-needed in-depth analyses of the propagation of uncertainty in fracture and fracture-network properties to fluid flow rates.

21.

Niederau, J., A. Ebigbo, G. Marquart, J. Arnold, and C. Clauser, On the impact of spatially heterogenous permeability on free convection in the Perth Basin, Australia, Geothermics, 66, pp. 119-133, 2017. [Download PDF] [View Abstract]We study the impact of spatially heterogeneous permeability on the formation and shape of hydrothermal porous flow convection in the Yarragadee Aquifer by modelling three simulation scenarios, each with differing permeability distributions. In all scenarios, the southern part of the model is characterised by convection rolls, while the north is dominated by a stable region of decreased temperatures at depth due to hydraulic interaction with shallower aquifers. This suggests that reservoir structure is a first-order controlling factor for the formation of the free con- vective system. The convective system adjusts to the spatially heterogeneous permeability distribution, yielding locally different convection patterns.

20.

Büsing, H., C. Vogt, A. Ebigbo, and N. Kitzsch, Numerical study on CO2 leakage detection using electrical streaming potential data, Water Resour. Res, 53, pp. 1-15, 2017. [Download PDF] [View Abstract]We study the feasibility of detecting carbon dioxide (CO2) movement in the overburden of a storage reservoir due to CO2 leakage through an abandoned well by self-potential (SP) measurements at the surface. This is achieved with three-dimensional numerical (SP) modeling of two-phase fluid flow and electrokinetic coupling between flow and streaming potential. We find that, in typical leakage scenarios, for leaky and/or injection wells with conductive metal casing, self-potential signals originating from injection can be identified at the surface. As the injection signal is also observed at the leaky well with metal casing, SP monitoring can be applied for detecting abandoned wells. However, leakage signals are much smaller than the injection signal and thus masked by the latter. We present three alternatives to overcome this problem: (i) simulate the streaming potential of the nonleaky scenario and subtract the result from the measured streaming potential data; (ii) exploit the symmetry of the injection signal by analyzing the potential difference of dipoles with the dipole center at the injection well; or (iii) measure SP during periods where the injection is interrupted. In our judgement, the most promising approach for detecting a real-world CO2 leakage is by combining methods (i) and (ii), because this would give the highest signal from the leakage and omit signals originating from the injection well. Consequently, we recommend SP as monitoring method for subsurface CO2 storage, especially because a leakage can be detected shortly after the injection started even before CO2 arrives at the leaky well.

19.

Ebigbo, A., J. Niederau, G. Marquart, I. Dini, M. Thorwart, W. Rabbel, R. Pechnig, R. Bertani, and C. Clauser, Influence of depth, temperature, and structure of a crustal heat source on the geothermal reservoirs of Tuscany: numerical modelling and sensitivity study, Geothermal Energy, 4/5, 2016. [Download PDF] [View Abstract]Granitoid intrusions are the primary heat source of many deep geothermal reservoirs in Tuscany. The depth and shape of these plutons, characterised in this study by a prominent seismic reflector (the K horizon), may vary significantly within the spatial scale of interest. In an exploration field, simulations reveal the mechanisms by which such a heat source influences temperature distribution. A simple analysis quantifies the sensitivity of potentially measurable indicators (i.e. vertical temperature profiles and surface heat flow) to variations in depth, temperature, and shape of the heat source within given ranges of uncertainty.

18.

Seidler, R., K. Padalkina, H.M. Buecker, A. Ebigbo, M. Herty, G. Marquart, and J. Niederau, Optimal experimental design for reservoir property estimates in geothermal exploration, Computational Geomechanics, 20/375, 2016. [Download PDF] [View Abstract]During geothermal reservoir development, drilling deep boreholes turns out to be extremely expensive and risky. Thus, it is of great importance to work out the details of suitable borehole locations in advance. Here, given a set of existing boreholes, we demonstrate how a sophisticated numerical technique called optimal experimental design helps to find a location of an additional exploratory borehole that reduces risk and, ultimately, saves cost. More precisely, the approach minimizes the uncertainty when deducing the effective permeability of a buried reservoir layer from a temperature profile measured in this exploratory borehole. In this paper, we (1) outline the mathematical formulation in terms of an optimization problem, (2) describe the numerical implementation involving various software components, and (3) apply the method to a 3D numerical simulation model representing a real geothermal reservoir in northern Italy. Our results show that optimal experimental design is conceptually and computationally feasible for industrial-scale applications. For the particular reservoir and the estimation of permeability from temperature, the optimal location of the additional borehole coincides with regions of high flow rates and large deviations from the mean temperature of the reservoir layer in question. Finally, the presentation shows that, methodologically, the optimization method can be generalized from estimating permeability to finding any other reservoir properties.

17.

