A Computational Approach to Determine Average Reservoir Pressure in a Coalbed Methane (CBM) Well Flowing Under Dominant Matrix Shrinkage Effect

Desorption of gas from coal matrix alters the pore volume of fracture network. Consequently, cleat porosity and permeability of reservoir changes as pressure depletes. The method of standard pressure analysis calculations produces incorrect results in the case of coalbed methane reservoirs producing under dominant matrix shrinkage effect. The change in cleat porosity and permeability due to shrinkage of coal matrix following gas desorption with pressure depletion invalidates the underlying assumptions made in the derivation of diffusivity equation. Consequently, equations of pseudo-steady state commonly used in conventional reservoirs no longer remain valid as the porosity and permeability values change with pressure depletion. In this paper, effort has been made to describe pseudo-steady-state flow in coalbed methane reservoirs in the form of a new equation that accounts for pressure dependency of cleat porosity and permeability due to shrinkage of coal matrix. The concept of Al-Hussainy et al. (1966) has been extended to define a new pseudo-pressure function which assimilates within itself the pressure dependence of porosity and permeability Palmer and Mansoori (1998). Equation has been used to relate the cleat porosity with pressure. The equation-based computational method suggested in this paper finds its usefulness in estimating average reservoir pressure for any known flowing bottom hole pressure and thus reducing the frequency of future pressure buildup tests. The new equation is also useful in predicting reservoir pressure under the situation when coal matrix shrinks below desorption pressure. The equation used in the computational method has been validated with the help of numerical simulator CMG-GEM.     

Study of Hydraulic Properties of Uncoated Paper: Image Analysis and Pore-Scale Modeling

In this study, uncoated paper was characterized. Three-dimensional structure of the layer was reconstructed using imaging results of micro-CT scanning with a relatively high resolution \((0.9~\upmu \hbox {m})\). Image analysis provided the pore space of the layer, which was used to determine its porosity and pore size distribution. Representative elementary volume (REV) size was determined by calculating values of porosity and permeability values for varying domain sizes. We found that those values remained unchanged for domain sizes of \(400\times 400\times 150\,\upmu \hbox {m}^{3}\) and larger; this was chosen as the REV size. The determined REV size was verified by determining capillary pressure–saturation Open image in new window imbibition curves for various domain sizes. We studied the directional dependence of Open image in new window curves by simulating water penetration into the layer from various directions. We did not find any significant difference between Open image in new window curves in different directions. We studied the effect of compression of paper on Open image in new window curves. We found that up to 30% compression of the paper layer had very small effect on the Open image in new window curve. Relative permeability as a function of saturation was also calculated. Water penetration into paper was visualized using confocal laser scanning microscopy. Dynamic visualization of water flow in the paper showed that water moves along the fibers first and then fills the pores between them.     

Blast waves from cylindrical charges

Comparisons of explosives are often carried out using TNT equivalency which is based on data for spherical charges, despite the fact that many explosive charges are not spherical in shape, but cylindrical. Previous work has shown that it is possible to predict the over pressure and impulse from the curved surface of cylindrical charges using simple empirical formulae for the case when the length-to-diameter (L/D) ratio is greater or equal to 2/1. In this paper, by examining data for all length-to-diameter ratios, it is shown that it is possible to predict the peak over pressure, P, for any length-to-diameter ratio from the curved side of a bare cylindrical charge of explosive using the equation $P=K_PM(L/D)^{1/3}/R^3$ , where M is the mass of explosive, R the distance from the charge and $ K_P$ is an explosive-dependent constant. Further out where the cylindrical blast wave ‘heals’ into a spherical one, the more complex equation $P=C_1(Z^{\prime \prime })^{-3}+C_2(Z^{\prime \prime })^{-2}+C_3(Z^{\prime \prime })^{-1}$ gives a better fit to experimental data, where $ Z^{\prime \prime } = M^{1/3}(L/D)^{1/9}/D$ and $C_1,\, C_2 $ and $ C_3$ are explosive-dependent constants. The impulse is found to be independent of the L/D ratio.     

