Sensitivity Analysis of CO2 Injection within Saline Aquifers for Storage

Article pubs.acs.org/jced

Sensitivity Analysis of CO2 Injection within Saline Aquifers for Storage Purposes in the Form of Hydrate Using a Reactive Transport Simulator Khadijeh Qorbani,* Bjørn Kvamme, and Richard Olsen Department of Physics and Technology, University of Bergen, 5020 Bergen, Norway S Supporting Information *

ABSTRACT: One method to mitigate the impact of fossilfuel-generated CO2 on the climate is to store it in geological structures in the form of CO2 hydrate. Geological sequestration of CO2 involves risks and the capability to predict the response of a geologic system to variations in thermodynamic variables for short- and long-term situations is needed. We have utilized an existing CO2 hydrate reactive transport simulator, which incorporates a full kinetic description of competing hydrate phase transitions through Gibb’s free energy minimization under the constraints of mass and heat flux. Hydrate formation from gas and liquid water and from water and dissolved hydrate formers was considered. Simulations were used to conduct sensitivity studies on some of the main reservoir parameters to understand which characteristics that appeared to have most impact on stability of CO2 storage in the form of hydrate. Hydrate formation was studied for various operational conditions of CO2 injection using a twodimensional model reservoir. CO2 was injected into a structure consisting of two aquifer zones, one caprock zone, one fracture, and two injection wells. At this stage of the simulator, a fracture is modeled as a zone of very high porosity and permeability. It was found that porosity in the regions of hydrate stability varied linearly with respect to fracture porosity, matrix porosity, injection temperature, injection pressure and water saturation, within the studied ranges. However, porosity followed approximately a second-order polynomial with respect to fracture permeability. Our model was most sensitive to changes in the matrix porosity, whereas changes in temperature, within a realistic range, appeared to have small effects. Variations in either pure calcite or pure quartz only resulted in moderate effects on porosity. A geochemical mineral composition of equal amounts of calcite and quartz, however, appeared to result in substantial reduction in hydrate formation according to the samplings from the model studies.

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INTRODUCTION CO2 emissions to the atmosphere have been increasing proportional to the development of the modern industrial world as we know it today. As such, CO2 is considered as one of the main human created factors that promote climate warming.1 As a result, CO2 capture and storage has become an important strategy to mitigate climate change. Several methods have been proposed to reduce CO2 emission into the atmosphere. Storing CO2 into saline aquifers in the form of hydrate is one of the possibilities. CO2 hydrate is heavier than water and CO2 could potentially provide safe long-term storage. Aquifers are the most prevalent geological structures that provide high capacity for CO2 storage.2 CH4 in the atmosphere is a more aggressive greenhouse gas than CO2. Maybe as much as 20 times more aggressive than CO2 but lifetime in the atmosphere is shorter due to the lower density.2−4 The average time that released CH4 remain in the earth atmosphere depends on temperature and pressure but 12 years is a typical indicative value.5 Thus, CH4 that is released through dissociation of hydrates in natural gas hydrate © 2016 American Chemical Society

reservoirs (NGHs) could potentially add to the climate changes.6 Several methods have been proposed for CH4 production from NGHs,7,8 with pressure reduction as the method that presently attracts most attention in pilot tests as well as in theoretical evaluations of value potential of specific hydrate reservoirs. An alternative method suggested for CO2 sequestration is the injection of CO2 into CH4 hydrate reservoirs.9−14 This method serves a dual purpose. First of all, safe long-term storage of CO2 in a solid phase beneath a sealed formation has a substantial value by itself. The fact that the in situ CH4 hydrate has been there for a long time, even millions of years, proves that the sealing (clay, shale, ice) is stable. The second purpose is the release of CH4. If CO2 only replace CH4 in large cavities there will theoretically be a 1:1 Special Issue: Proceedings of PPEPPD 2016 Received: July 1, 2016 Accepted: September 15, 2016 Published: September 27, 2016 4148