Ebigbo, A., P.A. Lang, A. Paluszny, and R.W. Zimmerman, Inclusion-based effective medium models for the permeability of a 3D fractured rock mass, Transport in Porous Media, 113/1, pp. 137-158, 2016. [Download PDF] [View Abstract]Effective permeability is an essential parameter for describing fluid flow through fractured rock masses. This study investigates the ability of classical inclusion-based effective medium models (following the work of Sævik et al. in Transp Porous Media 100(1):115–142, 2013. doi:10.1007/s11242-013-0208-0) to predict this permeability, which depends on several geometric properties of the fractures/networks. This is achieved by comparison of various effective medium models, such as the symmetric and asymmetric self-consistent schemes, the differential scheme, and Maxwell’s method, with the results of explicit numerical simulations of mono- and poly-disperse isotropic fracture networks embedded in a permeable rock matrix. Comparisons are also made with the Hashin–Shtrikman bounds, Snow’s model, and Mourzenko’s heuristic model (Mourzenko et al. in Phys Rev E 84:036–307, 2011. doi:10.1103/PhysRevE.84.036307). This problem is characterised by two small parameters, the aspect ratio of the spheroidal fractures, α, and the ratio between matrix and fracture permeability, κ. Two different regimes can be identified, corresponding to α/κ<1 and α/κ>1. The lower the value of α/κ, the more significant is flow through the matrix. Due to differing flow patterns, the dependence of effective permeability on fracture density differs in the two regimes. When α/κ≫1, a distinct percolation threshold is observed, whereas for α/κ≪1, the matrix is sufficiently transmissive that such a transition is not observed. The self-consistent effective medium methods show good accuracy for both mono- and polydisperse isotropic fracture networks. Mourzenko’s equation is very accurate, particularly for monodisperse networks. Finally, it is shown that Snow’s model essentially coincides with the Hashin–Shtrikman upper bound.

16.

Qin, C.-Z., S.M. Hassanizadeh, and A. Ebigbo, Pore-scale network modeling of microbially induced calcium carbonate precipitation: Insight into scale dependence of biogeochemical reaction rates, Water Resources Research/52, 2016. [Download PDF] [View Abstract]The engineering of microbially induced calcium carbonate precipitation (MICP) has attracted much attention in a number of applications, such as sealing of CO2 leakage pathways, soil stabilization, and subsurface remediation of radionuclides and toxic metals. The goal of this work is to gain insight into pore-scale processes of MICP and scale dependence of biogeochemical reaction rates. This will help us develop efficient field-scale MICP models. In this work, we have developed a comprehensive pore-network model for MICP, with geochemical speciation calculated by the open-source PHREEQC module. A numerical pseudo-3-D micromodel as the computational domain was generated by a novel pore-network generation method. We modeled a three-stage process in the engineering of MICP including the growth of biofilm, the injection of calcium-rich medium, and the precipitation of calcium carbonate. A number of test cases were conducted to illustrate how calcite precipitation was influenced by different operating conditions. In addition, we studied the possibility of reducing the computational effort by simplifying geochemical calculations. Finally, the effect of mass transfer limitation of possible carbonate ions in a pore element on calcite precipitation was explored.

15.

Hommel, J., E. Lauchnor, A. Phillips, R. Gerlach, A.B. Cunningham, R. Helmig, A. Ebigbo, and H. Class, A revised model for microbially induced calcite precipitation: Improvements and new insights based on recent experiments, Water Resources Research, 51/5, pp. 3695-3715, 2015. [Download PDF] [View Abstract]The model for microbially induced calcite precipitation (MICP) published by Ebigbo et al. (2012) has been improved based on new insights obtained from experiments and model calibration. The challenge in constructing a predictive model for permeability reduction in the underground with MICP is the quantification of the complex interaction between flow, transport, biofilm growth, and reaction kinetics. New data from Lauchnor et al. (2015) on whole-cell ureolysis kinetics from batch experiments were incorporated into the model, which has allowed for a more precise quantification of the relevant parameters as well as a simplification of the reaction kinetics in the equations of the model. Further, the model has been calibrated objectively by inverse modeling using quasi-1D column experiments and a radial flow experiment. From the postprocessing of the inverse modeling, a comprehensive sensitivity analysis has been performed with focus on the model input parameters that were fitted in the course of the model calibration. It reveals that calcite precipitation and concentrations of math formula and math formula are particularly sensitive to parameters associated with the ureolysis rate and the attachment behavior of biomass. Based on the determined sensitivities and the ranges of values for the estimated parameters in the inversion, it is possible to identify focal areas where further research can have a high impact toward improving the understanding and engineering of MICP.

14.

