Summary Storage of carbon dioxide (CO 2 ) in depleted gas reservoirs or large aquifers is one of the available solutions to reduce anthropogenic greenhouse gas emissions. Numerical modeling of these processes requires the use of large geological models with several orders of magnitude of variations in the porous media properties. Moreover, modeling the injection of highly concentrated and cold CO 2 in large reservoirs with the correct physics introduces numerical challenges that conventional reservoir simulators cannot handle. We propose a thermal formulation based on a full equation of state (EoS) formalism to model pure CO 2 and CO 2 mixtures with the residual gas of depleted reservoirs. Most of the reservoir simulators model the phase equilibriums with a pressure-temperature-based formulation. With this usual framework, it is not possible to exhibit two phases with pure CO 2 contents. Moreover, in this classical framework, the crossing of the phase envelope is associated with a large discontinuity in the enthalpy computation, which can prevent the convergence of the energy conservation equation. In this work, accurate and continuous phase properties are obtained, basing our formulation on enthalpy as a primary variable. We first implement a new phase-split algorithm with input variables as pressure and enthalpy instead of the usual pressure and temperature, and we validate it on several test cases. This algorithm can model situations in which the mixture can change rapidly from one phase to the other at constant pressure and temperature. Then, treating enthalpy instead of temperature as a primary variable in both the reservoir and the well modeling algorithms, our reservoir simulator can model situations with pure or near pure components, as well as crossing of the phase envelope that usual formulations implemented in reservoir simulators cannot handle. We first validate our new formulation against the usual formulation on a problem in which both formulations can correctly represent the physics. Then, we show situations in which the usual formulations fail to represent the correct physics and that are simulated well with our new formulation. Finally, we apply our new model for the simulation of pure and cold CO 2 injection in a real depleted gas reservoir from the Netherlands.

Summary Coupling polymer with low-salinity water (LSW) to promote enhanced oil recovery (EOR) in carbonate reservoirs has attracted significant interest in the petroleum industry. However, low-salinity polymer (LSP) application to improve oil extraction from such rocks remains a challenge because of the complex synergism between these two EOR agents. Thus, this paper highlights the main factors that govern the LSP displacement process in carbonate reservoirs in terms of wettability alteration and mobility control. A series of experiments including contact angle, spontaneous imbibition, injectivity, adsorption, and oil displacement tests were performed. The impact of mineral dissolution on the polymer/brine and polymer/rock surface interactions and its possible connection to the efficiency of the LSP in carbonates was also investigated using ζ potential analysis following an elaborative procedure. All experiments were executed at elevated temperature (75°C) using two polymers (SAV10) of different molecular weights (MWs) prepared at varying concentrations and salinities. Contact angle measurements showed that increasing the polymer concentration and MW and, at the same time, decreasing the solution salinity could effectively rend homogeneous oil-wet calcite surfaces strongly water-wet. Conversely, spontaneous imbibition tests using heterogonous oil-wet Indiana limestone cores showed that the polymer viscosity and its molecular size hinder the performance of the polymer to modify the wettability of the core samples at high concentration and MW because they could limit its penetration into the porous medium. On the other hand, the results obtained from polymer injectivities showed that LSP had better propagation with lower filtration effects in comparison with high-salinity polymer (HSP). However, polymer adsorption and inaccessible pore volume (IPV) increased with the decrease of salinity. Calcite mineral dissolution triggered by LSP, which is associated with an increase in pH and [Ca 2+ ], considerably influenced the polymer viscosity. In addition, ζ potential measurements showed that the LSP altered the rock surface charge from positive toward negative and at the same time, the Ca 2+ released due to mineral dissolution could modify the polymer molecule charge toward positive. This confirms that mineral dissolution impressively results in better wettability alteration performance; however, it could lead to undesirable high polymer adsorption at low salinity. These findings provide new insight into the influence of mineral dissolution on polymer performance in carbonates. Finally, forced oil displacement tests revealed that both HSP and LSP extracted approximatively the same amount of oil. The HSP could enhance the oil recovery through mobility control. By contrast, wettability alteration could take part in the improvement of oil recovery at LSP, as proved by spontaneous imbibition tests, along with mobility control. Despite possessing high wettability alteration potential, LSP could not yield very high recovery because of its low accessibility into the porous medium. Shearing of the LSP was found effective in improving oil recovery through enhancing the polymer accessibility. This will lead us to simply say that polymer accessibility into carbonates is crucial for the success of the wettability alteration and mobility control processes, which is remarkably important not only for this specific study but also for other various polymer EOR applications.

