Universität Stuttgart - Institut für Wasserbau Lehrstuhl für Hydromechanik und Hydrosystemmodellierung Prof. Dr.-Ing. Rainer Helmig.

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1 Universität Stuttgart - Institut für Wasserbau Lehrstuhl für Hydromechanik und Hydrosystemmodellierung Prof. Dr.-Ing. Rainer Helmig Diploma Thesis Numerical Simulations of CO 2 Injection into Saline Aquifers: Estimation of Storage Capacity and Arrival Times using Multiple Realizations of Heterogeneous Permeability Fields Submitted by Peter Probst Matrikelnummer Stuttgart, 5th August 2008 Examiners: Prof. Dr.-Ing. Rainer Helmig, Dr.-Ing. Holger Class Supervisor: Dipl.-Ing. Andreas Kopp, Dr. Suzanne Hurter, Marie Ann Giddins

2 Author s Statement I herewith certify that I have prepared this diploma thesis independently, and that only those sources, aids, and advisors that are duly noted herein have been used and/or consulted. Signature

3 Acknowledgements The author gratefully acknowledge funding by the CO2SINK project (SES6-CT ) sponsored by the Commission of the European Communities and the industry (Schlumberger, Shell, Statoil, RWE, Vattenfall and VNG) and by the GEOTECHNOLO- GIEN program.

4 Contents 1. Introduction 1 2. Model Concept - Compositional Code Multi-Phase Multi-Component Approach Mass Transfer between Water and Gas Phase Salinity Rock Compressibility Fluid Properties Carbon Dioxide Water and Brine, respectively Diffusion Mathematical and Numerical Model Equations Conservation of Momentum Mass Conservation Solution Variables Solving the Equations Time Discretization - Adaptive Implicit Method AIM Definition of Storage Capacity Storage Capacity - Bachu et al Storage Capacity - Doughty et al Model Setup Geological Model Relative Permeability Capillary Pressure Boundary Conditions and Output Definition of the Storage Reservoir Investigation on Grid Convergence Breakthrough Prediction Continuous Injection IV

5 Contents V 7.2. Varying Injection Regime Pressure Development at the Cap Rock Estimation of Storage Capacity Base Case Sensitivity Study on Net-to-Gross Sensitivity Study on Salinity Sensitivity Study on Injection Rates and Relative Permeability Final Remarks Conclusion Outlook A. Graphic Plots 64 Bibliography 67

6 List of Figures 1.1. Prospective areas in sedimentary basins Trapping mechanism importance Redlich-Kwong matching laboratory data Resource-Reverse Pyramid (Bachu et al., 2007) Sphere of capacity factors Volumetric and dissolved share Separating physical and numerical-dispersive front Facies model for the Base Case Effective porosity model for the Base Case Horizontal permeability model for the Base Case Relative permeability relations Capillary pressure - saturation relationship Modification for boundary condition Partition of the reservoir model Well section: Injection Well Ktzi Well sections for the grid convergence study Breakthrough curves for the grid convergence study Numerical grid for the estimation of storage capacity Numerical grid for the estimation of arrival times (zoom in) Numerical grid for the estimation of arrival times (zoom out) Detection area for analysing the breakthrough Cumulative injected mass of CO 2 vs. time Breakthrough Ktzi200: detected mass of CO 2 vs. time Breakthrough Ktzi200: detected mass of CO 2 vs. injected mass Pressure development for different strategies Volume averaged gas density ρ g (Base Case) Pore volumes and pore volume ratios filled with gas (Base Case) Volume average mass fraction of CO 2 in brine Xl CO2 (BaseCase) Partitioning of CO 2 between facies (Base Case) Volumetric and dissolved share and effective capacity C (Base Case) VI

7 List of Figures VII 8.6. Gas saturation after 100 years (Base Case) Accessible pore volumes (sensitivity on N/G) Capillary pressure - water saturation relationship (sensitivity on N/G) Pore volume ratios filled with gas (sensitivity on N/G) Volume averaged gas and water saturation (sensitivity on N/G) Volumetric share (sensitivity on N/G) Dissolved share (sensitivity on N/G) Effective capacity C (sensitivity on N/G) Partitioning of dissolved gas between facies (sensitivity on N/G) Partitioning of mobile gas between facies (sensitivity on N/G) Partitioning of immobile (residual) gas between facies (sensitivity on N/G) Volumetric and dissolved share and effective capacity C (sensitivity on salinity) Volumetric and dissolved share (sensitivity on injection rates and rel. permeability) Effective capacity C (sensitivity on injection rates and rel. permeability) Gas saturation for different relative permeability relations Volumetric and dissolved share and effective capacity C (sensitivity on injection rates and rel. permeability) Partitioning of CO 2 into different states (sensitivity on injection rates and rel. permeability.) Pressure development for different injection regimes A.1. Horizontal permeability for N/G 30 and 35 vs. gas saturation A.2. Horizontal permeability for N/G 38, 40 and 46 vs. gas saturation A.3. Horizontal permeability for N/G 50 vs. gas saturation

8 List of Tables 5.1. Residual saturations for relative permeability relations Input data/parameters for Leverett J-function Cell size in the area of interest for different realizations Injection regimes besides continuous injection Breakthrough times for dissolved CO 2 for varying injection pattern Volumetric share (sensitivity on injection rates and rel. permeability) Volumetric share (sensitivity on injection rates and rel. permeability) Maximum pressure directly below the cap rock VIII

9 Abstract Concerns on man-made climate change due to high CO 2 concentrations in the atmosphere have led to the idea of storing CO 2 in deep geologic formations indefinitely. The feasibility of this idea is tested in the EC-project CO2SINK (GFZ-Potsdam, 2008). CO 2 is being injected into the Stuttgart Formation at Ketzin (close to Berlin). In addition to the injection well, 2 observation wells have been instrumented at 50 and 100 m distance from it, respectively. The present work uses numerical simulations to investigate storage capacity (effectiveness of storage) and estimate the time of CO 2 breakthrough at the observation wells. The author presents a modification of the storage capacity approach by Doughty et al. (2001) and its application to the CO2SINK storage project site. Storage capacity is defined as the maximum amount of CO 2 able to be sequestered in a specific reservoir. The effectiveness (amount of the pore space that can be occupied by this gas) depends on various factors such as heterogeneity. The effective storage capacity is defined as a product of four factors. We describe the product of the Geometric Capacity Factor C g and Heterogeneity Capacity Factor C h (Doughty et al., 2001) with one expression and split those up to account for the free-phase gas and dissolved gas in the brine. The geological model is based on a statistical model in which all realizations have equal likelihood. We obtain estimates of storage capacity as a function of absolute permeability distribution conducting simulation runs with varying Net-to-Gross (N/G). Moreover the impact of injection rates and relative permeability relations on storage capacity are examined. Dynamic simulations were also used to obtain estimates of breakthrough times for varying injection patterns. These estimates assist field work to be planned (e.g. cross-well seismic surveys to see the CO 2 ). When these estimates are accurate, they reflect a good knowledge of the reservoir and flow processes within it.

10 1. Introduction Since the end of the 1960s enhanced oil recovery (EOR) has been ongoing mostly in West Texas. Without EOR (and water flooding) almost half of the oil remains in the reservoir. CO 2 injection is one of the methods for EOR as well as, e.g. thermal recovery methods (steam drive and cycling steam stimulation). CO 2 is injected into oil reservoirs in order to improve the efficiency of oil recovery. When two phases are miscible, the interfacial tension and thus capillary pressure will be zero. This will be the case when injection gas become miscible with oil (pressure above the minimum miscibility pressure). In laboratory experiments (core flooding), practically all oil can be removed by CO 2 injection. In the reservoir this is less because of heterogeneities, poor sweep (how much reservoir can be touched by CO 2 ) and difficulty in maintaining miscible conditions, for example. However, this work will focus on the second application of CO 2 injection, the geological sequestration in saline aquifers. The system CO 2 and water or brine is always immiscible. With the idea of using the world s sedimentary basins as potential permanent storage sites for CO 2 (Figure 1.1), engineers plan to drill wells into a deep saline aquifer in order to inject this greenhouse gas. The first CO 2 storage / sequestration was Sleipner (Statoil, 2008) in the North Sea, offshore Norway, injecting 1 Mt/a since Ideally the gas would be injected very deep into the basins to achieve the intended supercritical state, through increasing temperature and pressure. This is because the supercritical state is associated with high density, so a higher mass can be stored per unit rock volume. The second advantage of deep injection is the decrease in gas viscosity. Site selection is critical for storage capacity. A reservoir (aquifer) with high porosity and high absolute permeabilities should be favored for its potential to provide as much pore volume as possible. CO 2 remains trapped in the subsurface through various mechanisms. As shown in Figure 1.2, each trapping mechanism occurs at different timescales. In the beginning the structural and stratigraphic trapping dominates, that is the trapping of the upwards migrating plume below a sealing cap rock. This cap rock made up of very low permeable layers forms a barrier which prevents the plume from rising up to higher levels or even to the surface. The residual trapping mechanism sets in when brine reimbibes zones through which CO 2 has flowed, leaving behind a fraction of the gas. This happens due to buoyancy effects or flow reversal at injection stop. Capillary forces prevent the CO 2 of draining completely and this residual saturation remains trapped in the pores. Depending on the salinity, pressure and temperature range of the aquifer, the injected CO 2 will dissolve more and more in the brine and increase its density. As a result, the heavy brine will move into deeper parts of the reservoir. This is the solubility trapping mechanism. The mineral trapping mechanism is the fixing of CO 2 by chemical reactions with minerals and brine 1

11 2 components and precipitation. In this presented order (structural and stratigraphic trapping residual trapping solubility trapping mineral trapping) the storage security is increasing as well as the storage capacity, on which we will finally focus in this work. The challenge is now to estimate storage capacity for the injection of CO 2 into a saline aquifer, since, beside the previously mentioned factors, complex phase behavior, chemical reactions and the high uncertainty in geology need to be considered. The first order estimate often used is to estimate the total pore space of the reservoir. However, this is not totally available for CO 2 storage due to residual water saturation and poor sweep efficiency of the injection process for example. Especially the high uncertainty in Net-to- Gross (N/G) is a problem. The larger the share of high permeable sand channels, the more suitable the reservoir would be. Therefore it is necessary to investigate how much effective capacity is changing with N/G and so with the uncertainty. This work will use numerical modeling to illustrate a published methodology and discuss its usefulness. Therefore it contributes to uncertainty management and will help to obtain estimate under limited information. Referring to Bachu et al. (2007), the assessment of CO 2 storage capacity may be conducted at a variety of levels. The Country-Scale assessment is a high level assessment performed for a continuous geographic area defined by national jurisdiction. Such an assessment should be performed to determine whether there is sufficient CO 2 storage capacity in a country and requires minimum data, usually found in the public domain. The Basin-Scale assessment is a more detailed level assessment focusing on a particular sedimentary basin. This level requires more data categories and a grater level of detail than the regional assessment, sometimes focusing on a specific type of storage (e.g. only oil and gas reservoirs). Increasing the level of detail for a large, geographically-continuous portion of sedimentary basin, one can define the Regional-Scale assessment. The fourth scale is the Local-Scale which allows one to investigate storage capacity. This is usually performed at a pre-engineering level when one or several candidate sites are examined to determine site capacity and injectivity. The Site-Scale assessment again is performed for a specific storage unit, usually to model the behavior of the injected CO 2. Within this work, we will address the Site-Scale assessment. The second focal point of this work is related to supporting monitoring planning of a specific project, CO2SINK (GFZ-Potsdam, 2008). The prediction of the gas breakthrough at the observation wells (and getting a good estimate) will help to see if we understand the reservoir and if the available data give a good description. It also helps in organizing the monitoring, here for example the repeated cross-well seismic campaigns. For logistics, costs, resources etc. it is indispensable to get a feeling for the potential time frame, within the scientific results can be obtained.