DOI: 10.1021/acs.jced.6b00567 J. Chem. Eng. Data 2016, 61, 4148−4156

Journal of Chemical & Engineering Data

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rates two parts: CodeBright and Retraso.18 Inside RCB, the CodeBright part implicitly solves the mass flow, heat flow, and geomechanical equations19−21 at every time step. Results from this code are delivered to Retraso,22 which is a code for solving two-dimensional reactive transport calculations. It solves the relevant geochemistry equations, including hydrate pseudoreactions, at every time step and at every node. From relevant available mass and thermodynamic conditions, Retraso determines which reactions are applicable within each node. Finally, after updating flow properties (i.e., porosity and permeability), output from this code is transferred back to the CodeBright part in preparation for the next time step. The consistent form of the van Genuchten model23 was applied to the liquid phase relative permeability, whereas the generalized power model was applied to the gas phase relative permeability and was adapted to work for hydrate-bearing sediments. In future extensions of the code, this correlation will be replaced by correlations derived from pore scale modeling of phase transition under hydrodynamic flow. One approach for this is the approach used by Toru Sato that involves a coupling between Boltzmann flow and a kinetic model for hydrate dissociation.24 A more advanced approach is the use of phase field theory.10,25 So far, fractures are still considered as geometrical regions of the reservoir with exceptionally high permeability, in contrast to considering these as a hydrodynamic region with boundary conditions toward Darcy flow in the connection reservoir boundaries. This is a very common approximation in academic reservoir simulators and even in some of the commercial simulators. Therefore, at this point, we only examine the responses to some variation range in permeability, which should visualize variations in fracture size and characteristics. Our group has previously extended RCB by adding an inhouse nonequilibrium thermodynamics package enabling two routes to CO2 hydrate formation from aqueous and gas phases.26,27 For further information about the code and relevant modifications, see refs 18, 26, 27 and 28. Theoretical Approach. A brief description of the theoretical background is given in this section. For further details, the reader is directed to previous publications26−28 on the simulator and integration algorithms. Gas hydrates in nature originate from various hydrate formers, where the different routes are shown in Figure 1. Hydrates in porous media can never reach thermodynamic equilibrium. This can be seen from the number of independent variables and the balance

exchange between injected CO2 and released CH4. The released CH4 will compensate for the costs of CO2 storage and likely also give a net economic revenue. The primary mechanism as CO2 is injected into CH4 hydrate reservoirs involves the formation of new CO2 hydrate from injected gas and free water in the pores. The second mechanism, which is rather slow, is a solid state transformation in which CO2 gas replaces CH4 from large cavities of the hydrate structure. Another advantage of storing CO2 into NGHs in the form of hydrate is that newly formed CO2 hydrate and mixed CO2/ CH4 hydrate are thermodynamically more stable than in situ CH4 hydrate.15 Replacing a solid ice-like structure with a similar structure will assist in retaining the geomechanical stability, as compared to pressure reduction assisted hydrate dissociation, which implies a reduction in filled pore volume density.16 Technology for injecting CO2 into an aquifer already exists.17 However, there is still limited knowledge about the fate of CO2 that is injected into aquifers or gas hydrate reservoirs. Any concept of geological storage of CO2 has to be verified in terms of safety and integrity for short-term storage as well as for longterm storage. Field scale experiments are costly and it normally takes a long time to get the required information. Computer simulation is the only tool that can imitate very long time scenarios, although the quality of the sampled results is highly dependent on how realistic the physical models of the simulators are. Uncertainties in the model descriptions can to some extent be compensated by running sets of simulations for the same problem but with a range of reservoir characteristics and flow-related parameters so as to build up a range of possible outcomes, which hopefully is representative enough for the real case. Because of the heterogeneity of underground structures, there exist many uncertainties in reservoir characterization and in plateau predictions (i.e., reservoir response). As a result, sensitivity analysis on the main reservoir parameters are of high importance. All conventional hydrate simulators work under the assumption that geochemical reactions will proceed to equilibrium. However, incorporation of competing hydrate reaction kinetics is needed for realistic models that provide accurate representations of the CO2 behavior. To the authors’ knowledge, RCB is the only hydrate simulator which contains nonequilibrium evaluation of competing phase transitions involving hydrate formation and dissociation. In this paper, some of the important properties that affected injected CO2 behavior toward hydrate formation were addressed through sensitivity analysis on some of the formation properties. A two-dimensional model that consists of two aquifers, one caprock, and two fractures was constructed and ran for several different scenarios to see the impact of different parameters on the reservoir. The second section reports the methodology, the third section contains results and a discussion of these and our findings are summarized in the last section.