Summary For many years, miscible gas injection has been the most beneficial enhanced oil recovery method in the oil and gas industry. However, injecting a miscible gas to displace oil often causes the flocculation and deposition of asphaltenes, which subsequently leads to a number of production problems. Nitrogen gas (N 2 ) injection has been used to enhance oil recovery in some oil fields, seeking to improve oil recovery. However, few works have implemented N 2 injection and investigated its effect on asphaltene precipitation and deposition. This research investigated the N 2 miscible flow mechanism in nanopores and its impact on asphaltene precipitations, which can plug pores and reduce oil recovery. First, a slimtube was used to determine the minimum miscibility pressure (MMP) of N 2 to ensure that all of the experiments would be conducted at levels above the MMP. Second, filtration experiments were conducted using nanocomposite filter membranes to study asphaltene deposition on the membranes. A filtration apparatus was designed specifically and built to accommodate the filter membranes. The factors studied include N 2 injection pressure, temperature, N 2 mixing time, and pore size heterogeneity. Visualization tests were conducted to highlight the asphaltene precipitation process over time. Increasing the N 2 injection pressure resulted in an increase in the asphaltene weight percent in all experiments. Decreasing the pore size of the filter membranes increased the asphaltene weight percent. More N 2 mixing time also resulted in an increase in asphaltene weight percent, especially early in the process. Visualization tests revealed that after 1 hour, the asphaltene particles were conspicuous, and more asphaltene clusters were found in the test tubes of the oil samples from the filter with the smallest pore size. Chromatography analysis of the produced oil confirmed the reduction in the asphaltene weight percent. Microscopy and scanning electron microscopy (SEM) imaging of the filter membranes indicated significant pore plugging from the asphaltenes, especially for the smaller pore sizes. This research highlights the severity of asphaltene deposition during miscible N 2 injection in nanopore structures so as to understand the main factors that may affect the success of miscible N 2 injection in unconventional reservoirs.

Summary New experiments using polyethylene oxide (PEO) polymer were performed to evaluate its potential for enhanced oil recovery (EOR) applications in low-permeability reservoirs. This is the first time that high molecular weight PEO solutions have been shown to have favorable transport in low-permeability (~20 md) carbonate cores and the first time PEO has been shown to improve oil recovery in a fractured carbonate core. Rheology measurements in synthetic seawater show the higher viscosity of PEO solutions compares favorably to the viscosity of acrylamide–sodium acrylate (AM-AA) copolymers of similar molecular weight because PEO is less sensitive to hardness and high salinity. Filtration experiments using 0.45 μm cellulose filters show very favorable filtration ratios of PEO with a molecular weight of 4 million g/mol, which is consistent with its favorable transport in low-permeability cores. Four coreflood experiments in Texas Cream Limestone (TC Limestone) cores demonstrate the viability of PEO for EOR in low-permeability carbonate rocks. Single-phase experiments show 4 million g/mol PEO solutions transported through 18 and 28 md TC Limestone cores. Oil recovery experiments show 4 million g/mol PEO solutions transported and was more efficient than waterflooding in aged TC Limestone with favorable retention of 40 µg/g rock. An oil recovery experiment in an artificially fractured TC Limestone core improved oil recovery by a remarkable 15% considering the very large fracture-matrix permeability contrast (>7,000). These experimental results as well as other favorable properties of PEO reported in the literature indicate PEO should be considered for some EOR applications, especially in low-permeability reservoirs.