12 3 IPCC (2006) Highly prospective Prospective Figure 1.1.: Prospective areas in sedimentary basins.

13 4 100 trapping contribution % 0 structural and stratigraphic trapping residual trapping increasing storage security solubility trapping mineral trapping dominating processes ,000 10,000 time after stop of CO 2 injection (years) multiphase behavior geochemical reactions phase transfer processes dissolution and diffusion advection dominated (viscous, buoyant, capillary) Figure 1.2.: Trapping mechanism importance; with increasing time, the different trapping mechanisms take different loadings and the project becomes more safe (IPCC (2005)(modified)).

14 2. Model Concept - Compositional Code This chapter gives a short overview of applying the Eclipse Compositional Code (E300) to the purpose of CO 2 sequestration. Besides the multi-phase multi-component approach, the method for calculating the mass transfer between the phases until equilibrium (flash calculation) and the properties of both phases, water (brine) and gas, are explained Multi-Phase Multi-Component Approach For geological storage of CO 2 in saline aquifers, a quasi-isothermal two-phase threecomponent model is considered, where both the CO 2 -rich phase (gas phase) and the H 2 O-rich phase (water phase) are able to contain the components CO 2 and H 2 O. The code accounts for the mutual solubilities of CO 2 in the water-phase and water in the gas phase which again includes all relevant processes from dissolution and degassing to evaporation and condensation. Up to now, the temperature effects are not completely taken into account i.e. by assigning a temperature gradient to the reservoir (aquifer) the properties (density and viscosity) are calculated at the prevailing temperature. However it is not possible to model injection temperatures differing from the reservoir temperature Mass Transfer between Water and Gas Phase As mentioned above, the CO2STORE-option predicts the mutual solubility of H 2 O and CO 2. The partitioning of CO 2 and H 2 O in both phases are predicted by a flash calculation. The code contains experimental data for typical CO 2 storage conditions (for a range of C and up to 600 bars), which have to be matched in the flash calculation, based on fugacity equilibration between the CO 2 -rich phase and H 2 O-rich phase (Spycher and Pruess, 2005). Assuming low concentration of a dissolved component in water, Henry s law is applicable, which implies the mole fraction of CO 2 in water x CO2 [-], the Henry s law constant Hα CO2 [P a] and the vapor pressure p CO2 g [P a]. p CO2 g = x CO2 H CO2 α (2.1) From that correlation again, the water fugacity is obtained for a certain pressure and temperature. 5

15 2.2 Rock Compressibility 6 0,1 0,04 y H2O [-] 0,08 0,06 0,04 0,02 0 Data by Spycher and Pruess CO2STORE Pressure [bar] x CO2 [-] 0,03 0,02 0,01 0 Data by Spycher and Pruess CO2STORE Pressure [bar] (a) mole fraction of H 2 O in gas phase at a temperature of 50 C vs. pressure in bar. (b) mole fraction of CO 2 in water phase at a temperature of 50 C vs. pressure in bar. Figure 2.1.: Redlich-Kwong matching laboratory data (Schlumberger, 2008a), pink points = data by Spycher and Pruess (2005), blue solid line = predicted values by CO2STORE (Schlumberger, 2008a). The CO 2 fugacity is calculated by using a modified Redlich-Kwong equation of state (EOS). Figure 2.1 shows the comparison of the mole fractions predicted by CO2STORE and the experimental values given by Spycher and Pruess (2005). Over a range of 600 bar and for a fixed temperature, the graphs show satisfying agreement for the mutual solubility of CO 2 in water (xco 2 ) and water in CO 2 (yh 2 O), respectively Salinity The salinity is taken into account by adding a third component (NaCl) to the two existing components H 2 O and CO 2 of the liquid phase. The two-phase two-component model described in Section 2.1 is in fact extended by a third component. The water salinity does not vary with depth. Salt remains in the liquid phase. Decrease in mobility, due to salt precipitation, is also not considered. In aquifers with a high share of salinity, one can expect a loss of injectivity since H 2 O (over saturated with NaCl) evaporates into the CO 2 and so reduces the porosity and permeability. In low saline aquifers, one will observe the opposite as the water dissolves in CO 2, finally resulting in a 100% gas saturated area in the near-wellbore zone. Even the irreducible water saturation may reduce to practically zero. This tends to increase the effective permeability resulting in enhanced injectivity (Hurter et al., 2007) Rock Compressibility Storage Capacity, which is the main subject of this work, is often estimated by considering the total pore volume of the formation. However, not all the pore space can be filled with CO 2. In addition to factors such as residual water saturation and sweep efficiency of

16 2.3 Fluid Properties 7 the injection process, increasing pressures caused by the amount of fluid, when added to the mass of a closed system, as well as by the injection itself, the effective pore volume available for CCS changes with time. The simulation accounts for this by including a simple rock compressibility model without any stress model or something comparable. φ eff = φ 0 (1 + X + X2 2 ) (2.2) Equation 2.2 (Schlumberger, 2008c) is used to calculate the effective porosity φ eff, where X = C (P P ref ) (2.3) C [1/bar] is the rock compressibility for the grid cell, P [bar] is the current pressure in the cell, P ref [bar] is the reference pressure for C and φ 0 is the effective porosity at reference pressure Fluid Properties The accuracy of each simulation is only as good as its input data. Besides the uncertainty of geological models, constitutive relationships and numerical sensitivities, the fluid properties impact largely on the results of simulations of multi-phase flow in porous media. The conditions of the underlying geological model of this framework are located near the critical point. It is therefore worth considering in more detail the way in which the fluid properties are implemented. Depending on pressure and temperature, the state of CO 2 can vary between being gaseous, liquid or supercritical. The main focus here lies on density and viscosity Carbon Dioxide Density Besides advection, buoyancy plays an important role when modeling CO 2 sequestration, since the gas is always less dense than the brine. Due to the difference in phase densities, the CO 2 migrates upwards. In order to model this transport process an accurate description of the gas density is achieved by a modified Redlich Kwong EOS. The transition between liquid CO 2 and gaseous CO 2 will lead to rapid density changes of the gas phase. The simulator uses a narrow transition interval between the liquid and gaseous density to represent the two phase CO 2 region (Schlumberger, 2008c) Viscosity For the calculation of the CO 2 gas viscosity, the simulator uses an equation of state, according to Fenghour et al. (1999) and Vesovic et al. (1990). They declare the viscosity as a function of temperature and pressure, which consists of three summands. η(p, T ) = η 0 (T ) + η(ρ, T ) + η c (ρ, T ) (2.4)

17 2.4 Diffusion 8 The Equation 2.4 includes, in addition to zero-density viscosity η 0 (T ) [µp as], which represents the viscosity of carbon dioxide in the limit of zero density, an excess viscosity η(p, T ) [µp as]. This represents the increase in viscosity at elevated density above the diluted gas value at the same temperature. A critical enhancement η c (p, T ) [µp as] accounts for the increase in viscosity in the immediate vicinity of the critical point (Vesovic et al., 1990) Water and Brine, respectively Density The brine density ρ [kg/m 3 ] is calculated in two steps. First, the density of pure water is calculated following the recommendation of Kell and Whalley (1975) by ρ(p) = ρ(p 0 ) + p p 0 u 2 dp + T p p 0 (α 2 /C p )dp (2.5) where p 0 equals 1 atm, u [m/s] stands for the speed of sound, C p [J/K] for the isobaric heat capacity and α for the thermal expansivity. This equation comes from the assumption, that the speed of sound u is related to the isentropic change of density with pressure. The input data for the equation is based on experimental data. Subsequently the density of pure water is modified using the Ezrokhi s method (Equation 2.6) to calculate the effect of salt and CO 2 (Zaytsev and Aseyev, 1993). lgρ = lgρ 0 + (A i c i ) (2.6) This comprises the density of pure water ρ 0, the mass fraction of each component c i as well as an activity coefficient for each component A i defined by A i = b 0,i + b 1,i T + b 2,i T 2 (2.7) where b n,i are coefficients for a series of electrolytes and T stands for temperature in degree C Viscosity For the viscosity of the brine a correlation is used, which is similar to that for density Diffusion The process of diffusion affects the reduction of a difference in concentration. For the application to CO 2 sequestration particularly the diffusion of dissolved CO 2 in the water phase is of interest. The diffusion model used in this study is driven by a concentration

18 2.4 Diffusion 9 gradient (no chemical potential gradient). The molar flux J i of each component i due to diffusion (Schlumberger, 2008c) is handled by J i = c D i x i d (2.8) where c is the total molar concentration given by c = 1 v m (v m [m 3 /mol] is the molar volume of the mixture), D i [cm 2 /s] is the diffusion coefficient of component i and x i is d the molar concentration gradient of component i.

19 3. Mathematical and Numerical Model The compositional reservoir simulator E300, written in FORTRAN90, uses for discretization purposes a finite difference approach. This chapter gives just a brief overview of the general equations and their formulation. For more details, the author refers the reader to the Technical Manual of the simulator (Schlumberger, 2008c) and references therein Equations In this chapter the author will give a short review of the equations, describing the isothermal multi-phase multi-component flow in porous media, used in Eclipse E Conservation of Momentum The extended Darcy law for multiphase flow (Equation 3.1), considering the velocity of each phase, is used to balance the momentums. v α = λ α K (gradp α ρ α g) (3.1) where λ α [m s/kg] is the phase mobility, K [m 2 ] is the permeability tensor, p α [Pa] the phase pressure and ρ α [kg/m 3 ] is the density of the phase. This law is valid for very small Reynolds-numbers (Re < 1) Mass Conservation For the compositional code the overall formulation follows that of Trangenstein and Bell (1989). Considering Equation 3.1, the total (advective) flux of each component is the sum of the phases of the molar densities n c α, times its flow rate vα u α where u α represents the ratio of the phase volume to the pore volume. Finally the mass conservation law, including the diffusive flux, can be written in the form (n c φ) t v l v g (n c l + n c g ) (c D i x i ) q c = 0 (3.2) u l u g The complementary conditions to solve Equation 3.2 and 3.1 are the following: 1. The sum of ratios of the phase volumes to the pore volume equals one: u l + u g = 1 (3.3) 10

20 3.2 Solution Variables Assuming thermodynamic equilibrium, the number of moles per volume of each component are balanced between the phases: n c = n c l + n c g (3.4) 3.2. Solution Variables In order to solve the equations, presented in Section 3.1, the primary and secondary variables need to be declared. Primary variables have to be independent from each other and the number of boundary conditions for each primary variable has to equal the number of equations. For this purpose the implementation provides the following variables: 1. Primary Variables: X primary =(p, n c ); c=1...n c 2. Secondary Variable: X secondary =f(x primary )=(J c, V) where J c = log(k i ) (K i is the K value) and V is the vapor mole fraction ( flash calculation) Solving the Equations For the non-linear equations, where the non linearity is caused by a constitutive relationship, the equations are solved by Newton s method, applied to linearize the equations. Therefore the simulator approximates the differential equation 3.2 by a first order Taylor series to approximate a function f(x) in the vicinity of any arbitrary root. Subsequently the matrix is preconditioned by a nested-factorization procedure to use the Orthomin method to solve the linear problem. For further information see Schlumberger (2008c) as well as Vinsome (1976) Time Discretization - Adaptive Implicit Method AIM The standard approach for E300 compositional is the adaptive implicit method, unifying the advantages of the fully implicit and IMPES (Implicit pressure, explicit saturation) method. This method allows to specify a fraction of cells with high throughput to be treated as implicit, to stabilize the solution obtaining large time steps, while the majority of cells can still be treated as IMPES where the solution may be changing little. The fully implicit method is generally the most stable one, but also the method with the poorest performance. All nodes in the next time step level are coupled with each other. In comparison to that, the IMPES method applies an explicit scheme to the calculation of the unsteady problem of all primary variables, except pressure. Strictly, the grid block pressures are solved implicitly while the component moles rather than the phase

21 3.4 Time Discretization - Adaptive Implicit Method AIM 12 saturation are obtained explicitly. The mass terms M t+ t in Equation 3.5 for the residual R are evaluated using both pressures and molar densities at the end of the time step. R = M t+ t M t dt + F (P t+ t, n) + Q(P t+ t, n) (3.5) In Equation 3.5 the F stands for the flow rate of a component (advective term), embedded in a phase, into a cell from the neighbouring cell and Q for the flow rate of a component, embedded in phase, into a well (sink/source term). Finally the flow terms between the cells are evaluated assuming the saturations, generalized mobilities and reservoir density terms are all fixed at the previous time step. Additionally, all cells that are part of wells are treated implicitly (Schlumberger, 2008c).

