Modeling of Spatiotemporal Thermal Response to CO2 Injection in Saline Formations: Interpretation for Monitoring

We evaluated the thermal processes with numerical simulation models that include processes of solid NaCl precipitation, buoyancy-driven multiphase SCCO₂ migration, and potential non-isothermal effects. Simulation results suggest that these processes??solid NaCl precipitation, buoyancy effects, JT cooling, water vaporization, and exothermic SCCO₂ reactions??are strongly coupled and dynamic. In addition, we performed sensitivity studies to determine how geologic (heat capacity, brine concentration, porosity, the magnitude and anisotropy of permeability, and capillary pressure) and operational (injection rate and injected SCCO₂ temperature) parameters may affect these induced thermal disturbances. Overall, a fundamental understanding of potential thermal processes investigated through this research will be beneficial in the collection and analysis of temperature signals collectively measured from monitoring wells.     

CO2 Injection into Saline Carbonate Aquifer Formations II: Comparison of Numerical Simulations to Experiments

Sequestration of carbon dioxide in geological formations is an alternative way of managing extra carbon. Although there are a number of mathematical modeling studies related to this subject, experimental studies are limited and most studies focus on injection into sandstone reservoirs as opposed to carbonate ones. This study describes a fully coupled geochemical compositional equation-of-state compositional simulator (STARS) for the simulation of CO₂ storage in saline aquifers. STARS models physical phenomena including (1) thermodynamics of sub- and supercritical CO₂, and PVT properties of mixtures of CO₂ with other fluids, including (saline) water; (2) fluid mechanics of single and multiphase flow when CO₂ is injected into aquifers; (3) coupled hydrochemical effects due to interactions between CO₂, reservoir fluids, and primary mineral assemblages; and (4) coupled hydromechanical effects, such as porosity and permeability change due to the aforementioned blocking of pores by carbonate particles and increased fluid pressures from CO₂ injection. Matching computerized tomography monitored laboratory experiments showed the uses of the simulation model. In the simulations dissolution and deposition of calcite as well as adsorption of CO₂ that showed the migration of CO₂ and the dissociation of CO₂ into HCO₃ and its subsequent conversion into carbonate minerals were considered. It was observed that solubility and hydrodynamic storage of CO₂ is larger compared to mineral trapping.     

Semianalytical Solution for \text{ CO}_{2} Plume Shape and Pressure Evolution During \text{ CO}_{2} Injection in Deep Saline Formations

The injection of supercritical carbon dioxide ( $\text{ CO}_{2})$ in deep saline aquifers leads to the formation of a $\text{ CO}_{2}$ rich phase plume that tends to float over the resident brine. As pressure builds up, $\text{ CO}_{2}$ density will increase because of its high compressibility. Current analytical solutions do not account for $\text{ CO}_{2}$ compressibility and consider a volumetric injection rate that is uniformly distributed along the whole thickness of the aquifer, which is unrealistic. Furthermore, the slope of the $\text{ CO}_{2}$ pressure with respect to the logarithm of distance obtained from these solutions differs from that of numerical solutions. We develop a semianalytical solution for the $\text{ CO}_{2}$ plume geometry and fluid pressure evolution, accounting for $\text{ CO}_{2}$ compressibility and buoyancy effects in the injection well, so $\text{ CO}_{2}$ is not uniformly injected along the aquifer thickness. We formulate the problem in terms of a $\text{ CO}_{2}$ potential that facilitates solution in horizontal layers, with which we discretize the aquifer. Capillary pressure is considered at the interface between the $\text{ CO}_{2}$ rich phase and the aqueous phase. When a prescribed $\text{ CO}_{2}$ mass flow rate is injected, $\text{ CO}_{2}$ advances initially through the top portion of the aquifer. As $\text{ CO}_{2}$ is being injected, the $\text{ CO}_{2}$ plume advances not only laterally, but also vertically downwards. However, the $\text{ CO}_{2}$ plume does not necessarily occupy the whole thickness of the aquifer. We found that even in the cases in which the $\text{ CO}_{2}$ plume reaches the bottom of the aquifer, most of the injected $\text{ CO}_{2}$ enters the aquifer through the layers at the top. Both $\text{ CO}_{2}$ plume position and fluid pressure compare well with numerical simulations. This solution permits quick evaluations of the $\text{ CO}_{2}$ plume position and fluid pressure distribution when injecting supercritical $\text{ CO}_{2}$ in a deep saline aquifer.     