Hommel, J., E. Lauchnor, R. Gerlach, A.B. Cunningham, A. Ebigbo, R. Helmig, and H. Class, Investigating the influence of the initial biomass distribution and injection strategies on biofilm- mediated calcite precipitation in porous media, Transport in Porous Media, 2015. [Download PDF] [View Abstract]Attachment of bacteria in porous media is a complex mixture of processes resulting in the transfer and immobilization of suspended cells onto a solid surface within the porous medium. Quantifying the rate of attachment is difficult due to the many simultaneous processes possibly involved in attachment, including straining, sorption, and sedimentation, and the difficulties in measuring metabolically active cells attached to porous media. Preliminary experiments confirmed the difficulty associated with measuring active Sporosarcina pasteurii cells attached to porous media. However, attachment is a key process in applications of biofilm-mediated reactions in the subsurface such as microbially induced calcite precipitation. Independent of the exact processes involved, attachment determines both the distribution and the initial amount of attached biomass and as such the initial reaction rate. As direct experimental investigations are difficult, this study is limited to a numerical investigation of the effect of various initial biomass distributions and initial amounts of attached biomass. This is performed for various injection strategies, changing the injection rate as well as alternating between continuous and pulsed injections. The results of this study indicate that, for the selected scenarios, both the initial amount and the distribution of attached biomass have minor influence on the Ca2+ precipitation efficiency as well as the distribution of the precipitates compared to the influence of the injection strategy. The influence of the initial biomass distribution on the resulting final distribution of the precipitated calcite is limited, except for the continuous injection at intermediate injection rate. But even for this injection strategy, the Ca2+ precipitation efficiency shows no significant dependence on the initial biomass distribution.

13.

Helmig, R., B. Flemisch, M. Wolff, A. Ebigbo, and H. Class, Model coupling for multiphase flow in porous media, Advances in Water Resources, 51/7, pp. 52-66, 2013. [Download PDF] [View Abstract]Numerical models for flow and transport in porous media are valid for a particular set of processes, scales, levels of simplification and abstraction, grids etc. The coupling of two or more specialised models is a method of increasing the overall range of validity while keeping the computational costs relatively low. Several coupling concepts are reviewed in this article with a focus on the authors’ work in this field. The concepts are divided into temporal and spatial coupling concepts, of which the latter is subdivided into multi-process, multi-scale, multi-dimensional, and multi-compartment coupling strategies. Examples of applications for which these concepts can be relevant include groundwater protection and remediation, carbon dioxide storage, nuclear-waste disposal, soil dry-out and evaporation processes as well as fuel cells and technical filters.

12.

Cunningham, A.B., E. Lauchnor, J. Eldring, E. Esposito, A.C. Mitchell, R. Gerlach, A.J. Phillips, A. Ebigbo, and L.H. Spangler, Abandoned well CO2 leakage mitigation using biologically induced mineralization: current progress and future directions, Greenhouse Gases: Science & Technology, 3, pp. 40-49, 2013. [Download PDF] [View Abstract]Methods of mitigating leakage or re-plugging abandoned wells before exposure to CO2are of high potential interest to prevent leakage of CO2 injected for geologic carbon sequestration in depleted oil and gas reservoirs where large numbers of abandoned wells are often present. While CO2resistant cements and ultrafine cements are being developed, technologies that can be delivered via low viscosity fluids could have significant advantages including the ability to plug small aperture leaks such as fractures or delamination interfaces. Additionally there is the potential to plug rock formation pore space around the wellbore in particularly problematic situations. We are carrying out research on the use of microbial biofilms capable of inducing the precipitation of crystalline calcium carbonate using the process of ureolysis. This method has the potential to reduce well bore permeability, coat cement to reduce CO2–related corrosion, and lower the risk of unwanted upward CO2 migration. In this spotlight, we highlight research currently underway at the Center for Biofilm Engineering (CBE) at Montana State University (MSU) in the area of ureolytic biomineralization sealing for reducing CO2 leakage risk. This research program combines two novel core testing systems and a 3-dimensional simulation model to investigate biomineralization under both radial and axial flow conditions and at temperatures and pressures which permit CO2 to exist in the supercritical state. This combination of modelling and experimentation is ultimately aimed at developing and verifying biomineralization sealing technologies and strategies which can successfully be applied at the field scale for carbon capture and geological storage (CCGS) projects. © 2013 Society of Chemical Industry and John Wiley & Sons, Ltd

11.

Kissinger, A., R. Helmig, A. Ebigbo, H. Class, T. Lange, M. Sauter, M. Heitfeld, J. Klünker, and W. Jahnke, Hydraulic fracturing in unconventional gas reservoirs: risks in the geological system, part 2, Environmental Earth Sciences, 70/8, pp. 3855-3873, 2013. [Download PDF] [View Abstract]Hydraulic fracturing is a method used for the production of unconventional gas resources. Huge amounts of so-called fracturing fluid (10,000–20,000 m3) are injected into a gas reservoir to create fractures in solid rock formations, upon which mobilised methane fills the pore space and the fracturing fluid is withdrawn. Hydraulic fracturing may pose a threat to groundwater resources if fracturing fluid or brine can migrate through fault zones into shallow aquifers. Diffuse methane emissions from the gas reservoir may not only contaminate shallow groundwater aquifers, but also escape into the atmosphere where methane acts as a greenhouse gas. The working group “Risks in the Geological System” as part of ExxonMobil’s hydrofracking dialogue and information dissemination processes was tasked with the assessment of possible hazards posed by migrating fluids as a result of hydraulic fracturing activities. In this work, several flow paths for fracturing fluid, brine and methane are identified and scenarios are set up to qualitatively estimate under what circumstances these fluids would leak into shallower layers. The parametrisation for potential hydraulic fracturing sites in North Rhine-Westphalia and Lower Saxony (both in Germany) is derived from literature using upper and lower bounds of hydraulic parameters. The results show that a significant fluid migration is only possible if a combination of several conservative assumptions is met by a scenario.