22 4. Definition of Storage Capacity In the last few years a vast amount of research power has been spent on developing accurate methods of prediction for CO 2 storage capacity. Publications i.e. from Brennan and Burruss (2003), Bachu et al. (2007) and Doughty et al. (2001) give different approaches for defining storage capacity and show the difficulty in formulating a universal method for this purpose. Kopp et al. (2009a) & (2009b) summarized and applied several of these approaches in two papers, performed a dimensionless analysis and gave an estimate for storage capacity coefficients. This chapter will describe in detail the capacity approach of Doughty et al. (2001), which is later applied to the Ketzin formation and its uncertainty analysis. Additionally, we will also give a short overview of the Carbon Sequestration Leadership Forums (CSLF) perspective of CO 2 storage capacity in geological media Storage Capacity - Bachu et al. A universal approach or rather a kind of nomenclature for storage capacity, which is dependent on various reservoir characteristics, is outlined in the publication Estimation of CO 2 Storage Capacity in Geological Media prepared by a group of world wide leading researchers (Bachu et al., 2007). Herein, they focus on the development of definitions and standards that could be used for estimating the CO 2 storage capacity and summarize with the Resource-Reverse Pyramid concept (Figure 4.1) the possible capacity types, which depend on a variety of aspects (e.g. availability of data, state of the art technology), and account for different weightings with time. These conceptual points of view distinguish between four different levels of capacity and establish a relationship between the economic profitability and the interlinked uncertainty of the storage potential. The theoretical capacity describes the entire pore volume potentially accessible (excluding residual water saturation). The next level up, the effective capacity accounts for just the upper three levels of the pyramid, having removed from the theoretical equation the capacity which, for geological and engineering reasons (e.g. heterogeneity, gravity override) will be inaccessible in reality. Going one step higher, practical capacity is illustrated as the top two tiers of the pyramid. This demonstrates how much of the effective capacity is accessible once highly volatile economic aspects such as technical detail, legislation and infrastructure, which can act as a barrier to CO 2 storage, have been taken into account. Finally the forth level gives the matched capacity. This takes the practical capacity and excludes the stranded storage capacity, which accounts for the CO 2 sources that are unserviceable for infrastructural or geographic reasons. The forth level therefore demonstrates 13

23 4.1 Storage Capacity - Bachu et al. 14 Figure 3. Techno-Economic Resource-Reserve pyramid for CO2 jurisdiction or geographic region (modified from CSLF, storage 2005; capacity Bradshaw in et geological al., 2006). media The pyramid within a shows the relationship between Theoretical, Effective, Practical and Matched capacities. Figure 4.1.: Resource-Reverse Pyramid, herein Bachu et al. (2007) define the four main types of capacity. The greater the volume of the pyramid, the less accurate the capacity estimate. the volume of storage capacity with the highest user potential. For the estimation of CO 2 storage capacity in deep saline aquifers, Bachu et al. (2007) provide a simple general approach to measuring both theoretical and effective capacity for the three major trapping mechanisms (hydrodynamic, solubility and residual trapping). A capacity factor is used to convert the values of the theoretical capacity to effective capacity. For the effective storage capacity V CO2,e,strat in structural and stratigraphic traps, which store mobile gas, Equation 4.1 is applied. V CO2,e,strat = C c,g φ(1 S w,irr )dxdydz (4.1) } {{ } V CO2,t This equation applies a specific capacity factor C c,g, used to calculate the effective capacity of structural and stratigraphic traps. Accounting for the theoretical volume V CO2,t, only the irreducible water saturation S w,irr and the porosity φ has to be considered. Furthermore Bachu et al. (2007) derives Equation 4.2, describing the theoretical dissolved mass M CO2,t,diss, dependent on the initial state (subscript 0) of the reservoir. M CO2,t,diss = φ(ρ X CO2 ρ 0 X0 CO2 )dxdydz (4.2) Now remaining is a relationship between the trapped CO 2 saturation (S CO2,t ) and the residually trapped mass in the system. Therefore Bachu et al. (2007) prepare the ground for further steps by providing Equation 4.3 V CO2,t,trap = V trap φ S CO2,t (4.3)

24 4.2 Storage Capacity - Doughty et al. 15 In this context, the volume V CO2,t,trap is that one which was saturated with CO 2 before a flow reversal at the end of injection. Here additional attention has to be payed so as not to mix up S CO2,t with the residual gas saturation S g,r, since S CO2,t can be less than S g,r due to vaporization and condensation. The assigned residual gas saturation S g,r only affects the advective part of the flow process Storage Capacity - Doughty et al. Referring to Doughty et al. (2001), in this context effective capacity C is the potential volume fraction (in terms of bulk volume) of a saline aquifer standing by for sequestration purposes. Based on a multi-phase multi-component model, the approach provides the impacts of heterogeneity, mass transfer between the phases and buoyancy. In contrast to Doughty s investigation on storage capacity, this work uses a much larger scale. Doughty et al. (2001) define the effective capacity C as C = C i C g C h φ (4.4) where each factor identifies one of the following major aspects on CO 2 storage: 1. Intrinsic Capacity C i The intrinsic capacity accounts for radial flow (Figure 4.2(a)) in a homogeneous field excluding gravity. In a two phase model it is possible to distinguish between the water-rich and CO 2 -rich phase. Considering C i = C ig + C il (4.5) C ig gives the fraction of pore space filled with gas and C il the fraction of pore space filled with dissolved CO 2, respectively. Solving the analytical Buckley-Leverett problem (excluding capillary pressure) Doughty et al. (2001) conclude that it is appropriate to approximate C ig = Sg (4.6) where S g is the average gas saturation behind the gas front and C il = Sl Xg l ρ l (4.7) ρ g where S l is the average water saturation (neglecting the fraction of water in gas), X g l is the average mass fraction of CO 2 dissolved in brine and ρ g and ρ l are the average mass densities of the CO 2 -phase and water-phase, respectively. All listed parameters are analyzed behind the gas front. 2. Geometric Capacity Factor C g Due to gravity segregation, aquifer dip and partly penetrating wells etc., the plume can not reach all parts of the aquifer. To consider this fact, the geometric capacity factor is introduced. Figure 4.2(b) illustrates that modification.

25 4.2 Storage Capacity - Doughty et al. 16 (a) Radial expansion C i (b) Plume expansion C g (c) Expansion in heterogeneous media C h Figure 4.2.: Illustration of the sphere of each factor after Doughty et al. (2001). 3. Heterogeneity Capacity Factor C h The heterogeneity in permeability and porosity of a real field, either decreasing or increasing the storage capacity, is taken into account by this factor. For this purpose, see Figure 4.2(c). 4. Porosity φ The average formation porosity is analyzed for the storage reservoir. The reader will find in Section 5.5 a detailed description of the storage reservoir and the associated pore volumes. All mean values, mentioned above, are obtained with a volume averaging method which can be written in the form P = Pi V i Vi (4.8) where P is the resulting volume weighted property and P i and V i are the discrete cell property and volume, respectively. The notation refers to the sum over all grid cells. As it is difficult to distinguish between C g and C h for a real field dataset, the product of both is estimated by a pore volume ratio. Particularly for the investigation of storage capacity for big time scales (>100 years) the approach of Doughty et al. (2001) (Equation 4.4) is now reformulated in a slightly different way: or in terms of volumetric and dissolved share C = (C ig (C gg C } {{ hg ) + C } il (C gl C hl )) } {{ } φ (4.9) C = C ig (C gg C hg ) } {{ φ + C } il (C gl C hl ) } {{ φ } volumetric share dissolved share (4.10) This is to clarify that the state of behind the gas front requires different frontdelimitations and therefore implicates different pore volume ratios as shown in Figure 4.3. In the following we distinguish between a (real) gas front and a dissolved front. The

26 4.2 Storage Capacity - Doughty et al. 17 Figure 4.3.: Volumetric (yellow) and dissolved (yellow & red) share according to Equation product C gg C hg in Equation 4.9 is going to be expressed by the pore volume ratio in Equation 4.11, P ORVfilled with gas = C gg C hg (4.11) P ORVaccess } {{ } pore volume ratio C ig the product C gl C hl by the pore volume ratio in Equation 4.12, P ORVfilled with X g l P ORVaccess = C gl C hl } {{ } pore volume ratio C il (4.12) where P ORV access describes the total pore volume of the storage reservoir (Section 5.5). The discrete pore volumes are analyzed dependent on time to account for compressibility effects. In order to avoid small concentrations and saturations caused by numerical dispersion, distorting the storage coefficients, it is necessary to define front criteria. These are applied to the analysis of the average saturations ( S g, Sl ), the average densities ( ρ g, ρ l ), the average mass fraction ( X g l ) and the evaluation of the appropriate volumes. Here the author lays emphasis on the issue that the average gas density ρ g is declared as the one which would be recorded, if gas exists there. The determination of the front criteria is chosen in the following way: The front for product * is delimited by S g > 10 4, the front for product ** is delimited by Xl CO2 > This is visually done on the basis of an approximate horizontal tangent in the cross plots for different layers and afterwards averaging out over the resulting front values. Figure 4.4 illustrates this procedure. Assuming the vertical y-axis represents Xl CO2, the area smaller than 10 4 (covered by the red arrow) is considered to be caused by numerical dispersion and is not included in the analysis. Finally, the mass, which is sequestered effectively, can be estimated by Equation 4.13, where V bulk stands for the total bulk volume of the storage reservoir. M eff = C V bulk ρ CO2 (T, p) (4.13) Given the fact that the approach of Doughty et al. (2001) refers to the bulk volume, previously published values for storage capacity C lit might show values one order of magnitude

27 4.2 Storage Capacity - Doughty et al x Figure 4.4.: Separating the physical and numerical-dispersive front, the graph represents Xl CO2 over the horizontal distance x. The red part is considered to be caused by numerical diffusion and therefore excluded from the analysis of the front. higher, because they refer to the pore volume. Equation 4.14 does justice to that aspect by dividing the effective capacity C by the mean porosity φ of the storage reservoir. C lit = C φ (4.14)