Summary Gel treatment is an effective way to attack excessive water production during oil development. The transport behavior of gel materials in reservoirs is of crucial importance to the effectiveness of gel treatments. The aim of this paper is investigating the transport behavior of swellable micrometer-sized preformed particle gels (PPGs, or microgels) through superpermeable (super-K) channels. Sandpacks with permeabilities ranging from 27 to 221 darcies were used to mimic the super-K channels. Multiple pressure sensors were applied along the sandpack models to monitor the propagation behavior of the microgels. The tested microgel particles could transport through the super-K channels, and a higher driving pressure gradient was required when the particle/pore size ratio was larger. The pressure gradient distribution along the super-K channels was relatively uniform when the particle/pore ratio was low (less than 1.3). However, the inlet section would show increasingly higher pressure gradients as the particle/pore ratio was increased, indicating increased difficulty in propagation. The propagation of the gel particles was significantly slower compared with the carrying fluid. The delayed propagation behavior was more pronounced when the particle/pore ratio was higher. The injection pressure was much less sensitive to the injection flow rate compared with a Newtonian fluid. The gel dispersion exhibited an apparent shear thinning (pseudoplastic) behavior when transporting through the porous channels. Breakage of the gel particles was observed especially at high superficial velocities. The particle breakage was partially responsible for the apparent shear thinning behavior. The breakage phenomenon was in favor of deep placement of the gel particles. The channel permeabilities were significantly reduced by the microgels, bringing sufficient resistance to subsequent waterflooding (more than 99.5%). At given matching size conditions, softer gels were more likely to establish in-depth placement and uniform water blocking capacity in the channels. The microgel particles exhibited salinity-responsive behavior to the post-brine flush. The gel particles could shrink and reswell according to the salinity of the injected water. Possibilities were discussed to use this salinity-responsive behavior. Also, the microgels exhibited a particular disproportionate permeability reduction (DPR) effect. After gel injection, the channel permeability to water flow was reduced by more than 20 to 92 times of the permeability to oil flow. This work provides important support to understand the transport behavior of gel particles in super-K channels. The achievements are helpful for gel product selection and gel treatment design.

Summary Nanoparticles have great potential to mobilize trapped oil in reservoirs because of their chemical, thermal, and interfacial properties. However, the direct application of magnetic forces on superparamagnetic nanoparticles in reservoir engineering applications has not been extensively investigated. We demonstrate the enhanced oil recovery (EOR) potential of hydrophilic superparamagnetic nanoparticles in oil production by direct observation using microfluidics. We studied the mobilization of oil blobs by a ferrofluid (a suspension of hydrophilic superparamagnetic nanoparticles in water) both in a converging/diverging micromodel channel and in a foot-long pore network micromodel, both with varying depth (so-called 2.5D micromodels). The water-based ferrofluid in all cases was the wetting fluid. Initial ferrofluid flooding experiments in single channels were performed without and then with a static magnetic field. This magnetic field caused oil droplet deformation, dynamic breakup into smaller droplets, and subsequent residual oil saturation reduction. During the flooding, after the magnetic field was applied, significant oil displacement was observed within 2 hours [6 pore volumes injected (PVI)], and 86.2% of the oil that was not mobilized without a magnetic field was mobilized within 64 hours (192 PVI). Then, in experiments in the micromodel and in a Hele-Shaw cell without flooding, we observed self-assembly of oil droplets, indicating the formation of the hydrophilic magnetic nanoparticle microstructures (chains under the magnetic field) and their interaction with the oil blobs. Further ferrofluid flooding experiments were performed in a foot-long micromodel under a rotating magnetic field. The oil saturation was reduced from 44.6 to 33.3% after 17 hours (8.5 PVI) of ferrofluid flooding after the rotating magnetic field was applied. Finally, a discussion of field application of ferrofluid flooding is presented.

Summary A class of monotone cell-centered nonlinear finite-volume methods has been proposed in the past decade to solve the anisotropic diffusion equation. The nonlinear two-point flux approximation (TPFA) (NTPFA) method preserves the nonnegativity of the solution values but can violate the discrete maximum/minimum principle (DMP). To enforce DMP, the nonlinear multipoint flux approximation (NMPFA) method ought to be used. In this work, we propose a novel NTPFA method that can reduce the severity of DMP violations significantly compared with the standard NTPFA method. The new formulation uses conormal decomposition for the construction of the one-sided fluxes. To define the unique flux through a connection between two cells, we choose a convex combination of the two one-sided fluxes such that the absolute differences of the magnitudes of the two transmissibility terms associated with the two neighboring cells are minimized, thus bringing the discrete coefficient matrix closer to having the zero row-sum property. Numerical experiments are conducted to test the performance of the new NTPFA method. The results demonstrate that the new scheme has comparable convergence order for both the solution and the flux compared with the standard NTPFA method or the classical multi-point flux approximation (MPFA-O) method. Moreover, the new NTPFA formulation shows marked improvements over the standard NTPFA in terms of reducing DMP violations. However, depending on the specific problem configuration, our new NTPFA formulation can lead to a system of nonlinear equations that is more difficult to solve.