Impact of Effective Stress and Matrix Deformation on the Coal Fracture Permeability

The permeability of coal is an important parameter in mine methane control and coal bed methane exploitation because it determines the practicability of methane extraction. We developed a new coal permeability model under tri-axial stress conditions. In our model, the coal matrix is compressible and Biot’s coefficient, which is considered to be 1 in existing models, varies between 0 and 1. Only a portion of the matrix deformation, which is represented by the effective coal matrix deformation factor $f_\mathrm{m}$ , contributes to fracture deformation. The factor $f_\mathrm{m}$ is a parameter of the coal structure and is a constant between 0 and 1 for a specific coal. Laboratory tests indicate that the Sulcis coal sample has an $f_\mathrm{m}$ value of 0.1794 for $\hbox {N}_{2}$ and $\hbox {CO}_{2}$ . The proposed permeability model was evaluated using published data for the Sulcis coal sample and is compared to three popular permeability models. The proposed model agrees well with the observed permeability changes and can predict the permeability of coal better than the other models. The sensitivity of the new model to changes in the physical, mechanical and adsorption deformation parameters of the coal was investigated. Biot’s coefficient and the bulk modulus mainly affect the effective stress term in the proposed model. The sorption deformation parameters and the factor $f_\mathrm{m}$ affect the coal matrix deformation term.     

Miscible and Immiscible Foam Injection for Mobility Control and EOR in Fractured Oil-Wet Carbonate Rocks

Foam injection is a proven enhanced oil recovery (EOR) technique for heterogeneous reservoirs, but is less studied for EOR in fractured systems. We experimentally investigated tertiary \(\text {CO}_{2}\) injections, and \(\text {N}_{2}\) - and \(\text {CO}_{2}\) -foam injections for enhanced oil recovery in fractured, oil-wet limestone core plugs. Miscible \(\text {CO}_{2}\) and \(\text {CO}_{2}\) -foam was compared with immiscible \(\text {CO}_{2}\) - and \(\text {N}_{2}\) -foam as tertiary recovery techniques, subsequent to waterfloods, in fractured rocks with different wettability preferences. At water-wet conditions waterfloods produced approximately 40 % OOIP, by spontaneous imbibition. Waterflood oil recovery at oil-wet conditions was below 20 % OOIP, due to suppressed imbibition where water predominantly flowed through the fractures, unable to mobilize the oil trapped in the matrix. Tertiary, supercritical \(\text {CO}_{2}\) -mobilized oil trapped in the matrix, particularly at weakly oil-wet conditions, by diffusion. Recovery by diffusion was high due to small core samples, high initial oil saturation and a continuous oil phase at oil-wet conditions. Both immiscible \(\text {CO}_{2}\) - and \(\text {N}_{2}\) -foams and miscible, supercritical \(\text {CO}_{2}\) -foam demonstrated high ultimate oil recoveries, but immiscible foam was less efficient (30 pore volumes injected) compared to miscible foam (2 pore volumes injected) to reach ultimate recovery. This is explained by the capillary threshold pressure preventing the injected \(\text {N}_{2}\) gas from entering the matrix, verified by computed X-ray tomography, and the mobilized oil was displaced by the aqueous surfactant in the foam. At miscible conditions, there exists no capillary entry pressure between the oil-saturated matrix and the injected \(\text {CO}_{2}\) , allowing foam to invade the matrix for efficient oil recovery.     