28 5. Model Setup This chapter gives an overview of the geological model used in this study. Additionally, the different constitutive relationships (p c S w & k r S w ) and the implementation of the boundary conditions will be described before turning over to the modification of the static model for the investigation on storage capacity Geological Model The underlying geological model of this work is based on the first European in-situ research project for geological CO 2 sequestration called CO2SINK (GFZ-Potsdam, 2008). Situated in the northeast of Germany, the Ketzin storage layer forms an anticline below a low permeable cap rock. The aim of the project is to drill into the saline aquifer of the Upper Triassic Stuttgart Formation and inject CO 2. This lithologically heterogeneous formation comprises muddy floodplain-facies rocks alternating with sandy string-facies rocks of good reservoir properties that may attain a thickness of several tens of meters, where sub-channels are stacked (Förster et al., 2006). Extensive surveys (seismic profiles, stratigraphic and lithological information) and the three boreholes (one injection well and two observation wells) support these assumptions and the information from all measurements provide a basis for the facies and petrophysical modeling, given by Frykman et al. (2008). This results in the final property model for the simulations. In the following Base Case refers to the original geological model by Frykman et al. (2008). The geological model does not represent the cap rock with specific layers, but with an impermeable boundary condition. This can be justified by the fact that the capillary pressure in this model does not exceed the entry pressure of this sealing formation. The facies modeling, yielding the distribution of high permeable (sand-)channels throughout the floodplain is produced by a stochastic modeling, based on upscaled facies well-logs. In this context, upscaling means the process of assigning facies-values to the cells in the 3D grid, that are penetrated by the well log (Schlumberger, 2007). Subsequent to the facies modeling process, the petrophysical modeling (modeling permeability and porosity) is applied to the grid. Frykman et al. (2008) distinguishes between total and effective porosity. Whereas the total porosity, representing the total void pore space in the rock, whether or not it contributes to the flow, provides the basis for creating the permeability property as well as for modeling the effective porosity. Effective porosity, excluding the isolated pores, goes straight into the simulation. In order to model effective and total porosity, Frykman et al. (2008) uses different distribution functions (histograms), linked 19

29 5.2 Relative Permeability 20 Figure 5.1.: Facies model for the Base Case; yellow = sand channels, lavender = floodplain. to fluvial channel or floodplain facies. Furthermore, Frykman et al. (2008) applies the resulting total porosity as co-krigging input parameter (secondary variable) to model the effective porosity. For modeling the permeability distribution, two functions take into account the different facies- and total-porosity-dependence throughout the reservoir. The Figures 5.1, 5.2 and 5.3 display the results of the facies, porosity and permeability models. With the exception of vertical permeability, which is assumed to be 30% of the horizontal one, the properties have not been changed for the Base Case simulation (Section 8.1), but of course for the Sensitivity Study (Section 8.2) Relative Permeability Considering multi-phase flow in porous media, the Darcy Law has to be extended (Helmig, 1997), resulting in Equation 5.1. This is due to the aspect that if the pore volume is filled with more than one phase, the flow of each phase affects the other. v α = k r,α µ α K (gradp α ρ α g) (5.1)

30 5.2 Relative Permeability 21 Figure 5.2.: Effective porosity model for the Base Case ranging between and

31 5.2 Relative Permeability 22 Figure 5.3.: Horizontal permeability (P erm x and P erm y ) model for the Base Case ranging between 0.00 and md.

32 5.3 Capillary Pressure 23 rel. Permeability [-] 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 krw Mueller and Maas (2008) krg Mueller and Maas (2008) krw Bennion and Bachu (2005) krg Bennion and Bachu (2005) 0,2 0, ,2 0,4 0,6 0,8 1 Water Saturation [-] Figure 5.4.: Relative permeability relations after Mueller and Maas (2008) and Bennion and Bachu (2005). This is taken into account by introducing the relative permeability k r,α [-], which correlates with phase saturation. In Equation 5.1, K [m 2 ] represents the permeability tensor, µ α [kg/ms] the phase dynamic viscosity and ρ α [kg/m 3 ] the phase density, respectively. In this study, two different relative permeability relations are used, illustrated in Figure 5.4. The author reverts to laboratory data by Bennion and Bachu (2005) and a Brooks & Corey approach matching experimental data by Mueller and Maas (2008) (dashed lines). Table 5.1 compares the residual gas (S gr ) and water (S wr ) saturation for both data sets. S gr S wr Bennion and Bachu (2005) Mueller and Maas (2008) Table 5.1.: Residual saturations for relative permeability relations Capillary Pressure Because of a lack of experimental data for the capillary pressure in the Ketzin aquifer, the modified dimensionless Leverett J-function is used to upscale the capillary pressure

33 5.3 Capillary Pressure 24 0,035 0,030 capillary pressure (Base Case) Plug and Bruining Capillary Pressure [bar] 0,025 0,020 0,015 0,010 0,005 0, ,2 0,4 0,6 0,8 1 Water Saturation [-] Figure 5.5.: Capillary pressure - saturation relationship after applying Equation 5.2. from existing laboratory data for different petrophysical parameters. p c,2 (S w ) = p c,1 (S w ) ( K h,1φ 2 K h,2 φ 1 ) σ 2cosΘ 2 σ 1 cosθ 1 (5.2) Equation 5.2 establishes a relation between capillary pressure p c, horizontal permeability K h, porosity φ, the angle Θ between the wetting and non wetting phase and the surface tension σ, which is further a function of temperature and pressure given by Kvamme et al. (2007). Subscript 2 indicates the parameter to be obtained, subscript 1 uses fitted experimental data 12 in Plug and Bruining (2007). For all simulation cases within this study, K h,2 and φ 2 are evaluated by a volume weighted average method for each specific realization. All remaining parameters are given in Table 5.2. Figure 5.5 shows the comparison of the experimental data and the resulting upscaled capillary pressure curve for the Base Case (referring to Section 8.1). In order to calculate the surface tension σ 2 the input data is based on the approximate BHP-conditions (Bottom Hole Pressure) (T=305.53K, 61.2 bar). Unfortunately, due to a mistake in unit conversion, the capillary pressure shown in Figure 5.5 is too low and therefore does not provide the correct input for the Leverett J-function. This implies an underestimation of the front thickness.

34 5.4 Boundary Conditions and Output 25 Subscript 1 Subscript 2 K h [md] 200 variable φ [-] 0.37 variable Θ [ C] σ [mn/m] Table 5.2.: Input data/parameters for Leverett J-function (Equation 5.2) Boundary Conditions and Output In all of the following investigations the same boundary conditions are used. The author distinguishes between two different boundary conditions: The outer boundary conditions/ initial conditions and the CO 2 injection boundary conditions. Outer boundary condition It is assumed here that the Ketzin aquifer is an infinite saline aquifer. Therefore the boundary condition should represent a hydrostatic pressure distribution at the boundary of the model. As it is not possible to assign explicitly a Dirichlet boundary condition, the grid is modified so that along the outermost cells the pore volume is multiplied by a factor. In doing so, it is guaranteed that the boundary condition behaves like a infinite aquifer. In Figure 5.6, the mint green cells represent the modified cells at the boundary, whereas the gray field includes the geological model by Frykman et al. (2008). The aquifer salinity is assumed to ppm (Salinity 0.2) (Mueller et al., 2007). As mentioned in Section 2.1 the code allows a temperature gradient to be assigned for the reservoir. The following temperature correlation (Henninges and Förster, 2007) T = x (5.3) for the Ketzin aquifer is applied to all simulation cases, where T stands for the temperature in C and x for the depth in meter. This relationship refers to a linear interpolation of measured data on the 10th November 2004 in well Ktzi 163/69. The rock compressibility is defined at a pressure of 62 bar as C= (referring to Equation 2.2) (Mueller et al., 2007). The initial CO 2 saturation is set to zero. CO 2 injection boundary condition The injection temperature refers to the initial temperature of the cells where the perforations are situated.

35 5.4 Boundary Conditions and Output 26 Figure 5.6.: Modification for boundary condition; mint green cell = boundary condition (pore volume multiplier applied); gray cells = simulation field. A constant (surface-)mass rate is specified: Q v = sm 3 /day (Q m =86400 kg/day) for approximately two years. Injection of pure CO 2 : mole fraction of CO 2 equal to one. Skin factor: The skin factor represents a dimensionless number, which accounts for changes in the formation due to drilling activity. Drilling mud may flow into the reservoir, resulting in parts of the pore space being blocked and finally reducing the permeability around the well (Dake, 2006). In this study a skin factor of 0.4 is used (Mueller et al., 2007). The diffusion coefficients for all simulation cases within this study is assumed to be [cm 2 /s] Bachu et al. (2007). The reason for choosing the diffusion coefficient for water in the gas phase at this level is so that the aspect of diffusion in the gas phase is not entirely neglected. Water diffusion coefficients are typically an order of magnitude lower than gas diffusion coefficients. Injection well: Ktzi201 with an open interval of 46.2 m in the uppermost region of the Stuttgart formation.

36 5.5 Definition of the Storage Reservoir 27 Observation wells: The two observation wells form together with the injection well a rectangular triangle. Ktzi200 is located 50m east to Ktzi201, Ktzi202 is located 100m north of Ktzi200 (Figure 6.4). Output CO 2 is injected for t = 0 for approximately two years (695 days), after which injection is stopped and further evolution of the fate of the CO 2 is followed up to 100 years. The output are: CO 2 saturation, pressure, CO 2 state (mobile, dissolved, residually trapped) as a function of time Definition of the Storage Reservoir In order to determine and analyze the storage capacity parameter in a well defined way, the simulation model has to be prepared before initialization. The most important part is to define the storage reservoir and its total pore volume ( P ORV access in Equation 4.11 and 4.12). For this purpose the grid is divided into two separate regions. Figure 5.7 shows in gray the area (Region 2), which is impossible to reach due to radial flow, and in light green the area (Region 1) representing the accessible region excluding gravity (see Figure 4.2(a)). To account for the departures from the idealized radial flow, the geometry is divided in the depth of the deepest perforation-point (see Figure 5.8). Therefore we consider Region 1 as our storage reservoir. As a result of the domed structure, the discretization disallows an exact partitioning of the reservoir which finally ends up with a zig-zag separation plane between Region 1 and Region 2. This is depicted in Figure 5.7 as well. For analyzing the average gas density ρ g the model is initialized as a fully saturated gas reservoir on the basis of the pressure distribution from the saline aquifer (hydrostatic pressure distribution with the density of brine). Hence, the average gas density ρ g for C il (Equation 4.7) does not take the pressure build up due to injection into account. This is warranted since the injection regime does not exceed the boundary for supercritical region (with its discontinuous change in viscosity and density), allowing it to return gradually to its initial (natural) conditions. With this configuration the author embraces all parameters defined by Doughty et al. (2001) and will show the need for reformulation of the approach for effective capacity (Equation 4.4).

37 FIPNUM (From property) FACIES_Base (From property) 5.5 Definition of the Storage Reservoir 28 Figure 5.7.: Partition of the reservoir model for the investigation of the different pore volumes, light green = area for idealized radial flow (Region 1), gray area = theoretically not accessible area (Region 2). Injection Well K_201 [MD] MD 630 Floodplain 640 Sand Channel 650 Region 1 Floodplain 660 Sand Channel 670 Floodplain Sand Channel 680 Floodplain 690 Region 2 Floodplain Sand Channel Floodplain Sand Channel Sand Channel Floodplain Figure 5.8.: Well section: Injection Well Ktzi201; first column: indicated triangles represent the position of the perforation; second column: partition in Regions 1 and 2; third column: Facies distribution.