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METHODOLOGY RCB Simulator Package. RetrasoCodeBright (RCB) is a numerical hydrate reactive transport simulator and, in its extended version, it is adopted for aquifer storage of CO2 and for hydrate formation during storage, as well as for natural hydrate production modeling. Therefore, it is fundamentally different from other hydrate reservoir simulators. It incorpo-

Figure 1. Routes to hydrate formation, where routes added to RCB are shown in red. 4149



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on pressure, temperature, and mole fraction. If the CO2 mole fraction in the system lies between the red plane and the blue line, then the aqueous phase will be supersaturated with respect to CO2 and hydrate formation will follow the reaction in eq 1. If the CO2 mole fraction is located below the blue line, the driving force will be toward hydrate dissociation according to eq 1. However, if the CO2 mole fraction is above the red plane, degassing will take place. Furthermore, if pressure and temperature is inside the hydrate stability region, hydrate will start to form following the reaction in eq 2. CO2 hydrate formed through the reaction of eq 1 has a different free energy than CO2 hydrate formed through the reaction of eq 2. This is because CO2 from the aqueous phase results in different filling fraction in hydrate structure I than CO2 from the gas phase. It was assumed that CO2 fills large cavities in hydrate structure I, then the filling fraction of CO2 in large cavities of hydrate structure I is calculated as

toward conservation laws. This, of course, is trivially known from equilibrium measurements of hydrate equilibrium for hydrate formed from gas methane and liquid water. Because of the Gibbs phase rule, only one independent thermodynamic variable can be fixed. In a pore within a sediment, both temperature and pressure is defined by fluid dynamics and geothermal gradients. But the situation inside a pore is even more complex due to the role of solid mineral surfaces, which adds to the number of active phases. Mineral surfaces acts like adsorption sites for up concentration of hydrate formers and kinetically efficient 2D heterogeneous hydrate nucleation. But the formed hydrate nuclei cannot stick to the mineral surfaces due to incompatibility between partial charges. Furthermore, in a nonequilibrium system, guest molecule chemical potentials within various phases are not the same. Hydrate formed from hydrate formers in gas and liquid water will form a hydrate of different composition and density compared to hydrate formers from water solution or adsorbed hydrate formers. Therefore, by thermodynamic definition, this will be separate phases. Adding more hydrate formers to the gas phase does not simplify the situation since by the combined first and second laws of thermodynamics the most stable phases forms first, under the constraints of mass- and heat-transport. As a result, because of the Gibbs phase rule and the combined first and second laws of thermodynamics26,27 hydrates in nature will be in nonequilibrium. Depending on the hydrate former phases, there will be separate hydrate formation paths. Thus, a reactive transport simulator which has the capability to consider all hydrate phase transition routes is required. Previously, in our group, RCB has been extended to include two routes leading to CO2 hydrate formation. These are 6CO(aq) 2

(liq)

+ 46H 2O

1

→ (hydrate)

(H , L)

+Δg inc, L}

(H , L)

1 + e{μCO2

+Δg inc, L}

(3)

where Δg is the energy of inclusion of CO2 into large cavities of hydrate structure I and is calculated using ref 29. Chemical potential of CO2 in the hydrate structure, μ(H,L) CO2 , is (g) equal to μ(aq) in eq 1 and equal to μ in eq 2, with CO2 CO2 inc,L

∞ (aq) (aq) ∞ μCO = μCO + RT ·ln(xCO ·γ ) 2 CO 2

2

(g) μCO 2

id.g. μCO 2

=

2

+

(g) RT ·ln(yCO ·ϕCO ) 2 2

The extended version of RCB, developed in refs 26, 27, and 28, was utilized to conduct the sensitivity analysis. In ref 26, the extensions were used to study CO2 hydrate formation through injection of CO2 into aquifers. In this work, fracture porosity and permeability, matrix porosity, and material of layers were varied to analyze their effect on hydrate formation. Each competing hydrate phase transition was modeled as a pseudoreaction and subsequently treated as a nonequilibrium reaction, subject to the free energy minimization algorithm. Only those hydrate phases that had a negative and low enough value of ΔG to pass the barrier for hydrate nucleation had the opportunity to form. Hydrate phase transitions are controlled by a mass and a thermodynamical term. Thus, classical nucleation theory was used to calculate the kinetic rate of hydrate formation and dissociation