Effect of Vertical Heterogeneity on Long-Term Migration of CO<Subscript>2</Subscript> in Saline Formations

For deep injection of CO₂ in thick saline formations, the movements of both the free gas phase and dissolved CO₂ are sensitive to variations in vertical permeability. A simple model for vertical heterogeneity was studied, consisting of a random distribution of horizontal impermeable barriers with a given overall volume fraction and distribution of lengths. Analytical results were obtained for the distribution of values for the permeability, and compared to numerical simulations of deep CO₂ injection and convection in heterogeneous formations, using multiple realizations for the permeability distribution. It is shown that for a formation of thickness H, the breakthrough times in two dimensions for deep injection scale as H ² for moderate injection rates. In comparison to heterogeneous shale distributions, a homogeneous medium with equivalent effective vertical permeability has a longer breakthrough time for deep injection, and a longer onset time for convection.     

Sensitivity Study of Simulation Parameters Controlling CO<Subscript>2</Subscript> Trapping Mechanisms in Saline Formations

The primary purpose of this study is to understand quantitative characteristics of mobile, residual, and dissolved CO₂ trapping mechanisms within ranges of systematic variations in different geologic and hydrologic parameters. For this purpose, we conducted an extensive suite of numerical simulations to evaluate the sensitivities included in these parameters. We generated two-dimensional numerical models representing subsurface porous media with various permutations of vertical and horizontal permeability (k _v and k _h), porosity (f{\phi}), maximum residual CO₂ saturation (S_gr^max{S_{\rm gr}^{\max}}), and brine density (ρ _br). Simulation results indicate that residual CO₂ trapping increases proportionally to k_v, k_h, S_gr^max{k_{\rm v}, k_{\rm h}, S_{\rm gr}^{\max}} and ρ _br but is inversely proportional to f.{\phi.} In addition, the amount of dissolution-trapped CO₂ increases with k _v and k _h, but does not vary with f{\phi } , and decreases with S_gr^max{S_{\rm gr}^{\max}} and ρ _br. Additionally, the distance of buoyancy-driven CO₂ migration increases proportionally to k _v and ρ _br only and is inversely proportional to k_h, f{k_{\rm h}, \phi } , and S_gr^max{S_{\rm gr}^{\max}} . These complex behaviors occur because the chosen sensitivity parameters perturb the distances of vertical and horizontal CO₂ plume migration, pore volume size, and fraction of trapped CO₂ in both pores and formation fluids. Finally, in an effort to characterize complex relationships among residual CO₂ trapping and buoyancy-driven CO₂ migration, we quantified three characteristic zones. Zone I, expressing the variations of S_gr^max{S_{\rm gr}^{\max}} and k _h, represents the optimized conditions for geologic CO₂ sequestration. Zone II, showing the variation of f{\phi} , would be preferred for secure CO₂ sequestration since CO₂ has less potential to escape from the target formation. In zone III, both residual CO₂ trapping and buoyancy-driven migration distance increase with k _v and ρ _br.     

CO2 Plume Evolution and Pressure Buildup of Large-scale CO2 Injection into Saline Aquifers in Sanzhao Depression, Songliao Basin, China

Large-scale injection of carbon dioxide (CO₂) into saline aquifers in sedimentary basins is a promising approach to mitigate global climate change. Songliao Basin, a large continental clastic sedimentary basin in northeastern China, is one of the great potential candidate sites for future CO₂ storage in China. In this paper, a three-dimensional CO₂ storage model was built to evaluate the CO₂ plume evolution and pressure buildup of large-scale CO₂ injection into the saline aquifers in the Sanzhao Depression of the Songliao Basin. CO₂ was injected into the aquifers through five wells, each with an annual injection rate of 3 Mt over 50?years. The results show that the clastic Yaojia formation at the depth between 900 and 1,600 m with thickness of 150 m might be the favorable layer to store a considerable amount of CO₂, and the overlying Nenjiang formation could ensure long-term CO₂ containment. The relative low permeability of the upper part of the Yaojia formation seems to play a role of a secondary seal on carbon storage. In current injection scenario, CO₂ plume migrates into the formations in the southeast of the depression, which could have potential risk of polluting the freshwater. Therefore, the injection site should stay far away from the southeast of the depression. Moreover, it is very crucial to investigate the permeability distribution of the Yaojia formation because it significantly dominates the CO₂ plume migration. After only 6?months of injection, the pressure buildup at each injection site is affected by pressure interference from neighboring sites. The maximum pressure buildup in the formations is 7.8?MPa after 50?years of injection, and it can even reach 10.5?MPa when the injection layers are with lower permeability. The maximum pressure buildup at the bottom of the Nenjiang formation is 6.7?MPa. The gradient of maximum limited formation pressure is about 18?MPa/km, which might cause fractures to open in the formations of the Sanzhao Depression. Continuous injection of CO₂ for 50?years may not cause damage to the caprock even when the lower permeability occurred in the upper part of the Yaojia formation. The safety of CO₂ storage will be enhanced if the upper part of the storage formation has lower permeability than the lower part.     