Coal Permeability Evolution and Gas Migration Under Non-equilibrium State

Laboratory test of coal permeability is generally conducted under the condition of gas adsorption equilibrium, and the results contribute to an understanding of gas migration in the original coal seams. However, gas flow under the state of non-equilibrium, accompanied by gas adsorption and desorption, is more common in coalbed methane (CBM) recovery and \(\hbox {CO}_{2}\) geological sequestration sites. Therefore, research on gas migration under the non-equilibrium state has a greater significance with regard to CBM recovery and \(\hbox {CO}_{2}\) geological sequestration. However, most permeability models, in which only one gas pressure has been considered, cannot be used to study gas flow under the non-equilibrium state. In this study, a new mathematical model, which includes both fracture gas pressure and matrix gas pressure, and couples the gas flow with the coal deformation, has been developed and verified. With the developed model, the spatial and temporal evolution of gas flow field during gas adsorption and desorption phases has been explored. The results show that the gas pressures present nonlinear distributions in the coal core, and the matrix gas pressure is generally lower than the fracture gas pressure during adsorption, but higher than the fracture gas pressure during desorption. For gas flow during adsorption, the main factor controlling permeability varies at different points. At the initial time, the permeability is dominated by the effective stress, and at the later time, the permeability in the part close to the gas inlet is mainly controlled by the matrix swelling, whereas that in the part close to the gas outlet is still dominated by the effective stress. For gas flow during desorption, from the gas inlet to the gas outlet, the permeability deceases at the initial time, and when the time is greater than 10,000 s, it shows a decreasing and then an increasing trend. The reason is that at the initial time, the permeability is dominated by the increased effective stress caused by the sharp decrease of the fracture gas pressure. Later, desorption of the adsorbed gas results in matrix shrinkage, which further leads to an increase of the permeability.     

A Model for Spontaneous Imbibition as a Mechanism for Oil Recovery in Fractured Reservoirs

The flow of oil and water in naturally fractured reservoirs (NFR) can be highly complex and a simplified model is presented to illustrate some main features of this flow system. NFRs typically consist of low-permeable matrix rock containing a high-permeable fracture network. The effect of this network is that the advective flow bypasses the main portions of the reservoir where the oil is contained. Instead capillary forces and gravity forces are important for recovering the oil from these sections. We consider a linear fracture which is symmetrically surrounded by porous matrix. Advective flow occurs only along the fracture, while capillary driven flow occurs only along the axis of the matrix normal to the fracture. For a given set of relative permeability and capillary pressure curves, the behavior of the system is completely determined by the choice of two dimensionless parameters: (i) the ratio of time scales for advective flow in fracture to capillary flow in matrix $\alpha =\tau ^f/\tau ^m$ ; (ii) the ratio of pore volumes in matrix and fracture $\beta =V^m/V^f$ . A characteristic property of the flow in the coupled fracture–matrix medium is the linear recovery curve (before water breakthrough) which has been referred to as the “filling fracture” regime Rangel-German and Kovscek (J Pet Sci Eng 36:45–60, 2002), followed by a nonlinear period, referred to as the “instantly filled” regime, where the rate is approximately linear with the square root of time. We derive an analytical solution for the limiting case where the time scale $\tau ^{m}$ of the matrix imbibition becomes small relative to the time scale $\tau ^{f}$ of the fracture flow (i.e., $\alpha \rightarrow \infty $ ), and verify by numerical experiments that the model will converge to this limit as $\alpha $ becomes large. The model provides insight into the role played by parameters like saturation functions, injection rate, volume of fractures versus volume of matrix, different viscosity relations, and strength of capillary forces versus injection rate. Especially, a scaling number $\omega $ is suggested that seems to incorporate variations in these parameters. An interesting observation is that at $\omega =1$ there is little to gain in efficiency by reducing the injection rate. The model can be used as a tool for interpretation of laboratory experiments involving fracture–matrix flow as well as a tool for testing different transfer functions that have been suggested to use in reservoir simulators.     

Evolution of Pore-Scale Morphology of Oil Shale During Pyrolysis: A Quantitative Analysis

This article describes experimental results and the numerical validation for multiphase, multicomponent evaporation in porous media 1d flow. We apply the model of Lindner et al. (Transp. Porous Media 112(2):313–332, 2016. doi: 10.1007/s11242-016-0646-6). The permeability of the porous medium is measured in an additional setup with a constant head permeameter to verify the validity of Darcy flow. The heat losses are considered in an analytical approach of correlating measured temperatures and heat inputs with enthalpies. A method of interpreting the experimental results is discussed to determine the phase state. We can show good qualitative agreement of the shift and position of the evaporation region when varying boundary conditions such as mass flux, concentration and heat input.     