38 6. Investigation on Grid Convergence Numerical methods are strongly influenced by the spatial discretization. On the one hand simulation grids with insufficient grid cells do not reflect the correct flow behavior in the porous media nor represent the high variability in geology. On the other hand an overestimated discretization affects the computational costs. The aim of the following chapter is to find a suitable discretization to identify the pressure and saturation in the area of interest correctly, to describe the gas segregation sufficiently and to provide a stable solution of the flow-equations. Initially for this work, the emphasis lays on representing the gravity override in order to achieve grid convergence in the near well region with as few cells as possible. In order to reflect this behavior correctly, different refinements are used. Here it is important that the different results are solely caused by the change of cell size and not due to any change in permeability and porosity. At this stage, the criteria for making an statement on grid convergence is the gas saturation in a certain grid block. Table 6.1 summarizes the spectrum of different discretizations between the wells. To assure the same gas saturation detection area for the different z-refinement steps, the cell which borders the next (property) layer above is always considered as shown in Figure 6.1. Figure 6.2 shows the interim results in terms of arrival times at the respective wells. We may conclude that the finer the grid in the z-direction, the faster the plume will arrive at the observation point. Additionally Figure 6.2 illustrates that one should aim to have at least 15 grid cells between the injection well and observation well in horizontal direction. At later times one observes in the temporarily chosen 2XZREFINE-realization for the investigation on arrival times, that the flow behavior is not presented correctly. In all analysed scenarios, including those not listed in this study, the dissolved gas front, which is expected to arrive slightly earlier than the mobile gas front, is detected in the simulation several days before the gas plume, which is incorrect. This error can be traced back to numerical dispersion. The author, therefore, has decided to change the discretization in order to amend the error within the numerical dispersion and two grids have been selected according to the objective of the investigation. A high-resolution grid for the investigation on arrival times, and a lower resolution grid for the investigation on storage capacity. Both discretizations are now briefly introduced: For the estimation of arrival times the grids are depicted in Figure 6.4 and 6.5, respectively. Between the wells, a high accuracy is reached by defining the dimension in both the x and y direction as 1.2 meter. Beyond this area, the cell size increases rapidly to 300 meters. Based on experience gained from the previous grid convergence investigations, for both grids a z of 0.5 meter is used throughout Region 1, introduced in Section 5.5. The grid, 29

39 30 Cell size [m] (in the near well region) x-direction y-direction z-direction COARSE XREFINE ZREFINE ZREFINEMORE XZREFINE XYREFINE YZREFINE XZREFINE XYZREFINE XZREFINEMORE Table 6.1.: Cell size in the area of interest for different realizations. prepared for investigation on storage capacity (Figure 6.3) is almost homogeneous with equidistant grid size.

40 Figure 6.1.: Well sections for the two observation wells for the grid convergence study. The red box illustrates the detection area. The first column shows the measured depth (MD), the second to forth column represents the three z-refinement steps (color represents the porosity-values). 31

41 32 0,7 0,6 Block Saturation [-] 0,5 0,4 0,3 0,2 0,1 0 COARSE XREFINE ZREFINE ZREFINEMORE XZREFINE XYREFINE YZREFINE 2XZREFINE 2XYZREFINE 2XZREFINEMORE Injection Time [hours] (a) Observation Well Ktzi200 Block Saturation [-] 0,4 0,35 0,3 0,25 0,2 0,15 COARSE XREFINE ZREFINE ZREFINEMORE XZREFINE XYREFINE YZREFINE 2XZREFINE 2XYZREFINE 2XZREFINEMORE 0,1 0, Injection Time [hours] (b) Observation Well Ktzi202 Figure 6.2.: Breakthrough curves for the first grid convergence study. Breakthrough is defined in terms of block gas saturation.

42 Figure 6.3.: Numerical grid for the estimation of storage capacity (from above), the colors represent the x discretization in meters. 33

43 Figure 6.4.: Numerical grid for the estimation of arrival times (zoom in, from above), the colors represent the x discretization in meter; red line = injection well Ktzi201, light blue line = observation well Ktzi200, orange line = observation well Ktzi

44 Figure 6.5.: Numerical grid for the estimation of arrival times (zoom out, from above). The colors represent the x discretization in meters. 35

45 7. Breakthrough Prediction Intensive work has been done on the Base Case realization up to now, providing the basis for the breakthrough-analysis of the Dynamic Flow Modeling Work Package (WP6.1) in CO2SINK (GFZ-Potsdam, 2008). The goals are to perform numerical simulations to assist risk assessment and to predict the plume evolution, phase change and pressure evolution in the Ketzin reservoir. Several simulations will be performed to obtain arrival times of injected CO 2 at observation wells Continuous Injection The major interest is here the prediction of the gas breakthrough at the observation wells. At the stage of writing this thesis, there were no observed data available. In this study breakthrough is analysed by plotting the detected mass [kg] in a defined area (representing the observation well) versus the cumulative injected mass [kg] or time [d]. Except for the fact that the observed mass depends on the detection volume, the results with this approach are independent from the injection pattern and more meaningful for future interpretations. The breakthrough is defined as the first 5 kg of CO 2 accumulating in the observation well. The detection area comprises all grid cells along the well trajectory (Figure 7.1). As expected, the dissolved CO 2 front arrives slightly before the gas front. Since the beginning of the injection, the gas plume pushes the transition zone (area between 100% water saturation and 100% CO 2 saturation) ahead. The first 5 kg of dissolved gas can be detected at Ketzin Ktzi200 after 9.44 days, which equals 815 tons injected CO 2. In comparison, the first 5 kg gaseous CO 2 can be observed after 9.64 days, which again equals 833 tons of injected CO Varying Injection Regime In addition to the continuous injection rate of 1 kg/s as outlined in Section 7.1, two other injection regimes are considered. The injection rate is varied. Table 7.1 shows the two different injection regimes for the first 158 hours, which are afterwards continued with an injection rate of 1 kg/s. Following Figure 7.2 compares the cumulative injected mass for all three injection regimes. The final results, also including the continuous injection, are shown in Figure 7.3 as well as Figure 7.4. Due to the variation of injection rate, the phase velocity decreases and only 96.43% of the injected mass is necessary to detect the 36

46 7.3 Pressure Development at the Cap Rock 37 Figure 7.1.: Detection area for analysing the breakthrough in Ktzi201, the cumulative mass is detected in all yellow cells (which are penetrated by the well). same mass of CO 2 using regime 2 (95.43% of injected mass using regime 3). Table 7.2 summarizes the varying breakthrough times for all three analysed injection pattern Pressure Development at the Cap Rock High risk is associated with the possibility of fracturing the sealing cap rock, which acts as a natural barrier. For that reason, it is essential to predict the pressure development below the cap rock layer. Under the assumption that the cap rock is impermeable, it is justifiable to model it with a no-flow boundary condition, even if the porosity is different from zero (affecting only the diffusion process). The formation fracture pressure, which represents the pressure above which the injection of fluids causes the rock formation to fracture hydraulically (Schlumberger, 2008b), was estimated at 82 bars (Mueller et al., 2007). The numerical results in Figure 7.5 prove that none of the injection regimes cause pressures higher than the formation fracture pressure. The pressures are recorded directly under the cap rock and 2m below it. The characteristic of the pressure curve shows immediate response to the pressure signal, sent out by the injector. Furthermore the results show that pressure development can significantly be controlled by the injection regime to ensure integrity of the stratigraphic barrier.

47 7.3 Pressure Development at the Cap Rock 38 Injection Interval [hours] Injection [kg/s] Regime 2 Regime Table 7.1.: Injection regimes besides continuous injection. Cumulative Injected Mass [kg] 1,4E+06 1,2E+06 1,0E+06 8,0E+05 6,0E+05 4,0E+05 2,0E+05 cumulative injected mass, regime 2 cumulative injected mass, continuous cumulative injected mass, regime 3 0,0E+00 0,0 5,0 10,0 15,0 Injection Time [days] Figure 7.2.: Comparison of the cumulative injected mass [kg] of CO 2 for different injection regimes over time [d].

48 7.3 Pressure Development at the Cap Rock 39 Mass CO2 in detection area [kg] mobile gas, continuous dissolved gas, continuous mobile Gas, regime 2 dissolved Gas, regime 2 mobile Gas, regime 3 dissolved Gas, regime ,00 5,00 10,00 15,00 20,00 Breakthrough time [days] Figure 7.3.: Breakthrough investigation for observation well Ktzi200, detected mobile and dissolved mass of CO 2 [kg] vs. injection time [days]. 10 Mass CO2 [kg] in detection area Ktzi Cumulative injected mass CO2 [kg] mobile gas, continuous dissolved gas, continuous mobile Gas, regime 2 dissolved Gas, regime 2 mobile Gas, regime 3 dissolved Gas, regime 3 Figure 7.4.: Breakthrough investigation for observation well Ktzi200, detected mobile and dissolved mass of CO 2 [kg] vs. cumulative injected mass [kg].

49 7.3 Pressure Development at the Cap Rock 40 Pressure [bar] Pressure below Cap Rock, continous injection Pressure 2m below Cap Rock, continuos injection Injection rate, continuous Injection Rate [kg/day] Injection Time [days] (a) Continuous Injection. Pressure [bar] Pressure below Cap Rock, Regime 2 Pressure 2m below Cap Rock, Regime 2 Injection rate, Regime Injection Rate [kg/day] Injection Time [days] (b) Injection Regime 2. Pressure [bar] Pressure below Cap Rock, Regime 3 Pressure 2m below Cap Rock, Regime 3 Injection rate, Regime Injection Rate [kg/day] Injection Time [days] (c) Injection Regimes 3. Figure 7.5.: Pressure development for different strategies.

50 7.3 Pressure Development at the Cap Rock 41 Breakthrough time [days] Continuous Regime 2 Regime 3 mobile gas dissolved gas Table 7.2.: Breakthrough times for the first 5 kg of dissolved CO 2 for varying injection pattern.