(1)

and 6CO(gas) + 46H 2O(liq) → (hydrate)2 2

e{μCO2

L θCO = 2

(2)

Whether CO2 hydrate formation will take place through the reaction in eq 1 or the reaction in eq 2 depends on the solubility of CO2. Figure 2 illustrates the solubility dependence

R = R 0·e−β ΔG

(4) 2

where R is the rate of hydrate phase transitions in mol/(m s), and R0 is the mass transport control term that is approximately 10.152 × 10−9 mol/(m2 s). ΔG, the Gibb’s free energy difference between the molecules in hydrate and former phases is calculated as26 H H p ΔG = xwH[μwH − μwp ] + xCO [μCO − μCO ] ,L 2, L 2

2

where p could be either CO2 in aqueous or in gas phase. In the future, it is a goal to incorporate more physically correct fracture model through Navier−Stokes hydrodynamics. However, even more urgent is the development of new correlations for the permeability/porosity relationships. A system of hydrate-filling pore volume is totally different than a system of almost nonpolar hydrocarbon gas and liquid.

Figure 2. Red surface showing the maximum CO2 solubility inside the aqueous phase and the blue line showing the minimum solubility of CO2 that is required to keep CO2 hydrate stable. 4150



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dissociation inside RCB was analyzed based on porosity variations at each node and each time step, described by

Because the hydrate cannot attach to mineral surfaces due to incompatibility in atomistic partial charge distributions on the surfaces the minimum distances between mineral and hydrate is a layer of more or less structured water. Practically, this layer will be enhanced by ions in the groundwater and diffusional flow. For that reason, most natural hydrates in Alaska have a hydrate pore saturation of less than 85%. The flow regime through the pores is therefore quite complex due to geometry of the hydrate filling and the polar nature of the hydrate crystals. Pore scale modeling using concepts from fluid dynamics with implicit couplings to verified models for hydrate dissociation kinetics is one way to move forward.

Δϕ = −∑ Vhyd, iΔC hyd, i i

where Vhyd is the molar volume of the hydrate and ΔChyd,i shows hydrate concentration changes in mol/m3 of hydrate. The sum in the above equation runs over the different hydrate phases. Nucleation and growth processes of hydrate govern the choice of habit for the hydrate. Hydrate nucleation starts out as pore filling, where formed hydrate grows freely within the pore space.30 In our model, cement-type hydrate structures are not possible, in a true sense, because partial charges on pore wall minerals are incompatible with the water partial charge distribution on hydrate surface (due to partial charges on hydrogens and oxygens). Thus, a minimum bridging of 3−5 water molecules is a minimum requirement (i.e., 1.5 nm) because mineral structures some water layers outside (roughly 3) and hydrate also impose a structure on surrounding waters (2−3 water layers). In between these two structuring water layers, the water molecules have higher diffusivity coefficients maybe even close to bulk water and some pore flow of water will be in place, normally above self-diffusion. That is why hydrate saturations hardly exceed 85% and some fraction of the liquid water will have low mobility (pore bounded or simply adsorbed to mineral surfaces). Therefore, hydrates are pore filling and can never be cementing in a true sense. The lowest limit of water thickness, if it is ever reached in real nature, will give fairly tight connection between hydrate and minerals through hydrogen bond bridges. Fracture Permeability. Within hydrate bearing sediments, dissolved gas as well as free gas transport is affected by permeability. This is also the case for concentrations, accumulation and distribution of hydrate. Strictly speaking the flow through a fracture is hydrodynamic and implementation of Navier−Stokes is on the agenda for future modifications of the code. At the present level of the code, a fracture is approximated by a region of very high permeability. Figure 4 shows changes in porosity, ϕn, as a function of fracture permeability, Kf, at a specific node that was chosen due to its position close to a point where hydrate nucleation was initiated. Porosities for different fracture permeabilities were plotted as a function of time, as well as

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RESULTS AND DISCUSSION Model Description. A two-dimensional finite element model, shown in Figure 3, was used as the hypothetical target

Figure 3. Reservoir model used in our simulations. The grid of the model represents the spacial discretization used in the simulations. Node number 450 was studied specifically and was chosen due to its position close to a point where hydrate nucleation was initiated.