Controlling Chaos in Porous Media Convection by Using Feedback Control

A method of using feedback control to promote or suppress the transition to chaos in porous media convection is demonstrated in this article. A feedback control suggested by Mahmud and Hashim (Transp Porous Media, doi:10.1007/s11242-009-9511-1, 2010) is used in the present article to provide a comparison between an analytical expression for the transition point to chaos and numerical results. In addition, it is shown that such a feedback control can be applied as an excellent practical means for controlling (suppressing or promoting) chaos by using a transformation made by Magyari (Transp Porous Media, doi:10.1007/s11242-009-9511-1, 2010). The latter shows that Mahmud and Hashim (Transp Porous Media, doi:10.1007/s11242-009-9511-1, 2010) model can be transformed into Vadasz-Olek’s model (Transp Porous Media 37(1):69–91, 1999a) through a simple transformation of variables implying that the main effect the feedback control has on the solution is equivalent to altering the initial conditions. The theoretical and practical significance of such an equivalent alteration of the initial conditions is presented and discussed.     

Effective Behavior Near Clogging in Upscaled Equations for Non-isothermal Reactive Porous Media Flow

For a non-isothermal reactive flow process, effective properties such as permeability and heat conductivity change as the underlying pore structure evolves. We investigate changes of the effective properties for a two-dimensional periodic porous medium as the grain geometry changes. We consider specific grain shapes and study the evolution by solving the cell problems numerically for an upscaled model derived in Bringedal et al. (Transp Porous Media 114(2):371–393, 2016. doi: 10.1007/s11242-015-0530-9). In particular, we focus on the limit behavior near clogging. The effective heat conductivities are compared to common porosity-weighted volume averaging approximations, and we find that geometric averages perform better than arithmetic and harmonic for isotropic media, while the optimal choice for anisotropic media depends on the degree and direction of the anisotropy. An approximate analytical expression is found to perform well for the isotropic effective heat conductivity. The permeability is compared to some commonly used approaches focusing on the limiting behavior near clogging, where a fitted power law is found to behave reasonably well. The resulting macroscale equations are tested on a case where the geochemical reactions cause pore clogging and a corresponding change in the flow and transport behavior at Darcy scale. As pores clog the flow paths shift away, while heat conduction increases in regions with lower porosity.     

Flow Dynamics of \hbox {CO}_{2}/brine at the Interface Between the Storage Formation and Sealing Units in a Multi-layered Model

Pressure distribution and \(\hbox {CO}_{2}\) plume migration are two major interests in \(\hbox {CO}_{2}\) geologic storage as they determine the injectivity and storage capacity. In this study, we adopted a three-layer model comprising a storage formation and the over- and underlying seals and determined three distinct flow regions based on the vertical flux exchange of \(\hbox {CO}_{2}\) and native brine. Regions 1 and 2 showed \(\hbox {CO}_{2}\) flowing from the storage formation to adjacent seals with counter-flowing brine. The characteristics of these fluxes in Region 1 were governed by permeability change due to salt precipitation whereas buoyancy force controlled the flux pattern in Region 2. Region 3 showed brine flowing from storage formation toward the over- and underlying seals, which enabled the displaced brine to escape from the storage formation and make room for \(\hbox {CO}_{2}\) to store as well as reduce the pressure build-up. In the multi-layered model, the counter-flowing brine in flow Region 1 resulted in localized salt precipitation at the upper and lower boundary of storage formation. We assessed the bottom-hole pressure and \(\hbox {CO}_{2}\) mass in caprock with respect to reservoir size. While the formation thickness influenced the bottom-hole pressure in the early stage of injection, the horizontal extension of the reservoir was more influential to pressure build-up during the injection period, and to the stabilized pressure during the post-injection period. The \(\hbox {CO}_{2}\) mass in caprock gently increased during the injection period as well as during the post-injection period and reached about 4–5 % of injected \(\hbox {CO}_{2}\) . The percentage of escaped brine from the storage formation ranged from 80–100 % of the \(\hbox {CO}_{2}\) mass stored in the storage formation depending on the reservoir scale.     