Impact of Capillary Pressure, Salinity and In situ Conditions on CO2 Injection into Saline Aquifers

This article presents a numerical investigation of the combined effects of capillary pressure, salinity and in situ thermodynamic conditions on CO₂-brine-rock interactions in a saline aquifer. We demonstrate that the interrelations between capillary pressure, salinity, dissolution and drying-out affect CO₂ injectivity and storage capacity of a saline aquifer. High capillary forces require a high injection pressure for a given injection rate. Depending on salinity, the increase in injection pressure due to capillary forces can be offset by the dissolution of CO₂ in formation water and its compressibility. Higher capillary forces also reduce gravity segregation, and this gives a more homogeneous CO₂ plume which improves the dissolution of CO₂. The solubility of CO₂ in formation water decreases with increasing salinity which requires an increased injection pressure. Higher salinity and capillary pressure can even block the pores, causing an increased salt precipitation. Simulations with various pressure-temperature conditions and modified salinity and capillary pressure curves demonstrate that, with the injection pressures similar for both cold and warm basins at a given injection rate, CO₂ dissolves about 10% more in the warm basin water than in the cold basin. The increase in dissolution lowers the injection pressure compensating the disadvantage of low CO₂ density and compressibility for storage in warm basins.     

Spontaneous Switching between Permeability Enhancement and Degradation in Fractures in Carbonate: Lumped Parameter Representation of Mechanically- and Chemically-Mediated Dissolution

Principal mechanical and chemical processes contributing to the observed spontaneous switching from net decrease in permeability to net increase in a fracture in carbonate are examined. The evolution of permeability, and related fracture aperture, is represented through a lumped parameter model. The significant processes of pressure solution beneath bridging asperities, transport of dissolved mass to the fracture void, and subsequent precipitation or dissolution within the fracture void enable the principal characteristics of observed behavior to be followed. The evolution of dissolved mass concentration in the pore fluid is followed for arbitrary applied stress, temperature, and pH conditions, with appropriate feedback to the evolution of fracture permeability. Comparisons with experimental measurements in limestone (Polak et al., 2004, Water Resour. Res. Vol. 40, W03502, doi: 10.1029/2003GL017575) show satisfactory agreement for the evolution of fracture aperture and to a lesser degree in calcium concentrations in the effluent pore fluid. Importantly, the spontaneous switching in permeability change, from aperture reducing to aperture increasing, with no change in environmental conditions, is replicated without the need for an ad hoc trigger. Although this switch is accurately replicated, the lumped parameter model is incapable of replicating the rapid observed growth in permeability that directly follows. This inability results from the assumed form of the lumped asperity model, that is incapable of representing the spatially distributed change in aperture that is seen to occur within the fracture. Despite this inconsistency, the model is shown capable of representing the principal behaviors evident in the response.     

On the Validation of a Compositional Model for the Simulation of $$\text {CO}_2$$ Injection into Saline Aquifers

In this work we apply a recently proposed Bayesian Markov chain Monte Carlo framework (Akbarabadi et al. in Comput Geosci 19(6):1231–1250, 2015) to quantify uncertainty in the three-dimensional permeability field of a rock core. This process establishes the credibility of a compositional two-phase flow model to describe the displacement of brine by \(\text {CO}_2\) and \(\text {CO}_2\) storage in saline aquifers. We investigate the predictive capabilities of the compositional model in the context of an unsteady-state \(\text {CO}_2\)-brine drainage experiment at the laboratory scale, performed at field-scale aquifer conditions. We employ forward models consisting of a system of discretized partial differential equations along with relative permeability curves obtained by a curve fitting of experimental measurements. We consider a forward model to be validated when: (1) numerical simulations reveal that the Bayesian framework has accurately characterized the core’s permeability and (2) Monte Carlo predictions show excellent agreement between measured and simulated data. A large set of numerical studies with an accurate compositional simulator shows that forward models have been successfully validated. For such models, our numerical results show that we are able to capture all the dominant features and general trends of the \(\text {CO}_2\) saturation fields observed in the core. Our study is consistent with the design and findings of real experiments. Fluid properties, relative permeability data, measured porosity field, physical dimensions, and thermodynamic conditions are the same as those reported in Akbarabadi and Piri (Adv Water Resour 52:190–206, 2013). However, the measured saturation data are from flow experiments different from those reported in Akbarabadi and Piri (2013), and will be presented here.     