10.

Lange, T., M. Sauter, M. Heitfeld, K. Schetelig, K. Brosig, W. Jahnke, A. Kissinger, R. Helmig, A. Ebigbo, and H. Class, Hydraulic fracturing in unconventional gas reservoirs: risks in the geological system, part 1, Environmental Earth Sciences, 70/8, pp. 3839-3853, 2013. [Download PDF] [View Abstract]Hydraulic fracturing of unconventional gas reservoirs rapidly developed especially in the USA to an industrial scale during the last decade. Potential adverse effects such as the deterioration of the quality of exploitable groundwater resources, areal footprints, or even the climate impact were not assessed. Because hydraulic fracturing has already been practised for a long time also in conventional reservoirs, the expansion into the unconventional domain was considered to be just a minor but not a technological step, with potential environmental risks. Thus, safety and environmental protection regulations were not critically developed or refined. Consequently, virtually no baseline conditions were documented before on-site applications as proof of evidence for the net effect of environmental impacts. Not only growing concerns in the general public, but also in the administrations in Germany promoted the commissioning of several expert opinions, evaluating safety, potential risks, and footprints of the technology in focus. The first two publications of the workgroup “Risks in the Geological System” of the independent “Information and Dialogue process on hydraulic fracturing” (commissioned by ExxonMobil Production Deutschland GmbH) comprises the strategy and approaches to identify and assess the potential risks of groundwater contamination of the exploitable groundwater system in the context of hydraulic fracturing operations in the Münsterland cretaceous basin and the Lower Saxony Basin, Germany. While being specific with respect to local geology and the estimation of effective hydraulic parameters, generalized concepts for the contamination risk assessment were developed. The work focuses on barrier effectiveness of different units of the overburden with respect to the migration of fracking fluids and methane, and considers fault zones as potential fluid pathway structures.

9.

Ebigbo, A., F. Golfier, and M. Quintard, A coupled, pore-scale model for methanogenic microbial activity in underground hydrogen storage, Advances in Water Resources, 61, pp. 74-85, 2013. [Download PDF] [View Abstract]Underground hydrogen storage (UHS) as a means of energy storage is an efficient way of compensating for seasonal fluctuations in the availability of energy. One important factor which influences this technology is the activity of methanogenic microorganisms capable of utilising hydrogen and carbon dioxide for metabolism and leading to a change in the stored gas composition. A coupled, pore-scale model is presented which aids in the investigation of the mechanisms that govern the conversion of hydrogen to methane, i.e. advective hydrogen flow, its diffusion into microbial biofilms of multiple species, and its consumption within these biofilms. The model assumes that spherical grains are coated by a film of residual water and treats the biofilm development within each film in a quasi one-dimensional manner. A sample simulation using the presented model illustrates the biofilm growth process in these films as well as the competition between three different microbial species: methanogens, acetogens, and acetotrophs.

8.

Ebigbo, A., A. Phillips, R. Gerlach, R. Helmig, A.B. Cunningham, and H. Class, Darcy-scale modeling of microbially induced carbonate mineral precipitation in sand columns, Water Resources Research, 48/7, W07519, 2012. [Download PDF] [View Abstract][1] This investigation focuses on the use of microbially induced calcium carbonate precipitation (MICP) to set up subsurface hydraulic barriers to potentially increase storage security near wellbores of CO2 storage sites. A numerical model is developed, capable of accounting for carbonate precipitation due to ureolytic bacterial activity as well as the flow of two fluid phases in the subsurface. The model is compared to experiments involving saturated flow through sand-packed columns to understand and optimize the processes involved as well as to validate the numerical model. It is then used to predict the effect of dense-phase CO2 and CO2-saturated water on carbonate precipitates in a porous medium.

7.

van Noorden, T.L., I.S. Pop, A. Ebigbo, and R. Helmig, An upscaled model for biofilm growth in a thin strip, Water Resources Research, 46/6, W06505, 2010. [Download PDF] [View Abstract][1] The focus of this paper is the derivation of an effective model for biofilm growth in a porous medium and its effect on fluid flow. The starting point is a pore-scale model in which the local geometry of the pore is represented as a thin strip. The model accounts for changes in pore volume due to biomass accumulation. As the ratio of the width of the strip to its length approaches zero, we apply a formal limiting argument to derive a one-dimensional upscaled (effective) model. For a better understanding of the terms and parameters involved in the equations derived here, we compare these equations to a well-known core-scale model from the literature.