51 8. Estimation of Storage Capacity 8.1. Base Case In this section, all relevant capacity parameters (referring to Doughty et al. (2001)) and their occurrence for the Base Case are described in detail ending up with the effective capacity C after approximately 100 years. Before proceeding to the discrete characteristics, for the sake of completeness, some aspects resulting from the model preparation (Section 5.5) have to be mentioned here. Due to the distinction between Region 1 and 2 and considering only parameters from Region 1, one per mill of the injected mass gets lost because of entering into Region 2. The undoubted cause lies on the one hand in the irregular boundary between the regions (no planar plane) and on the other hand due to some gas flow from Region 1 to Region 2. However, almost all CO 2 in Region 2 is to be portioned to the mass transfer between the phases (dissolution). That mass, which equals only kg, also establishes that buoyancy driven flow is most important and necessitates the fine grid resolution in z-direction. In the following, this overspill is neglected. For the Base Case, the petrophysical modeling yields a pore volume P ORV access = rm 3 for the storage reservoir (Region 1). First of all the average densities are discussed. Whereas the average water density stays almost constant (ρ l = 1139kg/m 3 ), Figure 8.1 illustrates the drop in gas density. As mentioned in Section 5.5, the density does not reflect the increase of pressure due to injection. After a mild decrease within the first month, a steep decrease follows, indicating the ascension of the plume for 15 years. Finally, the plume accumulates below the cap rock, resulting in constant density. In a next step, we examine the sum of the pore volumes filled with CO 2 (referring to P ORVfilled with gas and P ORV filled with X g l in Section 4.2) and the resulting pore volume ratios (referring to C gg C hg and C gl C hl in Section 4.2). After a steady rise in both shares until the end of injection, the characteristics show an extreme partitioning. Figure 8.2 displays the accumulation in pore volume occupied by gas for about 15 years, which monotonically decreases afterwards until the end of the simulation. The reason for this is that after shutdown, the plume, still driven by viscous forces and buoyancy, displaces water further whereas the residual saturation remains in the imbibition area. The graph 8.2 also conveys, how difficult it is to define accurately the front because capacity coefficients are determined behind the gas front. In particular, up to half a year of CO 2 injection the total pore volume of dissolved gas (Xl CO2 ) is overestimated. The gas is expected to push the dissolved front, but not more than one additional grid cell during the whole injection period. On the one hand this phenomena can be traced back 42

52 8.1 Base Case 43 to numerical dispersion, on the other hand however one should keep in mind that the heavy (in terms of dissolved CO 2 ) water slumps, as Figure 4.3 illustrates. With increasing simulation time, the plume forms a bigger surface, which increases the dissolution. As a consequence, the mass fraction of CO 2 in brine (X CO2,l in Figure 8.3), decreases due to the volume averaging determination of the parameter, which covers a huge amount of cells with low mass fraction values in the transition zone. As the area for analysing the saturations is behind the front, the gas saturation increases until injection end, whereas the water saturation behaves reverse. At first glance it is a little irritating that the average liquid and gas saturations in Figure 8.3 do not equal one in sum. The values are obtained from volume averaging over different areas, implicating different pore volumes. The averaging area describing S l covers more space than S g. In the end the sum of both saturations is bigger than one. The decrease in residual trapped gas in Figure 8.4 can be attributed to a flooding process of the residual gas area with fresh water absorbing gas until it exceeds the solubility product. The ensuing drop down of the pore volume filled with gas (Figure 8.2) is the result of several interlinked mechanisms. In agreement with the decreasing trapped (field-) mass as well as with the massive increase in dissolved (field-) mass in Figure 8.4 and the almost constant average gas saturation in Figure 8.3 after ten years, this analysis acknowledges the importance of the dissolution process, finally resulting in very large pore volume filled with dissolved gas (Xl CO2 in Figure 8.2). Having discussed all the necessary parameters we may now apply them to Equation The analysis of Equation 4.10 then gives us the result presented in Figure 8.5. The logarithmic chart is chosen to display the time dependent course in more detail, especially after injection end. The graph 8.5 shows the potential volume fraction contributing to volumetric and dissolved share, relating to Equation With time, the fraction of both converge increasingly because the dissolved share becomes more important while the volumetric trapping exceeds its maximum right after injection end. Therefore the effective capacity C only increases during the first 25 years thereafter decreasing as a response of the loss of injection pressure. Further on the effective capacity decreases slightly, because of the high load of volumetric share decreasing. The dissolved share increases further on, finally showing once more the varying of the trapping mechanism with time. In the short-term, the advective processes (capillarity, viscous forces) dominate, whereas in the long-term the phase transfer process (dissolution) and the diffusion process become more and more important. The decrease in effective capacity shown in the graph is related to inaccuracy in determining the front in the numerical simulation. Therefore storage capacity of the Ketzin formation (Base Case) after 100 years is about 0.6 per mill (in terms of bulk volume) and 5.7 per mill (in terms of pore volume), respectively. It is important to note that these values are obtained based on a total injected mass of tons. At last, the numerical simulation illustrates the dependence of the particular storage mechanism on the facies. Although the floodplains have quite a small (mean) permeability (23mD) in comparison to very high permeable sand channels (276mD) the simulation shows that almost 84 percent of the remaining mobile gas accumulates in the floodplain.

53 8.2 Sensitivity Study on Net-to-Gross Gas Density Gas Density [kg/m³] Injection Stop 135 0,01 0, Simulation Time [Years] Figure 8.1.: Volume averaged gas density ρ g (c.f. Equation 4.7) in the Xl CO2 delimited area over time. The density is monotonically decreasing since the plume migrates upwards and the reservoir almost reaches the (natural) initial condition. Moreover the dissolved CO 2 shows exactly the opposite behavior, nearly 74 percent of the final dissolved mass can be found in the sandy channels. Focusing on the (residually) trapped mass of CO 2, the previously mentioned water imbibition becomes apparent. The immobile mass of CO 2 decreases continuously after five and a half years in the sand channels (Figure 8.4), whereas it increases solely in the floodplain. Finally Figure 8.6 illustrates the distribution of gas saturation, showing the shape of the gas plume. As expected, most of the gas can be observed in the first few layers below the cap rock (cap rock is not shown here) Sensitivity Study on Net-to-Gross The second aim of this thesis is to estimate the storage capacity, dependent on Net-to- Gross (N/G). N/G refers to the ratio of sand channel to floodplain facies in the Ketzin reservoir. A set of different N/G realizations have been created, covering a range from 30% to 50% (N/G of the Base Case: 41.16%). This study selected six different N/G to investigate their impact on storage capacity. All realizations are generated in PETREL, following the proceeding in Section 5.1. The total pore volume of each realization is shown in Figure 8.7. Whereas the pore volume in the field (P ORV field in Figure 8.7) increases with N/G, the pore volume in Region 1 ( P ORV access ) also increases in a different rate. During the creation of the different realizations attention is payed to the fact that the

54 8.2 Sensitivity Study on Net-to-Gross 45 Pore Volume [rm³] 4,50E+06 4,00E+06 3,50E+06 3,00E+06 2,50E+06 2,00E+06 1,50E+06 1,00E+06 5,00E+05 Pore Volume covered by Sg Pore Volume covered by X CO2,l Pore Volume Ratio Cig Pore Volume Ratio Cil Injection Stop 0,05 0,045 0,04 0,035 0,03 0,025 0,02 0,015 0,01 0,005 Pore Volume Ratio [-] 0,00E ,01 0, Simulation Time [Years] Figure 8.2.: Pore volumes and pore volume ratios (c.f. Equation 4.11 and 4.12) after delimiting the gas and dissolved front; whereas the gaseous volume reaches its maximum after 10 years, the volume filled with dissolved gas only increases due to solubility trapping. three upscaled facies logs from the Base Case are retained. This leads to the fact that the perforated cells show the N/G of percent (Base Case), but in all remaining cells the sand channels and floodplain facies are distributed according to N/G. The boundary condition for this study is based on the input data, summarized in Section 5.4, except the capillary pressure - saturation relationship. For each realization this constitutive relationship is evaluated dependent on the properties (see Figure 8.8). In the following the same procedure as in Section 8.1 is used for the analysis of each capacity parameter. First we will elaborate on the key aspect of storage capacity which enters into the Equation The characteristics in Figure 8.9 show for the different realizations the pore volume ratio, which is delimited by the gas front (referring to Equation 4.11) and mass fraction front (referring to Equation 4.12), respectively. Except for minor deviations, Figure 8.9 illustrates the expected trend in CO 2 filled pore volume. The less the N/G the greater the pore volume ratio C ig and pore volume ratio C il. Gas, respectively dissolved gas occupy in all realizations almost the same pore volume. The pore volume ratios C ig increase slowly to a maximum of 20 years, decreasing thereafter while the pore volume ratio C il (dissolved CO 2 ) increases monotonically. The associated saturations in the plume display opposite behaviour as one can see in Figure The injected gas displaces the brine and the liquid (brine) saturation in the X g l - delimited region decreases until the injection well is shut down. Immediately afterwards, the average liquid saturation converges towards the initial condition. What still stands out for explanation in all analyzed cases is the

55 8.2 Sensitivity Study on Net-to-Gross ,012 Saturation [-] 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 Injection Stop 0 0 0,01 0, Simulation Time [Years] S gas S liquid X CO2, l 0,01 0,008 0,006 0,004 0,002 Figure 8.3.: Volume average mass fraction of CO 2 in brine Xl CO2, gas and water saturation in their delimited area over time. Note that the saturations do not add up to 1, since they are averaged over different areas (due to different front delimitation). Mass fraction of CO2 in brine [kg/kg] Mass CO2 [kg] 4,50E+07 4,00E+07 3,50E+07 3,00E+07 2,50E+07 2,00E+07 1,50E+07 Mobile CO2 (field) Mobile CO2 (Channel) Mobile CO2 (Floodplain) Dissolved CO2 (field) Dissolved CO2 (Channel) Dissolved CO2 (Floodplain) Trapped CO2 (field) Trapped CO2 (Channel) Trapped CO2 (floodplain) Injection Stop 1,00E+07 5,00E+06 0,00E+00 0,01 0, Simulation Time [Years] Figure 8.4.: Mobile, residual and dissolved mass for the field and their partitioning between the facies sand-channel and floodplain.

56 8.2 Sensitivity Study on Net-to-Gross 47 Capacity Parameters [-] 0,0008 0,0007 0,0006 0,0005 0,0004 0,0003 0,0002 volumetric share dissolved share effec. Capacity C Injection Stop 0, ,01 0, Simulation Time [Years] Figure 8.5.: Volumetric and dissolved share and effective capacity C (c.f. Equation 4.10). After shut in, the volumetric share does not increase any more, whereas the dissolution process still goes on. slight increase in gas saturation after 40 years. In order to explain this phenomena one has to consider the dissolution process of the trapped gas, which is also included in the gas saturation S g. Additionally the gas accumulates in a small area below the cap rock which results in higher values for the gas saturation S g. As a next step, the volumetric and dissolved share is determined and displayed in the Figures 8.11 and First we will focus on the volumetric share. Following the increasing mass of injected gas, the volumetric part is continuously rising, but more or less independent from the N/G. In the subsequent period, it is worth mentioning the difference recorded. Whereas some realizations show a decrease in the volumetric share after 2.5 years, it is also possible for this to increase over a more extended period, such as for the N/G 46 case. The dissolved share, illustrated in Figure 8.12, however shows in all analyzed cases the same trend. The expected trapping contribution, due to solubility, is accommodated in the right way. With increasing simulation time the dissolved share is monotonically increasing and is still ongoing. Finally we sum up the volumetric and dissolved share to create effective capacity C (c.f. Equation 4.10). Referring to the resulting Figure 8.13, between the analyzed cases with different N/G ratios, we should note that in the long-run the difference is no bigger than The first greater variance in all characteristics can be registered after about 10.5 years, where some cases tend to stagnate, some decrease in effective capacity, and others still increase. Therefore variation in N/G seem not to influence storage capacity. This is a non expected result.