aquifer. The model domain was 1000 m in the horizontal direction and 300 m in the vertical direction and consisted of 1500 grid-blocks (i.e., 50 horizontal by 30 vertical), where each grid block was 20 m by 10 m. Two injection wells were placed in the two corners of the model. The model reservoir contained one caprock, two aquifers, and two fractures. Within this generic fracture model, the fracture porosity was set to 0.5 and permeability to 10−10 m2. The rock matrix in the aquifer was designated a porosity of 0.3 and a permeability of 10−13 m2. Porosity and permeability in the caprock were set to 0.03 and 10−17 m2, respectively. Boundary conditions, layer properties, material properties, CO2 hydrate specifications, and the species that were used for geochemical reactions are all listed in the Supporting Information. To investigate the response of the reservoir with respect to different input parameters, the model was run with several scenarios including variation in fracture permeability and porosity, matrix porosity, and injection pressure and temperature as well as layer mineralogy. These parameters are just a selection of typical parameters and variables that are unique for each individual hydrate reservoir and the focus has been on the sensitivity of these parameters for one specific example. Other examples with other locations of injection wells, producing wells, and fractures will show differences in sensitivity, but the general trends are still expected to have some transferability. The upper aquifer had pressures and temperatures located inside the hydrate stability region. After injected gas had penetrated through the fractures toward the upper aquifer, hydrate started to form. By definition, porosity is the fraction of the pore volume which is occupied with fluid phases. Hydrate formation and

Figure 4. Porosity, ϕn, as a function of time for a selection of fracture permeabilities, Kf, (left) and porosity as a function of fracture permeability at three separate time steps, where solid lines are secondorder polynomial fits and points are taken from the simulations (right). All values were probed at node 450 in the two-dimensional reservoir model (see Figure 3). 4151



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porosities as a function of permeability at three different time steps. When gas entered the upper aquifer, where pressures and temperatures were within the hydrate stability region, hydrate started to form, thus resulting in a reduction of porosity. From Figure 4, it can be seen that for all studied fracture permeabilities, porosity started to decrease after approximately one year due to hydrate formation. After approximately 3.5 years, the hydrate formation slowed down. No hydrate formation was observed during the first year since gas had not yet reached the upper aquifer. However, distinct changes in the porosity as a function of time could be observed due to changes in fracture permeability. It can be seen that at distinct time steps the calculated porosity as a function of fracture permeability showed a nonlinear behavior (see right-hand plot of Figure 4). For fracture permeabilities in the range between 10−13 and 10−8 m2, a good fit to the data points was achieved using a fit to a second-order polynomial function, where distinct minima of the porosity were observed within the studied range. During samplings from the conducted simulations, the highest amounts of hydrate was formed around the fracture with an associated estimated fracture permeability of approximately 10−10 m2 (see orange curve in left plot of Figure 4). The changes in fracture permeability resulted in a change in porosity of as much as 24%, thus indicating a high sensitivity to this parameter. When fracture permeability was low, gas flux passing the fracture toward the upper aquifer would be small compared to situations where the fracture permeability was high. Thus, the amount of CO2 accessible for hydrate to form was lower. As a result, the hydrate formation rate was lower at low fracture permeability, as can be seen from the right-hand plot in Figure 4. However, with higher fracture permeability, gas flux inside the fracture was higher toward the upper aquifer and hydrate formation took place faster, due to CO 2 accessibility. As fracture permeability increased even further, we again observed a decrease in hydrate formation, which may be explained by hydrate formation being an exothermic reaction and that heat needs to be transported away from the formed hydrate for further growth to occur. Thus, when fracture permeability reaches a critical value, hydrate formation may be fast enough to form such large amounts of hydrate that lack of heat transport by porous media (which is a competing effect) results in overall reduction of hydrate growth. Fracture Porosity. Using our model, effects on the hydrate formation rate from varying fracture porosity, ϕf, were analyzed. Figure 5 shows the changes in porosity, ϕn, at the selected node as a function of fracture porosity. A maximum reduction in porosity in the model simulations (as results of hydrate formation) was observed during the first 2.5 years of injection for all investigated fracture porosities. After four years, porosities were approximately stabilized. As can be seen from Figure 5, the change in porosity behaves linearly, apart from some computational fluctuations due to the accepted convergence errors. The trend of the porosity changes around the studied node was nearly identical for the selected values of fracture porosity. Moreover, aside from a small negative slope, the changes in porosity of the fracture has a low to moderate effect on the hydrate formation rate (approximately 7% change of the linear fit to porosity in the studied range of fracture porosity). Matrix Porosity. Figure 6 shows time evolutions of porosity, ϕn, at a specific node for various matrix porosities,

Figure 5. Porosity, ϕn, as a function of time for a selection of fracture porosities, ϕf, (left) and porosity as a function of fracture porosity at three separate time steps, where solid lines are linear fits and points are taken from the simulations (right). All values were probed at node 450 in the two-dimensional reservoir model (see Figure 3).