6.

Ebigbo, A., R. Helmig, A.B. Cunningham, H. Class, and R. Gerlach, Modelling biofilm growth in the presence of carbon dioxide and water flow in the subsurface, Advances in Water Resources, 33/7, pp. 762-781, 2010. [Download PDF] [View Abstract]The concentration of greenhouse gases – particularly carbon dioxide (CO2) – in the atmosphere has been on the rise in the past decades. One of the methods which have been proposed to help reduce anthropogenic CO2 emissions is the capture of CO2from large, stationary point sources and storage in deep geological formations. The caprock is an impermeable geological layer which prevents the leakage of stored CO2, and its integrity is of utmost importance for storage security. Due to the high pressure build-up during injection, the caprock in the vicinity of the well is particularly at risk of fracturing. Biofilms could be used as biobarriers which help prevent the leakage of CO2 through the caprock in injection well vicinity by blocking leakage pathways. The biofilm could also protect well cement from corrosion by CO2-rich brine. The goal of this paper is to develop and test a numerical model which is capable of simulating the development of a biofilm in a CO2 storage reservoir. This involves the description of the growth of the biofilm, flow and transport in the geological formation, and the interaction between the biofilm and the flow processes. Important processes which are accounted for in the model include the effect of biofilm growth on the permeability of the formation, the hazardous effect of supercritical CO2 on suspended and attached bacteria, attachment and detachment of biomass, and two-phase fluid flow processes. The model is tested by comparing simulation results to experimental data.

5.

Skjaelaaen, I., A. Ebigbo, M. Espedal, and R. Helmig, A model for transport of hydrogen sulfide in oil- and water-saturated porous media, Computing and Visualization in Science, 13/6, pp. 265-273, 2010. [Download PDF] [View Abstract]In several oilfields, reservoir souring by generation of hydrogen sulfide (H2S) occurs in secondary recovery during which seawater is injected into originally sweet reservoirs. At the production site, high concentrations of H2S can cause severe damage to both equipment and human personnel. Proper modeling of H2S concentration in produced fluids can be useful for decision-making during field development design. We present a model for the transport of H2S in an oil- and water-saturated, water-wet porous medium. The different retardation mechanisms for the H2S are described. For the adsorption of H2S to rock, we include two distinct phases of adsorption. In addition, we introduce a functional relationship between adsorption capacity and permeability. As H2S mixes with oil, fractions become immobile as part of the residual oil. Communicated by Gabriel wittum. This article is dedicated to the memory of our dear colleague, friend and mentor, Magne Espedal, who passed away during the preparation of this manuscript.

4.

Kopp, A., A. Ebigbo, A. Bielinski, H. Class, and R. Helmig, Numerical simulation of temperature changes caused by CO2 injection in geological reservoirs, AAPG Studies in Geology, 59/26, pp. 439-456, 2009. [Download PDF] [View Abstract]Injection of CO 2 into the subsurface for geological storage has an effect on the temperature of the storage formation and the CO 2 itself. Numerical investigations are an essential tool in describing the relevant processes that determine such changes and the impact they may have on the migration and the storage mechanisms of CO 2 in the subsurface. This chapter focuses on the numerical simulation of such thermal effects and their consequences. Simulating the temperature changes in a storage site can be of interest for temperature-based monitoring. Determining whether or how such thermal effects change the transport of CO 2 in the formation is important for the success of a CO 2 storage effort. In particular, this chapter examines a leakage scenario and how temperature changes could affect the leakage flow. The second part of the chapter presents results of a complex reservoir-scale simulation. The target formation forms an anticlinal structure at a depth of about 570-900 m (1870-2953 ft). Strong temperature effects can be expected because of the possible tran Numerical simulation of temperature changes caused by CO2 injection in geological reservoirs. Available from: https://www.researchgate.net/publication/230838241_Numerical_simulation_of_temperature_changes_caused_by_CO2_injection_in_geological_reservoirs [accessed May 3, 2017].

3.

Class, H., A. Ebigbo, R Helmig, H.K. Dahle, J.M. Nordbotten, M.A. Celia, P. Audigane, M. Darcis, J. Ennis-King, and Y. Fan, A benchmark study on problems related to CO2 storage in geologic formations , Computational Geosciences, 13/4, Sp. Iss. SI, pp. 409-434, 2009. [Download PDF] [View Abstract]This paper summarises the results of a benchmark study that compares a number of mathematical and numerical models applied to specific problems in the context of carbon dioxide (CO2) storage in geologic formations. The processes modelled comprise advective multi-phase flow, compositional effects due to dissolution of CO2 into the ambient brine and non-isothermal effects due to temperature gradients and the Joule–Thompson effect. The problems deal with leakage through a leaky well, methane recovery enhanced by CO2 injection and a reservoir-scale injection scenario into a heterogeneous formation. We give a description of the benchmark problems then briefly introduce the participating codes and finally present and discuss the results of the benchmark study.