Spatiotemporal complexity of a three-species ratio-dependent food chain model

In this paper, we investigate the complex dynamics of a ratio-dependent spatially extended food chain model. Through a detailed analytical study of the reaction–diffusion model, we obtain some conditions for global stability. On the basis of bifurcation analysis, we present the evolutionary process of pattern formation near the coexistence equilibrium point $(N^*,P^*,Z^*)$ via numerical simulation. And the sequence cold spots $\rightarrow $ stripe–spots mixtures $\rightarrow $ stripes $\rightarrow $ hot stripe–spots mixtures $\rightarrow $ hot spots $\rightarrow $ chaotic wave patterns controlled by parameters $a_1$ or $c_1$ in the model are presented. These results indicate that the reaction–diffusion model is an appropriate tool for investigating fundamental mechanism of complex spatiotemporal dynamics.     

Temporal and Spatial Evolutions of Permeability During CBM Drainage Under Different Initial Conditions

Physical simulations of coalbed methane (CBM) drainage using different initial gas pressures and different crustal stresses were conducted, and the gas pressures were obtained. The permeability evolutions were calculated based on a permeability model that used the same preconditions and parameters that were obtained from experiments. The permeability decreased rapidly during the initial phase of CBM drainage and then recovered slowly with time. During the initial phase of CBM drainage, the permeability decreased more rapidly near the borehole than further away. The distributions of \(k/k_0 (k\) is permeability, \(k_{0}\) is initial permeability) on the section, surface and longitudinal section that were analyzed were all funnel-shaped, and the distributions were shaped like circular rings, circular cones and circular cones, respectively. After a period of time, the permeability near the borehole recovered slightly, and the distributions of \(k/k_0\) reversed. At the end of CBM drainage, the values of \(k/k_0\) on the section, surface and longitudinal section were almost equal. The higher the crustal stress, the more slowly the permeability decreased, and the higher the initial gas pressure, the more rapidly the permeability decreased.     

Gas Sorption and the Consequent Volumetric and Permeability Change of Coal I: Experimental

Experimental and numerical investigations were conducted to study adsorption and desorption of pure and multicomponent gas on coal, and the sorption-induced volumetric strain and permeability change of the coal. This paper presents the experimental work. Using CO \(_2\) , N \(_2\) , and CO \(_2\) and N \(_2\) binary mixtures of different composition as injection gases, the measurements were conducted on a cylindrical composite coal core at varying pore pressures and constant effective confining pressure. Sorption was measured using a volumetric method. The initial and equilibrium system pressure and gas phase composition were measured. The total amount of adsorption and the composition of the adsorbed phase (for adsorption of binary gas mixtures) were calculated based on material balance. During the process of sorption, the volume of the core was monitored by recording the volume of the water in the confining pressure vessel. Sorption-induced strain was calculated as the ratio of the sorption-induced volumetric change to the initial volume of the core. After adsorption equilibrium was reached, the permeability of the core was measured based on the Darcy equation for gas flow. Sorption and permeability measurements were conducted for each test gas at first increasing and then decreasing pressures. Volumetric strain was only measured while pore pressure increased. To our knowledge, this is the first study measuring adsorption, volumetric strain, and permeability on the same piece of core with the same apparatus.     