57 8.2 Sensitivity Study on Net-to-Gross 48 Figure 8.6.: Gas saturation after 100 years (Base Case). In the following, the author will examine these simulation results for the floodplain facies and the sand channel facies separately to understand the results summarized in Figure The Figures 8.14, 8.15 and 8.16 show the share of the dissolved, mobile and residually trapped CO 2 for the sand channels and the floodplain facies, respectively. As it was expected, all Figures show that the gas is preferring to enter the sand channel facies. Due to the pressure gradient, the mobile gas is displacing the brine in the high permeable sand channels and is finally residually trapped after re-imbitioned by the aquifer following injection stop. The higher the fraction of sand channels in the field, the smaller the mass of dissolved gas that will stay inside the floodplain. Almost 60 percent more mass dissolves within the same time period in the case of N/G equal to 30, in comparison to N/G equal to 50. The same mass accumulation trend, in terms of separating into the two facies, can also be observed for the mobile and immobile gas (Figure 8.15 and 8.16). The mobile mass distribution for the floodplain facies in Figure 8.15 can not easily be explained and exceeds the scope of this study. Overall the mass balance is honored. Finally, although effective capacity does not seem to change much for different N/G, as displayed in Figure 8.13, the differences have been evident when analysing separately sand

58 8.3 Sensitivity Study on Salinity 49 1,04E+08 1,02E+08 4,50E+14 4,00E+14 Pore Volume PORV access [rm³] 1,00E+08 9,80E+07 9,60E+07 9,40E+07 9,20E+07 9,00E+07 8,80E+07 8,60E+07 0,00E N/G PORV access PORV (field) 3,50E+14 3,00E+14 2,50E+14 2,00E+14 1,50E+14 1,00E+14 5,00E+13 Pore Volume PORV (field) [rm³] Figure 8.7.: Pore volumes in the (whole) field (P ORV (f ield)) and Region 1 ( P ORV access ), which is potentially accessible for CO 2. channels and floodplain facies. Additional illustrations of the N/G-realizations are given in the Appendix. Summarizing this study, the influence of the property N/G on storage capacity is minor based on the approach of Doughty et al. (2001). This is not satisfactory, because intuitively high N/G should provide higher storage capacity. Therefore the approach needs to be adapted for specific fields. This task exceeds the scope of the study Sensitivity Study on Salinity Since in reality the composition of the brine presumably varies with depth (salinity gradient) and differs from one to another storage site, it is of major interest whether storage capacity depends on these structural conditions. For this purpose we compare the already known Base Case scenario (salinity 0.2) with another one, having increased the share of the component NaCl in that way to get an aquifer with a salinity of In Figure 8.17 we contrast both shares (volumetric and dissolved) of the Base Case with the ones of the higher saline case. The physical-chemical behavior describing a decrease in solubility of CO 2 in brine for a more saline reservoir is accurately reflected in the analysis of the parameters of the effective storage capacity C. Whereas the volumetric share, representing the mobile gas, increases for a salinity of 0.22, the dissolved share decreases. These expected results are additionally verified by the overlapping developing of the effective storage capacity C for both salinities, as the injection regimes (same injection rate, same

59 8.3 Sensitivity Study on Salinity 50 Capillary Pressure [bar] 0,035 0,030 0,025 0,020 0,015 0,010 Plug and Bruining N/G 30 N/G 35 N/G 38 N/G 40 N/G 46 N/G 50 0,005 0, ,2 0,4 0,6 0,8 1 Water Saturation [-] Figure 8.8.: Capillary pressure - water saturation relationship for the sensitivity study on different N/G, the differences are caused by the variation of the average porosity and permeability depending on the upcoming realization. Pore Volume Ratio [-] 0,045 0,04 0,035 0,03 0,025 0,02 0,015 0,01 Pore Volume Ratio Cig N/G 30 Pore Volume Ratio Cil N/G 30 Pore Volume Ratio Cig N/G 35 Pore Volume Ratio Cil N/G 35 Pore Volume Ratio Cig N/G 38 Pore Volume Ratio Cil N/G 38 Pore Volume Ratio Cig N/G 40 Pore Volume Ratio Cil N/G 40 Pore Volume Ratio Cig N/G 46 Pore Volume Ratio Cil N/G 46 Pore Volume Ratio Cig N/G 50 Pore Volume Ratio Cil N/G 50 Injection Stop 0, ,01 0, Simulation Time [Years] Figure 8.9.: Pore volume ratios (c.f. Equation 4.11 and 4.12) after delimiting the gas and dissolved front for different N/G.

60 8.3 Sensitivity Study on Salinity 51 1 Saturation [-] 0,9 0,8 0,7 0,6 0,5 0,4 0,3 S gas N/G 30 S liquid N/G 30 S gas N/G 35 S liquid N/G 35 S gas N/G 38 S liquid N/G 38 S gas N/G 40 S liquid N/G 40 S gas N/G 46 S liquid N/G 46 S gas N/G 50 S liquid N/G 50 Injection Stop 0,2 0,1 0,01 0, Simulation Time [Years] Figure 8.10.: Volume averaged gas and water saturation within the delimited plume, note that the saturations do not add up one (c.f. Figure 8.3). Volumetric share [-] 0,0004 0, ,0003 0, ,0002 0, ,0001 volumetric share N/G 30 volumetric share N/G 35 volumetric share N/G 38 volumetric share N/G 40 volumetric share N/G 46 volumetric share N/G 50 Injection Stop 0, ,01 0, Simulation Time [Years] Figure 8.11.: Volumetric share (c.f. Equation 4.10) for a variety of different N/G.

61 8.3 Sensitivity Study on Salinity 52 0,00035 Dissolved share [-] 0,0003 0, ,0002 0, ,0001 dissolved share N/G 30 dissolved share N/G 35 dissolved share N/G 38 dissolved share N/G 40 dissolved share N/G 46 dissolved share N/G 50 Injection Stop 0, ,01 0, Simulation Time [Years] Figure 8.12.: Dissolved share (c.f. Equation 4.10) for a variety of different N/G. effective Capacity C [-] 0,0007 0,0006 0,0005 0,0004 0,0003 0,0002 effect. Capacity C N/G 30 effect. Capacity C N/G 35 effect. Capacity C N/G 38 effect. Capacity C N/G 40 effect. Capacity C N/G 46 effect. Capacity C N/G 50 Injection Stop 0, ,01 0, Simulation Time [Years] Figure 8.13.: Effective capacity C (c.f. Equation 4.10) for a variety of different N/G.

62 8.3 Sensitivity Study on Salinity 53 dissolved gas CO2 [kg] 2,0E+07 1,8E+07 1,6E+07 1,4E+07 1,2E+07 1,0E+07 8,0E+06 6,0E+06 4,0E+06 2,0E+06 N/G 30, channels N/G 30, floodplain N/G 35, channels N/G 35, floodplain N/G 38, channels N/G 38, floodplain N/G 40, channels N/G 40, floodplain N/G 46, channels N/G 46, floodplain N/G 50, channels N/G 50, floodplain Injection Stop 0,0E+00 0,01 0, Simulation Time [Years] Figure 8.14.: Cumulative dissolved gas [kg] in the sand channels and floodplain for a variety of different N/G. mobile gas CO2 [kg] 4,5E+07 4,0E+07 3,5E+07 3,0E+07 2,5E+07 2,0E+07 1,5E+07 1,0E+07 N/G 30, channels N/G 30, floodplain N/G 35, channels N/G 35, floodplain N/G 38, channels N/G 38, floodplain N/G 40, channels N/G 40, floodplain N/G 46, channels N/G 46, floodplain N/G 50, channels N/G 50, floodplain Injection Stop 5,0E+06 0,0E+00 0,01 0, Simulation Time [Years] Figure 8.15.: Cumulative mobile gas [kg] in the sand channels and floodplain for a variety of different N/G.

63 8.4 Sensitivity Study on Injection Rates and Relative Permeability 54 5,0E+06 immobile gas CO2 [kg] 4,5E+06 4,0E+06 3,5E+06 3,0E+06 2,5E+06 2,0E+06 1,5E+06 N/G 30, channels N/G 30, floodplain N/G 35, channels N/G 35, floodplain N/G 38, channels N/G 38, floodplain N/G 40, channels N/G 40, floodplain N/G 46, channels N/G 46, floodplain N/G 50, channels N/G 50, floodplain 1,0E+06 5,0E+05 Injection Stop 0,0E+00 0,01 0, Simulation Time [Years] Figure 8.16.: Cumulative immobile (residual) gas [kg] in the sand channels and floodplain for a variety of different N/G. mass) as well as the characteristic values of the reservoir (same relative permeability, same N/G realization etc.) are retained Sensitivity Study on Injection Rates and Relative Permeability As already outlined, the previous study has shown that the extended approach by Doughty et al. (2001) is suitable to give an approximate value for the storage capacity of a reservoir. The following section applies varying injection rates and another established relative permeability - saturation relationship from the literature to the investigation on storage capacity. We will first have a look at four injection regimes, injecting over the same period but each with multiple injection rates. Figure 8.18 and 8.19 summarize the results of this study and show clearly the increase in storage capacity by increasing the injection rate. If one doubles the injection rate and injects for the same period, even after 100 years, this multiplicator can be applied to the capacity factor as well. All injection regimes follow the same trend - the higher the injection rate, the higher the effective capacity. In addition the two different relative permeability relations, shown in Figure 5.4, have been examined. Residual saturation trapping can not be demonstrated with the Bennion and Bachu (2005) relative permeability - saturation relationship. The decrease in volumetric share right after injection end is the result of the missing residual gas saturation. Whereas

64 8.4 Sensitivity Study on Injection Rates and Relative Permeability 55 Capacity Parameters [-] 0,0008 0,0007 0,0006 0,0005 0,0004 0,0003 0,0002 volumetric share S = 0.2 dissolved share S = 0.2 effect. Capacity C S = 0.2 volumetric share S = 0.22 dissolved share S = 0.22 effect. Capacity C S = 0.22 Injection Stop 0, ,01 0, Simulation Time [years] Figure 8.17.: Volumetric and dissolved share and effective capacity C (c.f. Equation 4.10) for different Salinities S. Injection Regime volumetric share [-] Mueller and Maas (2008) Bennion and Bachu (2005) 1 kg/s kg/s no simulation 3 kg/s no simulation 4 kg/s Table 8.1.: Volumetric share (c.f. Equation 4.10) for different injection rates and relative permeability relations after 100 years. in the Base Case, the drop down detects 35 percent, for the case with 4 times injection rate, the drop down detects half. After injection stop, the zero residual gas saturation causes the plume not to leave any trace back from the area where it has already been. The brine returns to its initial condition. This phenomena implicates a decrease in the pore volume delimited by S g, finally resulting in lower capacity factors. Table 8.1 summarizes the volumetric share (referring to Equation 4.10) for four different injection rates (1 kg/s - 4 kg/s), particularly with both, a residual (Mueller and Maas, 2008) and a non residual (Bennion and Bachu, 2005) assigned relative permeability curve. Besides this, one can observe that a change in the relative permeability curve also entails a slight change in the distribution of the CO 2 plume throughout the reservoir. Figure 8.20 displays these slight differences in the movement of the plume. The plots are created for a cross-section through the injection well and show the plume after 40 and 60 days of constant injection.