2.

Ebigbo, A., H. Class, and R. Helmig, CO2 leakage through an abandoned well: problem- oriented benchmarks, Computational Geosciences, 11/2, pp. 103-115, 2007. [Download PDF] [View Abstract]The efficiency and sustainability of carbon dioxide (CO2) storage in deep geological formations crucially depends on the integrity of the overlying cap-rocks. Existing oil and gas wells, which penetrate the formations, are potential leakage pathways. This problem has been discussed in the literature, and a number of investigations using semi-analytical mathematical approaches have been carried out by other authors to quantify leakage rates. The semi-analytical results are based on a number of simplifying assumptions. Thus, it is of great interest to assess the influence of these assumptions. We use a numerical model to compare the results with those of the semi-analytical model. Then we ease the simplifying restrictions and include more complex thermodynamic processes including sub- and supercritical fluid properties of CO2 and non-isothermal as well as compositional effects. The aim is to set up problem-oriented benchmark examples that allow a comparison of different modeling approaches to the problem of CO2 leakage.

1.

Class, H., A. Bielinski, R. Helmig, A. Kopp, and A. Ebigbo, Numerical simulation of CO2 storage in geological formations, Chemie Ingenieur Technik, 78/4, pp. 445-452, 2006. [Download PDF] [View Abstract]Die Speicherung von Kohlendioxid in geologischen Formationen wird derzeit als ein möglicher Beitrag zur Reduktion von Treibhausgaskonzentrationen in der Atmosphäre diskutiert und untersucht. Ein wichtiges Werkzeug begleitend zu experimentellen Untersuchungsmethoden ist die numerische Simulation. Hier wird ein Einblick in die physikalischen bzw. thermodynamischen Vorgänge im Untergrund während und nach einer Injektion von Kohlendioxid gegeben sowie deren modellkonzeptionelle Beschreibung durch nichtisotherme Mehrphasensysteme dargestellt. Die elementaren Schritte der physikalisch/mathematischen Modellbildung und numerischen Lösung der daraus entstehenden Gleichungssysteme werden erklärt. Anhand von Simulationsbeispielen werden dominierende Prozesse während und nach einer Injektion diskutiert.

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### PROCEEDINGS REFEREED

5.

Niederau, J., A. Ebigbo, and M. Saar, Characterization of Subsurface Heat-Transport Processes in the Canton of Aargau Using an Integrative Workflow, Proceedings World Geothermal Congress 2020, (

*in press*). [View Abstract]In a referendum in May 2017, Switzerland decided to phase out nuclear power in favor of further developing renewable energy sources. One of these energy sources is geothermal energy, which, as a base-load technology, fills a niche complementary to solar and wind energy. A known surface-heat-flow anomaly exists in the Canton of Aargau in Northern Switzerland. With measured specific heat-flow values of up to 140 mW m-2, it is an area of interest for deep geothermal energy exploration. In a pilot study, which started in late 2018, we want to characterize the heat-flow distribution in the vicinity of the anomaly in more detail to facilitate future assessment of the geothermal potential of this region. To achieve a complete characterization of the heat-flow values as well as their spatial uncertainty, we develop a workflow comprising: (i) assimilation and homogenization of different types of geologic data, (ii) development of a geological model with focus on heat transport, and (iii) numerical simulations of the dominant heat-transport processes. Due to its nature as a pilot study, the developed workflow needs to be integrative and adaptable. This means that data generated during the course of the project can easily be integrated in the modeling and simulation process, and that the generated workflow should easily be adaptable to other regions for potential future studies. One further goal of this project is that the generated models and simulations provide insights into the nature of the heat-flow anomaly in Northern Switzerland and to test the hypothesis that upward migration of deep geothermal fluids along structural pathways is the origin of this particular heat-flow anomaly.4.

Niederau, J., A. Ebigbo, and M. O. Saar, Characterization of Subsurface Heat-Transport Processes in the Canton of Aargau Using an Integrative Workflow, Proceedings World Geothermal Congress 2020, Reykjavik, Iceland, April 26 - May 2, 2020, 2020. [View Abstract]In a referendum in May 2017, Switzerland decided to phase out nuclear power in favor of further developing renewable energy sources. One of these energy sources is geothermal energy, which, as a base-load technology, fills a niche complementary to solar and wind energy. A known surface-heat-flow anomaly exists in the Canton of Aargau in Northern Switzerland. With measured specific heat-flow values of up to 140 mW m-2, it is an area of interest for deep geothermal energy exploration. In a pilot study, which started in late 2018, we want to characterize the heat-flow distribution in the vicinity of the anomaly in more detail to facilitate future assessment of the geothermal potential of this region. To achieve a complete characterization of the heat-flow values as well as their spatial uncertainty, we develop a workflow comprising: (i) assimilation and homogenization of different types of geologic data, (ii) development of a geological model with focus on heat transport, and (iii) numerical simulations of the dominant heat-transport processes. Due to its nature as a pilot study, the developed workflow needs to be integrative and adaptable. This means that data generated during the course of the project can easily be integrated in the modeling and simulation process, and that the generated workflow should easily be adaptable to other regions for potential future studies. One further goal of this project is that the generated models and simulations provide insights into the nature of the heat-flow anomaly in Northern Switzerland and to test the hypothesis that upward migration of deep geothermal fluids along structural pathways is the origin of this particular heat-flow anomaly.