Experimental Ivestigation of the Temperature and Pore Pressure Effect on Permeability of Lignite Under the In Situ Condition

The worldwide primary demand of energy will keep rising over the coming decades. It becomes essential and desirable to exploit lignite, 23 % reservation of the whole coal energy, by a suitable and effective technique. However, the current technology limitations of the exploiting and utilizing of lignite have caused low exploiting rate and high pollution situation. Owing to the development of the in situ gasification techniques, the lignite has become more attractive in the energy field than ever. The permeability of coal is a crucial factor in determining the tars (liquid phases) and gases production during the in situ gasification process. And the transport properties of the coal will in turn affect the thermal and chemical-mechanical reactions. Here, in this work, the permeability of lignite has been tested from room temperature (25  $^{\circ }$ C) up to as high as 650  $^{\circ }$ C through a triaxial rock permeability testing system under different pore pressures. A remarkable decrease of permeability can be observed during the whole temperature zone (25–650  $^{\circ }$ C) as the pore pressure increasing. The permeability curve versus temperature up to 650  $^{\circ }$ C has been divided into four stages based on the three peak values of the permeability. The competition between the strength of the frame structure with the shrinkage due to pyrolysis determines the significant fluctuation of the permeability versus temperature. Furthermore, the combined effect of temperature and pressure shows that the valleys and peaks in stage II will shift to higher temperature zone, while the valleys and peaks stay in the same temperature place in stage III and IV. The current investigation results of the permeability property of lignite will provide essential and valuable information for the exploiting and utilizing of lignite, especially by the in situ pyrolysis technique.     

Gas Sorption and the Consequent Volumetric and Permeability Change of Coal II: Numerical Modeling

The permeability of coalbed methane reservoirs may evolve during the recovery of methane and injection of gas, due to the change of effective stress and gas adsorption and desorption. Experimental and numerical studies were conducted to investigate the sorption-induced permeability change of coal. This paper presents the numerical modeling part of the work. It was found that adsorption of pure gases on coal was well represented by parametric adsorption isotherm models in the literature. Based on the experimental data of this study, adsorption of pure \(\hbox {N}_2\) was modeled using the Langmuir equation, and adsorption of pure \(\hbox {CO}_2\) was well represented by the N-Layer BET equation. For the modeling of CO \(_2\) & N \(_2\) binary mixture adsorption, the ideal adsorbed solution (IAS) model and the real adsorbed solution (RAS) model were used. The IAS model estimated the total amount of mixture adsorption and the composition of the adsorbed phase based on the pure adsorption isotherms. The estimated total adsorption and adsorbed-phase composition were very different from the experimental results, indicating nonideality of the CO \(_2\) –N \(_2\) –Coal-adsorption system. The measured sorption-induced strain was linearly proportional to the total amount of adsorption despite the species of the adsorbed gas. Permeability reduction followed a linear correlation with the volumetric strain with the adsorption of pure \(\hbox {N}_2\) and the tested CO \(_2\) & N \(_2\) binary mixtures, and an exponential correlation with the adsorption of pure \(\hbox {CO}_2\) .     

Statistical Scaling of Geometric Characteristics in Millimeter Scale Natural Porous Media

We analyze statistical scaling of structural attributes of two millimeter scale rock samples, Estaillades limestone and Bentheimer sandstone. The two samples have different connected porosities and pore structures. The pore-space geometry of each sample is reconstructed via X-ray micro-tomography at micrometer resolution. Directional distributions of porosity and specific surface area (SSA), which are key Minkowski functionals (geometric observables) employed to describe the pore-space structure, are calculated from the images, and scaling of associated order- $q$ sample structure functions of absolute incremental values is analyzed. Increments of porosity and SSA tend to be statistically dependent and persistent (tendency for large and small values to alternate mildly) in space. Structure functions scale as powers $\xi (q)$ of directional separation distance or lag, $s$ , over an intermediate range of $s$ , displaying breakdown in power law scaling at large and small lags. Powers $\xi \!\!\left( q \right) $ of porosity and SSA inferred from moment and extended self-similarity (ESS) analyses of limestone and sandstone data tend to be quasi-linear and nonlinear (concave) in $q$ , respectively. We observe an anisotropic behavior for $\xi (q)$ , which appears to be mild for the porosity of the sandstone sample while it is marked for both porosity and SSA of the limestone rock sample. The documented nonlinear scaling behavior is amenable to analysis by viewing the variables as samples from sub-Gaussian random fields subordinated to truncated fractional Brownian motion or fractional Gaussian noise.     