65 8.4 Sensitivity Study on Injection Rates and Relative Permeability 56 Injection Regime volumetric share [-] Mueller and Maas (2008) Bennion and Bachu (2005) 1 kg/s over 7.6 a kg/s over 1.9 a Table 8.2.: Volumetric share (c.f. Equation 4.10) for injecting tons with different injection pattern and relative permeability relations after 100 years. Injection Rate Maximum Pressure [bar] 1 kg/s over 7.6 a 61,96 4 kg/s over 1.9 a Table 8.3.: Maximum pressure directly below the cap rock. Additionally another injection case has been included: An arbitrary mass of tons of pure CO 2 is injected with two different regimes. The first injection regime equals half of the previous one, used for the Base Case and N/G - sensitivity study (injection over 1.9 years), the second one controls the injector to inject the same mass over 7.6 years, keeping a constant rate of 1 kg/s. The results, related to storage capacity, are displayed in Figure 8.21 and summarized in Table 8.2. Both injection strategies show their inflection point for the volumetric share and respectively the effective capacity directly after shutting down the well. One can see in Figure 8.21 that the final effective capacities C progressively approximate and almost overlap after the considered simulation time of 100 years. Referring to Equation 4.13, this analysis proves the consistency of the extended approach. Injecting the same mass M eff of CO 2 must result in almost the same effective capacity C since the average gas density differs only marginally after 100 years and the bulk volume is exactly the same for both injection regimes. However the volumetric share for both regimes is different. Whereas the long term injection results after 100 years in a volumetric share of , the injection of the same amount mass over a shorter period (1.9 years) gives a value of This little difference, at the first sight barely noticeable, must not be neglected as Figure 8.22 confirms. Injecting the same amount of mass, after 100 years the mobile mass can be reduced by a quarter only by injecting over a fourth of the period. Once more, this study shows, that the injection strategy has a major influence on the continuance in place of the CO 2 in mobile, immobile and residual state, whereby however the fracturing pressure of the cap rock must also be taken into account in the risk assessment. Figure 8.23 shows the drawback of the possibility to reduce the mobile gas, namely the additional pressure built up directly below the cap rock at the injector due to the high injection rate. The maximum pressure below the cap rock is detected after almost the same time for both regimes, but with difference of 7.7 bars. It has to be remarked that due to the log scale the initial pressure of the associated grid block of bars can not be displayed. Table 8.3 illustrates the maximum pressure evolving due to different constant injection rates.

66 8.4 Sensitivity Study on Injection Rates and Relative Permeability 57 Capacity Factors [-] 0,0014 0,0012 0,001 0,0008 0,0006 0,0004 volumetric share 1 kg/s dissolved share 1 kg/s volumetric share 1 kg/s (Viking) dissolved share 1 kg/s (Viking) volumetric share 2 kg/s dissolved share 2 kg/s volumetric share 3 kg/s dissolved share 3 kg/s volumetric share 4 kg/s dissolved share 4 kg/s volumetric share 4 kg/s (Viking) dissolved share 4 kg/s (Viking) 0,0002 Injection Stop 0 0,01 0, Simulation Time [Years] Figure 8.18.: Volumetric and dissolved share (c.f. Equation 4.10) for different injection rates (1kg/s, 2kg/s, 3kg/s and 4kg/s over 1.9 years) and relative permeability relations (Mueller and Maas (2008) and Bennion and Bachu (2005)). 0,0025 effective Capacity C [-] 0,002 0,0015 0,001 effec. Capacity C 1 kg/s effec. Capacity C 1 kg/s (Viking) effec. Capacity C 2 kg/s effec. Capacity C 3 kg/s effec. Capacity C 4 kg/s effec. Capacity C 4 kg/s (Viking) Injection Stop 0, ,01 0, Simulation Time [Years] Figure 8.19.: Effective Capacity C (c.f. Equation 4.10) for different injection rates (1kg/s, 2kg/s, 3kg/s and 4kg/s over 1.9 years) and relative permeability relations (Mueller and Maas (2008) and Bennion and Bachu (2005)).

67 8.4 Sensitivity Study on Injection Rates and Relative Permeability 58 (a) Mueller and Maas (2008) (b) Bennion and Bachu (2005) (c) Mueller and Maas (2008) (d) Bennion and Bachu (2005) Figure 8.20.: Gas saturation after 40 days (8.20(a) (b)) and 60 days (8.20(c) (d)) of continuous injection for different relative permeability relations (Mueller and Maas (2008) and Bennion and Bachu (2005)) based on the numerical grid for estimation of arrival times.

68 8.4 Sensitivity Study on Injection Rates and Relative Permeability 59 Capacity Factors [-] 0,0025 0,002 0,0015 0,001 volumetric share 4 kg/s dissolved share 4 kg/s effec. Capacity C 4 kg/s volumetric share 4 kg/s (Viking) dissolved share 4 kg/s (Viking) effec. Capacity C 4 kg/s (Viking) volumetric share 1 kg/s dissolved share 1 kg/s effec. Capacity C 1 kg/s volumetric share 1 kg/s (Viking) dissolved share 1 kg/s (Viking) effec. Capacity C 1 kg/s (Viking) Injection Stop 4 kg/s 0,0005 Injection Stop 1 kg/s 0 0,01 0, Simulation Time [Years] Figure 8.21.: Volumetric and dissolved share and effective capacity C (c.f. Equation 4.10) for injecting the same amount mass ( tons of injected CO 2 ); Two different injection regimes (4kg/s over 1.9 years and 1kg/s over 7.6 years) and two relative permeability relations (Mueller and Maas (2008) and Bennion and Bachu (2005)) are considered.

69 8.4 Sensitivity Study on Injection Rates and Relative Permeability 60 Field Mass CO2 [kg] 2,0E+08 1,8E+08 1,6E+08 1,4E+08 1,2E+08 1,0E+08 8,0E+07 6,0E+07 immobile gas 1 kg/s immobile gas 4 kg/s mobile gas 1 kg/s mobile gas 4 kg/s dissolved gas 1 kg/s dissolved gas 4 kg/s Injection Stop 4 kg/s Injection Stop 1 kg/s 4,0E+07 2,0E+07 0,0E+00 0,01 0, Simulation Time [Years] Figure 8.22.: Partitioning of the injected mass ( tons) into dissolved, mobile and immobile gas for two different injection regimes (4kg/s over 1.9 years and 1kg/s over 7.6 years) Injection of 1 kg/s Injection of 4 kg/s 66 Pressure [bar] Injection Stop 1 kg/s 58 Injection Stop 4 kg/s , Simulation Time [Years] Figure 8.23.: Pressure development directly below the cap rock for two different injection regimes (4kg/s over 1.9 years and 1kg/s over 7.6 years).

70 9. Final Remarks 9.1. Conclusion The numerical simulation provides an efficient tool for the modeling of CO 2 injection into geological formations. Here the author has used numerical tools to investigate effective capacity and breakthrough predictions. The combination of the use of a geological software tool and a reservoir simulator allows to be investigated the complex physical processes associated with CO 2 sequestration. I briefly summarize the findings of this work: The choice of discretization is of paramount importance to get accurate simulation results modeling CO 2 sequestration. In order to properly include gravity override of CO 2 modeler should select carefully the z. Here it is needed to be at least 0.5 meter. Furthermore the investigation on grid convergence in combination with the estimate of breakthrough indicated at least 3 meters for each grid block edge for that specific problem. In contrast to a continuous injection strategy, a pulsing one might also be of interest, since the pressure below the cap rock only gradually increases. In the case of the CO2SINK project (GFZ-Potsdam, 2008), the sensitivity of timing of the gas breakthrough due to different injection regimes is clearly recognized. For the saline aquifer of Ketzin the simulation comes up with an effective storage capacity C (Doughty et al., 2001) of 0.6 per mill in terms of bulk volume and 5.7 per mill in terms of pore volume. This specific value is the result when injecting tons of CO 2 within 695 days (equals an injection rate of 1 kg/s). In this study, the author could not derive an interrelation between the variation of N/G and the effective storage capacity. The numerical simulations illustrate that for all examined realizations there is definitely a N/G-dependency trend in the pore volume ratio of gaseous and dissolved CO 2. It is however not reflected in the effective capacity. The influence of the property N/G on storage capacity is minor based on the approach of Doughty et al. (2001). This is not satisfactory, because intuitively high N/G should provide higher storage capacity. The sensitivity study on injection rates over the same time ( increasing injected mass) illustrates, that effective storage capacity by Doughty et al. (2001) is always subject to the injected mass of CO 2 and it is always compulsory to mention that amount of mass when giving a specific estimate for a reservoir. 61

71 9.2 Outlook 62 As a result of the study, injecting the same amount of mass over different periods, the effective storage capacity (Doughty et al., 2001) after 100 years only shows marginal changes. However, the evolution towards the final state until these 100 years differs. The long term effective capacity (Doughty et al., 2001) is strongly dependent on relative permeability relations, especially with respect of the state of CO 2 (residually trapped, mobile and dissolved) Outlook This work can be considered as a starting point for more far-reaching investigations on storage capacity in the broader sense. The numerical simulations represented in this work helped to identify difficulties in the application of published storage capacity methodology to a specific field project. Improvements will be necessary not only in the methodology, but also in the numerics and its implemented physics. First of all the process of hysteresis has to be included in the simulation. This phenomena was not subject of the present work at all, but presumably changes the volumetric and dissolved share. Bennion and Bachu (2005) provides measurements for displacement characteristics accounting for the drainage and imbibition process. Moreover the drainage imbibition process affects the capillary pressure - saturation relationship and so the parts of the displaced phase, which can be held back in the pore channels, and the residual saturation. However, the residual saturation is not only influenced by the kind of displacement process, but also by the number of drainage and imbibition cycles (Helmig, 1997). The delimitation of the dissolved front in the simulation is a difficult problem, potentially the biggest source of error in the analysis of the dissolved share. The root of that problem can be traced back to the numerical dispersion. The author suggests investigating three concepts: Application of adaptive mesh refinement has several advantages: Considering the long term storage of CO 2 as large scale problem, which in fact generally requires an accurate specification of the gas front propagation, the use of a dynamic gridding scheme instead of an overall high resolution static grid would unify several advantages. By tracking the fronts and adapting the numerical discretization to it, one would be able to reduce numerical dispersion, involving a better reproduction of the physical processes (front propagation, diffusion). Storage savings due to smaller file sizes. Computational savings: Less memory (RAM) is necessary and one can achieve a better performance.

72 9.2 Outlook 63 Combination of the numerical (compositional) simulator with an analytical solver: The idea is to separate the CO 2 in the liquid phase (Xl CO2 ) from the other phases and apply an analytical solver, which addresses the Buckley Leverett problem to model a sharp front propagation. Since we consider only the liquid phase as incompressible, the scheme of Front-Tracking definitely qualifies for that modeling purposes. Thereby one might achieve a more accurate dissolved front. Additionally, the determination of the front might be more accurate by applying a time dependent criteria for the dissolution of CO 2. However, this approach would entail many changes in the model, including the local equilibrium assumption. The underlying assumption of thermodynamic equilibrium would no longer be satisfied, since there is no chemical equilibrium and the processes could not be treated as reversible any more. The solution of an additional balance equation (entropy) is essential as well as the consideration of the chemical potential of the components in both phases. If the kinetics are implemented in the code the computational cost would increase, whereas the question arises, whether this effort achieves relevant changes in storage capacity. A statistical analysis of about 100 geological realizations strikes the author more meaningful. Nevertheless this proposal can not be accomplished with the numerical simulator used in this work within a reasonable amount of time due to high computational costs. Therefore a compositional streamline code is proposed, which has the ability to represent the gravity segregation. This numerical scheme combines high performance and an acceptable accuracy for a more general statement concerning storage capacity.

73 A. Graphic Plots (a) Horizontal permeability N/G 30. (b) Gas saturation N/G 30. (c) Horizontal permeability N/G 35. (d) Gas saturation N/G 35. Figure A.1.: Horizontal permeability (P erm x and P erm y ) for different N/G vs. gas saturation after 100 yeras. 64

74 65 (a) Horizontal permeability N/G 38. (b) Gas saturation N/G 38. (c) Horizontal permeability N/G 40. (d) Gas saturation N/G 40. (e) Horizontal permeability N/G 46. (f) Gas saturation N/G 46. Figure A.2.: Horizontal permeability (P ermx and P ermy ) for different N/G vs. gas saturation after 100 yeras.