3.

Hefny, M., C.-Z. Qin, A. Ebigbo, J. Gostick, M.O. Saar, and M. Hammed, CO2-Brine flow in Nubian Sandstone (Egypt): Pore-Network Modeling using Computerized Tomography Imaging, European Geothermal Congress (EGC), 2019. [Download PDF] [View Abstract]The injection of CO2 into the highly permeable Nubian Sandstone of a depleted oil field in the central Gulf of Suez Basin (Egypt) is an effective way to extract enthalpy from deep sedimentary basins while sequestering CO2, forming a so-called CO2-Plume Geothermal (CPG) system. Subsurface flow models require constitutive relationships, including relative permeability and capillary pressure curves, to determine the CO2-plume migration at a representative geological scale.
Based on the fluid-displacement mechanisms, quasi-static pore-network modeling has been used to simulate the equilibrium positions of fluid-fluid interfaces, and thus determine the capillary pressure and relative permeability curves. 3D images with a voxel size of 650 nm3 of a Nubian Sandstone rock sample have been obtained using Synchrotron Radiation X-ray Tomographic Microscopy. From the images, topological properties of pores/throats were constructed. Using a pore-network model, we performed a cycle of primary drainage of quasi-static invasion to quantify the saturation of scCO2 at the point of a breakthrough with emphasis on the relative permeability–saturation relationship.
We compare the quasi-static flow simulation results from the pore-network model with experimental observations. It shows that the Pc-Sw curve is very similar to those observed experimentally.

2.

Hommel, J., A. Ebigbo, R. Gerlach, A. B. Cunningham, R. Helmig, and H. Class, Finding a Balance between Accuracy and Effort For Modeling Biomineralization, Energy Procedia, 97, pp. 379-386, 2016. [Download PDF]

1.

Hommel, J., A. B. Cunningham, R. Helmig, A. Ebigbo, and H. Class, Numerical Investigation of Microbially Induced Calcite Precipitation as a Leakage Mitigation Technology, Energy Procedia, 40, pp. 392-397, 2013. [Download PDF]

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### THESES

2.