Figure 6. Porosity, ϕn, as a function of time for a selection of matrix porosities, ϕm, (left) and porosity as a function of matrix porosity at four separate time steps, where solid lines are linear fits and points are taken from the simulations (right). All values were probed at node 450 in the two-dimensional reservoir model (see Figure 3).

ϕm. It also shows porosities of the specified node as functions of matrix porosity at four selected time steps. The blockage percentage when the matrix porosity was set to ϕm = 0.5 was approximately 45%, whereas it was 60% for the lowest matrix porosity (i.e., ϕm = 0.2). Moreover, it was found that hydrate formation started earlier at lower matrix porosities. Lower matrix porosities also implied that hydrate formation stopped at an earlier time (i.e., porosity changes vanished at an earlier time). In the case of lower matrix porosity, due to the smaller opening of the pores in the medium, pore blockage took place faster and its percentage is higher than with higher matrix porosity. Increasing matrix porosity, increases the amount of available pore space for hydrate to form as well as more available space for fluid flow within the porous media. However, higher matrix porosity may also reduce capillary pressure, which in turn, can result in a decrease of the residual water saturation, which implies that less water would be available for hydrate to form. Thus, there would also be less CO2 hydrate former available within the aqueous phase at higher matrix porosities. This may also help to explain the decrease in hydrate formation observed in the right-hand plot of Figure 6. As can be seen from Figure 6, changes in matrix porosity resulted in porosity changes of up to 84% within the selected range of matrix porosities, thus indicating a high sensitivity to this parameter. Furthermore, it could also be observed that porosity changes due to changes in matrix porosity had a linear behavior, and as time evolved, the steepness of the curves became constant. 4152



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Injection Temperature. To determine the sensitivity of the models with respect to injection temperature, simulations were run for injected CO2 temperatures ranging from 1 to 20 °C. Figure 7 shows the porosity, ϕn, around a selected node

Figure 8. Porosity, ϕn, as a function of time for a selection of injection pressures, P, (left) and porosity as a function of injection pressure at three separate time steps, where solid lines are linear fits and points are taken from the simulations (right). All values were probed at node 450 in the two-dimensional reservoir model (see Figure 3). Figure 7. Porosity, ϕn, as a function of time for a selection of injection temperatures, T, (left) and porosity as a function of injection temperature at three separate time steps, where solid lines are linear fits and points are taken from the simulations (right). All values were probed at node 450 in the two-dimensional reservoir model (see Figure 3).

high pressures, CO2 prefers to remain within the hydrate structure compared to lower pressures, thus lowering hydrate dissociation rates. This may explain the overall increase in hydrate formation rate observed for increased injection pressures. In contrast to changes in temperature, the pressure change at the injection well affected the probed node, approximately 300 m away, due to the overall increase in gas pressure. Reservoir Layer Compositions. The reactivity of calcite in sour environments (dissociated CO2) is significant and will influence CO2 sequestration especially at the early stages of injection.31 Quartz is a more prevalent mineral in nature and it is the most abundant mineral that can be found in calcite rocks. The dissolution rate of quartz is slow. Thus, it may hold the pores open for longer periods of time and this will affect longterm CO2 storage.31 CO2 storage can be viewed as an acid−base reaction. Therefore, those mineral reactions that consume protons (H+) and as a result increase pH levels become important. High pH values lead to higher solubility of CO2 in the form of bicarbonate (HCO3−) into the aqueous phase.31 Because composition can influence hydrate formation, we performed simulations for six different scenarios of typical material compositions to understand which mineral kinetic reactions were of importance during CO2 sequestration in the form of hydrate, as well as to study rock, water, and CO2 interactions. In the first two simulations, mineralogy of the reservoir layer was composed of 10% calcite and 20% calcite, respectively. In the third and fourth simulations, layers were composed of 10% quartz and 20% quartz, respectively, and in the two last ones, a mix of 10% calcite and 10% quartz (volume fraction) as well as a mix of 20% calcite and 20% quartz were composed. The chosen primary and secondary species are listed in Table 1. All these simulations were compared against the base simulation setup having the same compositions as described in the Model Description section. Figure 9 shows the reservoir behavior with respect to hydrate formation when employing the different mineral compositions. For the first two years, the base model had the highest reduction in porosity in the selected node. For 10% calcite and 10% quartz, the porosity, as a function of time, had approximately the same trend, where 10% quartz reached a moderately lower porosity than with calcite. At later simulation times, an increased hydrate formation was observed (i.e., lower porosity) when increasing to 20% calcite, as well as to 20% quartz, where the largest hydrate formation was seen for an