On Mathematical Models of Average Flow in Heterogeneous Formations

We consider a general model of transient flow in media of random conductivity and storativity. The flow is driven by the spatially distributed source function (x, t) and the initial head distribution h ₀(x). The function models sources and wells and can be deterministic, random or a sum of both. The deterministic source function corresponds to singularities of deterministic strength, whereas the random models the head boundary condition. In the latter case, is shown to be proportional to the hydraulic conductivity. The aim of the study is to analyze the feasibility of averaging the flow equations and of developing the mathematical model of average flow (AFM) without solving problems in detail. It is shown that the problem of averaging is reduced to deriving two constitutive equations. The first equation, the effective Darcy's law (EDL) stems from averaging Darcy's law at local scale. The second one is related to the medium ability to store a fluid and expresses the correlation between the storativity and head in terms of the mean head. Both relationships are required to be completely determined by the medium structure (conductivity and storativity statistical properties) and independent of the flow configuration (functions and h ₀). We show that if one of the constitutive equations exists, the same is true respective to the second. This reduces the problem of averaging to the classic one of deriving the EDL. For steady flows the EDL is shown to exist for flows driven by sources (wells) of either deterministic flux or head boundary conditions. No EDL can be derived if both types of sources are present in the flow domain. For unsteady flows the EDL does not exist if the initial head correlates with the medium properties. For uncorrelated initial head distribution, its random residual (due to the measurement errors and scarcity of the data) has no impact on the EDL and is immaterial. For deterministic h ₀, the only case for which the EDL exists is the flow by sources of deterministic discharge. For sources of given head boundary condition the EDL can be derived only for uniform initial head distribution. For all other cases, the EDL does not exist. The results of the study are not limited by usually adopted assumptions of weak heterogeneity and of stationarity of the formation random properties.     

Dynamically Equilibrium Shape of Intrusive Vortex Formations in the Ocean

The problem of finding the dynamically equilibrium shape of a rotating mass of liquid with homogeneous density (lens) submerged in a stratified ocean at rest on the rotating Earth is formulated. An equation for the shape of the interface between water masses is derived. An exact solution of the problem for an anticyclonically rotating lens in a linearly stratified ocean in the neighborhood of the lens depth shows that the dynamically equilibrium shape of the interface is a triaxial ellipsoid inclined with respect to the horizon and similar to an ellipsoid of revolution for real parameters of the phenomenon. The limiting values of the latitudes at which these formations can exist are determined. Degeneration of the shape with decrease in the intrinsic lens angular rate is investigated.     

Vortex Formations in Plane Flows of Viscous and Ideal Fluids

An analytic representation of individual vortex formations with different cross-sections is obtained for plane-parallel flows of viscous and ideal fluids. A flow in which one of the streamlines has cusp is also found. In these flows the vorticity is constant; therefore, the solutions obtained for the equations describing the kinematic variables in ideal fluid flows must simultaneously satisfy the Navier-Stokes equations.     

CO2 Injection in Geological Formations: Determining Macroscale Coefficients from Pore Scale Processes

Carbon dioxide (CO₂) injections in geological formations are usually performed for enhanced hydrocarbon recovery in oil and gas reservoirs and storage and sequestration in saline aquifers. Once CO₂ is injected into the formation, it propagates in the porous rock by dispersion and convection. Chemical reactions between brine ions and CO₂ molecules and consequent reactions with mineral grains are also important processes. The dynamics of CO₂ molecules in random porous media are modeled with a set of differential equations corresponding to pore scale and continuum macroscale. On the pore scale, convective–dispersive equation is solved considering reactions on the inner boundaries in a unit cell. A unit cell is the smallest portion of a porous media that can reproduce the porous media by repetition. Inner boundaries in a unit cell are the surfaces of the mineral grains. Dispersion process at the pore scale is transformed into continuum macroscale by adopting periodic boundary conditions for contiguous unit cells and applying Taylor-Aris dispersion theory known as macrotransport theory. Using this theory, the discrete porous system changes into a continuum system within which the propagation and interaction of CO₂ molecules with fluid and solid matrix of the porous media are characterized by three position-independent macroscopic coefficients: the mean velocity vector , dispersivity dyadic , and mean volumetric CO₂ depletion coefficient .     

Simulation of liquid solvent atomization in compressed CO2

The work investigates numerically the atomization regime of a liquid injected into compressed CO₂ under subcritical conditions, i.e. below the CO₂-solvent critical pressure. To vary the conditions within the atomization regime whilst keeping up with realistic experimental background, ethanol and methylene chloride were selected as injected fluid and pressure was modified as well. Results first show that the jet indeed breaks up by atomization, which confirms the validity at high pressure of the breakup classification diagram. Aiming at evaluating the size distribution of the droplets formed by the jet atomization, two methods of interface tracking were investigated. Compared to the VOF-PLIC classical method, the novel sub mesh (VOF-SM) approach allows for determining smaller sized droplets without digital broadcasting.