Pore-Scale Numerical Investigation on Chemical Stimulation in Coal and Permeability Enhancement for Coal Seam Gas Production

Permeability is a controlling factor for gas migration in coal seam reservoirs and has invariably been the barrier to economically viable gas production in certain deposits. Cleats are the main conduits for gas flow in coal seams though cleat mineralisation is known to significantly reduce permeability. Cleat demineralisation by the use of acids may enhance the effective cleat aperture and therefore permeability. This modelling study examines how acids transport through coal subject to reactive cleat mineralisation, and develops a fundamental understanding of the mechanisms controlling permeability change from pore scale to sample scale. A novel Lattice Boltzmann Method (LBM)-based numerical model for the simulation, prediction, and visualisation of the reaction transport is proposed to numerically investigate relationships between physio-chemical changes and permeability during coal stimulation. In particular, the work studies the interaction of acidic fluids (HCl) with reactive mineral (e.g. calcite) and assumed non-reactive mineral (e.g. coal) surfaces, mineral dissolution and mass transfer, and resultant porosity change. The reaction of a calcite cemented core sub-plug from the Bandanna Formation of Bowen Basin (Australia), is used as a study case. LBM simulations revealed a permeability enhancement (27.15 times of the pre-flooding permeability) along the x-axis after 20 min HCl flooding of a \(5.3~\hbox {cm} \times 5.3~\hbox {cm} \times 1.3~\hbox {cm}\) sub-section. The analysis and evaluation of the 4D permeability evolution is conducted as a contribution work for the fluid flow modelling in the subsurface petrophysical conditions, at the micron to centimetre scales. The simulation results demonstrate the proposed algorithm is capable for studies of multiple mineral reactions with disparate reaction rates.     

CT Imaging of Low-Permeability, Dual-Porosity Systems Using High X-ray Contrast Gas

Low-permeability, dual-porosity media such as coal and gas shale (i.e., mudstone) exhibit structural and chemical features across a range of scales spanning from tens of meters to nanometers. Characterization methods and efforts for these porous media are needed to understand gas in place, gas flow behavior, and storage capacity for potential CO $_{2}$ sequestration. Characterizing the structure and heterogeneity of representative samples helps determine how the physical and chemical processes associated with CO $_{2}$ transport in coal and gas shale affect injectivity and storage capacity (over long periods of time), and the ability of these media to sequester CO $_{2}$ (as both a free and adsorbed phase) for thousands of years. In this study, an imaging technique focused on the submillimeter scale is applied to shale and coal samples of interest. In particular, porosity, component matrix distribution, and evidence of gas transport through these tight media were studied.     

Residual Trapping Beneath Impermeable Barriers During Buoyant Migration of \mathrm{CO}_2

The presence of impermeable barriers in a reservoir can significantly impede the buoyant migration of $\mathrm{CO}_2$ injected deep into a heterogeneous geological formation. An important consequence of the presence of these impermeable barriers in terms of the long-term storage of $\mathrm{CO}_2$ is the residual trapping that takes place beneath the barriers, which acts to both increase the storage potential of the reservoir and improve the storage security of the $\mathrm{CO}_2$ . Analytical results for the total amount of $\mathrm{CO}_2$ trapped in a reservoir with an uncorrelated random distribution of impermeable barriers are obtained for both two and three-dimensional cases. In two dimensions, it is shown that the total amount of $\mathrm{CO}_2$ contained in this fashion scales as $n^{5/4}$ , where $n$ is the number of barriers in the vertical direction. In three dimensions, the trapped amount scales as $n^c$ , where $5/4 \le c \le 2$ depending on the aspect ratio of the barriers. The analytical two-dimensional results are compared with results of detailed numerical simulations, and good agreement is observed.