during injection of CO2 into the aquifer with various injection temperatures. It was observed that trends of the porosity were linear with respect to injection temperature for all injection temperatures. Furthermore, the linear fits have a nearly vanishing slope. Thus, injection temperature in the range between 1 and 20 °C had very little impact on hydrate formation in the upper aquifer. Thus, even though lower temperatures promote hydrate formation rate, but injection temperature in the range between 1 and 20 °C had very little impact on hydrate formation in the upper aquifer. In this context, it is important to keep in mind the substantial difference in heat capacity between water and CO2, as well as the mineral heat capacity that will also buffer out some temperature difference between initial temperatures in the reservoir and the temperature of the incoming CO2. The nearly vanishing effect observed from change in the injection temperature of the gas is easily explained by the length and time scales of the simulated systems. Because the injection well was placed approximately 300 m away from the probed node, the gas had enough time to cool down to the surrounding temperatures, which remained approximately unchanged, in vicinity of the probed node. Injection Pressure. To analyze the effects of fluctuations in injection pressure on CO2 hydrate formation, the injection pressure was stepwise changed from 4 to 4.5 MPa. Figure 8 shows the porosity behavior, ϕn, at a selected node for different injection pressures of CO2 into the aquifer. It could be seen that porosity around the specified node reduced approximately linearly with increase in injection pressure. Due to convergence problems the variation in injection pressure was chosen to be relatively small for our simulations. Nevertheless, within this limited variation of pressure, porosity changed by as much as 14 to 26% (see variations in green and orange linear fits in Figure 8, respectively). Moreover, because of the linear behavior and because high pressure is required for hydrate formation, larger injection pressures will have an even higher impact on hydrate formation inside the upper aquifer. At higher pressures, two factors promote hydrate formation and growth. The first is the solubility of CO2, as a hydrate former, which increases with increasing pressure. Moreover, at 4153



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Table 1. Chemical Species for Each Layer Composition calcite

quartz

calcite/quartz

Ca2+ H2O HCO3− OH− CaHCO3+ CaCO3(aq) CO2(aq) CO32−

SiO2(aq) H2O HCO3− OH− HSiO3− H2SiO42− CO2(aq) CO32−

Ca2+ SiO2(aq) H2O HCO3− OH− HSiO3− CO2(aq) CO32− CaCO3(aq) CaH2SiO4(aq) CaHCO3+ CaOH+ H2SiO42− H+

Figure 10. Porosity, ϕn, as a function of time for a selection of residual water saturations, Sw, (left) and porosity as a function of residual water saturation at three separate time steps, where solid lines are linear fits and points are taken from the simulations (right). All values were probed at node 450 in the two-dimensional reservoir model (see Figure 3).

the highest residual saturation, with Sw = 0.225. As can be seen from porosity versus water saturation, porosity decreases approximately linearly as a function of water saturation within the selected range. It was also observed that the slope plotted at two years of injection was steeper than at three and four years, thus implying that the effects are higher in the earlier years of CO2 injection. Up to 24% changes in porosity was seen (see Figure 10) due to variations in residual water saturation, within the studied range. The trend seen in Figure 10 can be explained by the injected gas sweeping water from the pores within the reservoir. When the residual water saturation was high, larger amounts of water was left behind within the swept area. As a result, more CO2 could be dissolved within the residual water, which increased the driving force toward hydrate formation. Because water and CO2 were the main hydrate formers, hydrate formation increased with increasing residual water saturation.