Ebigbo, A., Modelling of biofilm growth and its influence on CO2 and water (two-phase) flow in porous media, Dissertation, University of Stuttgart, 131 pp., 2009. [Download PDF] [View Abstract]Bacterial biofilms are groups of microbial cells attached to surfaces and to each other. Cells in a biofilm are protected from adverse external conditions. In natural environments, this attached mode of growth is more successful than the suspended mode, and a major portion of microbial activity takes place at surfaces. In porous media, biofilms are used as bioreactors (e.g, in wastewater treatment) and as biobarriers (e.g., in enhanced oil recovery). They are also used in the containment and degradation of contaminants in groundwater aquifers. It has been proposed that biofilms be used as biobarriers for the mitigation of carbon dioxide (CO2) leakage from a geological storage reservoir. The concentration of greenhouse gases -- particularly carbon dioxide (CO2) -- in the atmosphere has been on the rise in the past decades. One of the methods which have been proposed to help reduce anthropogenic CO2 emissions is the capture of CO2 from large, stationary point sources and storage in deep geological formations. The caprock is an impermeable geological layer which prevents the leakage of stored CO2, and its integrity is of utmost importance for storage security. As mentioned above, biofilms could be used as biobarriers which help prevent the leakage of CO2 through the caprock in injection well vicinity. Due to the high pressure build-up during injection, the caprock in the vicinity of the well is particularly at risk of fracturing. The biofilm could also protect well cement from corrosion by CO2-rich brine. The goal of this work is to develop and test a numerical model which is capable of simulating the development of a biofilm in a CO2 storage reservoir. This involves the description of the growth of the biofilm, flow and transport in the geological formation, and the interaction between the biofilm and the flow processes. Important processes which are accounted for in the model include the effect of biofilm growth on the permeability of the formation, the hazardous effect of supercritical CO2 on suspended and attached bacteria, attachment and detachment of biomass, and two-phase fluid flow processes. The partial differential equations which describe the system are discretised in space with a vertex-centered finite volume method, and an implicit Euler scheme is used for time discretisation. The model is tested by comparing simulation results to experimental data. In a test case simulation, the model predicts the extent of biomass accumulation near an injection well and its effect on the permeability of the formation. The simulations show that the biobarrier is only effective for a limited amount of time. Regular injection of nutrients would be necessary to sustain the biofilm. In future work, the model could be extended to account for the active precipitation of minerals by the biofilm which would lead to a more enduring barrier. The model also needs to be extended to account for more than one growth-limiting factor. This would allow for the simulation of injection strategies which aim at growing a biofilm at some distance from the injection well. Biofilme, die in einem porösen Medium wachsen, blockieren Poren und verändern dabei die Eigenschaften des porösen Mediums. Diese veränderten Eigenschaften werden bei der biologischen Filtration (z. B. bei der Abwasserbehandlung), bei der biologischen Altlastensanierung (z. B. für die Erstellung hydraulischer Barrieren) und bei anderen Fragestellungen auf diesem Gebiet genutzt. Eine hydraulische Barriere biologischen Ursprungs könnte z. B. auch in einer geologischen Kohlendioxid-Lagerstätte eingesetzt werden, um das Entweichen von CO2 zu verhindern. CO2 ist das derzeit für am Wichtigsten erachtete anthropogene Treibhausgas. Die globale Erderwärmung wird demnach sehr stark durch die in den letzten Jahrzehnten stattfindende Anreicherung von anthropogenen Treibhausgasen in der Atmosphäre mitverursacht. Die Freisetzung von CO2 kann mit Hilfe effizienterer Technologien und alternativer Energiequellen reduziert werden. CO2-Emissionen können aber auch reduziert werden, indem man CO2 aus Kraftwerksabgasen abscheidet und in tiefen geologischen Formationen speichert. Bei den physikalischen Bedingungen, die in diesen unterirdischen Lagerstätten herrschen, liegt CO2 im überkritischen Zustand vor, gekennzeichnet durch eine hohe Dichte und geringe Viskosität. Diese Lagerstätten enthalten oft salzhaltiges Wasser, das dichter ist als CO2. Eine möglichst undurchlässige geologische Deckschicht verhindert das Aufsteigen des leichteren CO2 an die Erdoberfläche. Jedoch müssen, z. B. im Rahmen von Risikostudien, mögliche Störungen oder Risse in dieser Deckschicht betrachtet werden, die zu einem Entweichen des CO2 führen könnten. Die Deckschicht in der Nähe eines CO2-Injektionsbrunnens ist besonders gefährdet. Der hohe Druckanstieg während der ersten Injektionsphase, Zementkorrosion am Brunnen aufgrund des CO2-reichen Formationswassers und eventuelle Beschädigungen der Deckschicht während der Erstellung des Bohrlochs sind als mögliche Ursachen für gestörte Deckschichten zu nennen. Biobarrieren könnten verwendet werden, um solche Risiken zu minimieren, z. B. indem sie Risse in der Deckschicht abdichten oder den Bohrlochzement vor Korrosion schützen. Eine Biobarriere kann aus einem Biofilm selbst bestehen, aber auch aus vom Biofilm begüngstigten mineralischen Ablagerungen. Die vorliegende Arbeit behandelt im Wesentlichen die Entwicklung eines numerischen Modells, um die Anreicherung von mikrobieller Biomasse im Untergrund simulieren zu können. Das entwickelte Modell soll in der Lage sein, das Abdichten der beschädigten geologischen Deckschicht einer unterirdischen Kohlendioxid-Lagerstätte mit Hilfe von Biofilmen zu simulieren. Dafür müssen einerseits Strömungsprozesse und andererseits auch die mikrobielle Aktivität sowie die Interaktion dieser Vorgänge in porösen Medien richtig beschrieben werden. Die Anreicherung von Bakterien in einem porösen Medium beeinflusst die hydraulischen Eigenschaften des Mediums und als Folge davon auch die darin stattfindende Strömung. Im Gegenzug bestimmt die Strömung den Transport der mikrobiellen Nährstoffe und damit auch die Verteilung mikrobieller Wachstumsraten. Dementsprechend ist die richtige Beschreibung der Wechselwirkung zwischen Strömung und mikrobiellen Prozessen eine wesentliche Herausforderung in der Modellbildung.

1.

Ebigbo, A., Thermal Effects of Carbon Dioxide Sequestration in the Subsurface. Diplomarbeit, Institut für Wasserbau, MSc Thesis, University of Stuttgart, 57 pp., 2005. [View Abstract]In order to secure long-term storage of CO 2 in the subsurface, one has to be able to model the mass transport of CO2. The physical properties of CO2 have a very strong influence on the mass transport. These physical properties, in turn are dependent on temperature (and pressure). Hence, the modelling of heat transport in the subsurface during CO2 injection should be part of mass transport. In the simple set-up examined in this thesis, the Joule-Thompson cooling (as a result of the pressure drop) plays an important role near the injection point. The amount of cooling at the injection point depends on the temperature of the injected CO2 (and of course on the pressure difference that brought about the cooling). The temperature at that region achieves a stable value with time. The impermeable layer should be deeper than the depth at which the CO2 becomes gaseous as it is easier to trap less mobile supercritical or liquid CO2.