Figure 9. Time evolution of porosity, ϕn, at node 450 (see Figure 3) for different layer compositions (left) and the porosity as a function of compositions at three separate time steps (right). B denotes the base simulation, C denotes calcite, Q denotes quartz, whereas CQ denotes a mix between calcite and quartz (the number gives the fraction of the respective minerals or mix of minerals).

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SUMMARY AND CONCLUSIONS In this work, the main features of the simulator has been described and an example reservoir was used to illustrate sensitivity of some critical parameters in the model. Two-dimensional reservoir simulations were used to investigate the effects of different reservoir parameters on CO2 hydrate formation rates over time periods of up to 20 years of injection. Results of the simulations indicate that most CO2 will migrate through the fracture network. It was found that the rate of hydrate formation varied linearly with respect to fracture porosity, matrix porosity, injection temperature, and injection pressure, as well as residual water saturation, within the studied ranges. Fracture porosity appeared to have only a moderate effect on the formation rate, whereas injection temperature had almost no effect within the temperature variations range of 1 to 20 °C in the model structure. However, the formation rate was significantly more sensitive to changes in matrix porosity, injection pressure, and residual water saturation. Although most parameter variations yielded a linear behavior in the porosity, and therefore the hydrate formation rate, we found that porosity approximately followed a second-order polynomial as a function of fracture permeability. It was found that also the mineral composition was of high importance for CO2 hydrate formation rates. After two years of injection, a near negligible increase in hydrate formation was observed as a result of both an increase from 10 to 20% calcite,

increase in the amount of calcite. However, when calcite and quartz were mixed, the rate of porosity reduction severely decreased, thus slowing down hydrate formation significantly. This phenomenon may be due to the fact that CO2 is mostly consumed by dissolution into the brine to form CaH2SiO4(aq). Thus, the concentration of CO2, which is one of the main hydrate formers, reduced in the aqueous phase subsequently reducing the driving force toward hydrate formation, leading to the observed high levels of porosity. At the present time, only chemical effects stemming from reactive transport calculations are taken into consideration between hydrate and the various minerals (i.e., we are only taking into account composition effects). However, we are in the process of implementing surface effects, which may improve the theoretical models to an extent where effects such as those seen in ref 32 may be modeled (i.e., that growth rates may in fact accelerate in the presence of some minerals). Within such a theoretical model one needs to take into account effects at the atomistic level (e.g., to account for realistic surface structuring). This can be achieved using tools such as molecular dynamics and phase field theory to provide detailed free energy profiles in vicinity of particular surface structures, which can subsequently be used within the thermodynamic models. Residual Water Saturation. Figure 10 shows how altering the residual water saturation in the reservoir affected hydrate formation. The highest reduction in porosity, ϕn, occurred at 4154



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as well as an increase from 10 to 20% quartz. However, in the case of mixing calcite and quartz a dramatic reduction in the rate of hydrate formation was seen. This phenomenon may have been due to CO2 being mostly consumed by dissolution into brine to form CaH2SiO4(aq). So far, our preliminary results indicate the possibility of safe long-term storage of CO2 in underground aquifers, although it depends on the reservoir characteristics. However, the results show that the amount of hydrate formed is strongly dependent on several parameters of the reservoir and the flow through the reservoir. Thus, possible changes in these parameters must be taken into account when evaluating the risk of hydrate dissociation, which potentially can release stored CO2.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00567. Detailed descriptions of the model and the applied reservoir conditions, as well as coefficients for polynomial fits. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

We acknowledge the grant and support from Research Council of Norway and Industrial partners through the following projects: CLIMIT “Safe long term sealing of CO2 in hydrate”, Research Council of Norway, project number: 224857, SSCRamore, “Subsurface storage of CO2Risk assessment, monitoring and remediation”, project number 178008/I30, FME-SUCCESS, project number 804831, PETROMAKS, “CO2 injection for extra production”, Research Council of Norway, project number 801445, PETROMAKS “CO 2 Injection for Stimulated Production of Natural Gas”, Research Council of Norway, project number 175968 and 230083, and STATOIL, under contract 4502354080. Notes

The authors declare no competing financial interest.

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REFERENCES

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Sensitivity Analysis of CO2 Injection within Saline Aquifers for Storage

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