Summary Legacy crushed rock analysis, as applied to unconventional formations, has shown great success in evaluating total porosity and water saturation over the previous three decades. The procedure of crushing rock into small particles improves the efficiency of fluid recovery and grain volume measurements in a laboratory environment. However, a caveat to crushed rock analysis is that water and volatile hydrocarbons evaporate from the rock during the preparatory crushing process, causing significant uncertainty in water saturation assessment. A modified crushed rock analysis incorporates nuclear magnetic resonance (NMR) measurements before and after the crushing process to quantify the volume of fluid loss. The advancements improve the overall total saturation quantification. However, challenges remain in the quantification of partitioned water and hydrocarbon loss currently derived from the NMR spectrum along with its uncertainty. Furthermore, pressure decay permeability from crushed rock analysis has been reported to have two to three orders of magnitude difference between different laboratories. The calculated pressure decay permeability of the same rock could even vary by several orders of magnitude with different crushed sizes, which questions the quality of the crushed pressure decay permeability. In this paper, we introduce an intact rock analysis workflow on unconventional cores for improved assessment of water saturation and enhanced quantification of fast pressure decay matrix permeability from intact rock. The workflow starts with acquisition of NMR T 2 and bulk density measurements on the as-received state intact rock. Instead of crushing the rock, the intact rock is directly transferred to a retort chamber and heated to 300°C for thermal extraction. The volumes of thermally recovered fluids are quantified through an image-based process. The grain volume measurement and a second NMR T 2 measurement are performed on post-retort intact rock. The pressure decay curve during the grain volume measurement is then used for calculating the pressure decay matrix permeability. Total porosity is calculated using the bulk volume and grain volume of the rock. Water saturation is quantified using the total volume of recovered water. In addition, the twin as-received-state rocks are processed through the crushed rock analysis workflow for an apple-to-apple comparison. Meanwhile, the pressure decay permeability of the post-retort intact sample is cross-validated against the steady-state gas permeability of the same post-retortsample. The introduced workflow has been tested successfully on different formations, including Bakken, Bone Spring, Eagle Ford, Cotton Valley, and Niobrara. The results show that total porosities calculated from intact rock analysis are consistent with total porosities from crushed rock analysis, while water saturations from the new workflow are an average 8% saturation unit (SU) [0.2 to 0.7% porosity unit (PU) of bulk volume water (BVW)] higher than those from the prior crushed rock workflows. The study also indicates that for some formations (e.g., Bone Spring), the fluid loss during the crushing process is dominated by water; however, for some other formations (e.g., Bakken), the hydrocarbon loss is significant. Pressure decay permeability quantified using intact rock analysis is also confirmed within an order of magnitude of steady-state matrix permeability.

Summary Recently, graphics processing units (GPUs) have been demonstrated to provide a significant performance benefit for black-oil reservoir simulation, as well as flash calculations that serve an important role in compositional simulation. A comprehensive approach to compositional simulation based on GPUs has yet to emerge, and the question remains as to whether the benefits observed in black-oil simulation persist with a more complex fluid description. We present a positive answer to this question through the extension of a commercial GPU-basedblack-oil simulator to include a compositional description based on standard cubic equations of state (EOSs). We describe the motivations for the selected nonlinear formulation, including the choice of primary variables and iteration scheme, and support for both fully implicit methods (FIMs) and adaptive implicit methods (AIMs). We then present performance results on an example sector model and simplified synthetic case designed to allow a detailed examination of runtime and memory scaling with respect to the number of hydrocarbon components and model size, as well as the number of processors. We finally show results from two complex asset models (synthetic and real) and examine performance scaling with respect to GPU generation, demonstrating that performance correlates strongly with GPU memory bandwidth. NOTE: This paper is published as part of the 2021 SPE Reservoir Simulation Conference Special Issue.

Summary The permeability characteristics of hydrate-bearing reservoirs are critical factors governing gas and water flow during gas hydrate exploitation. Herein, X-ray microcomputed tomography (CT) and the pore network model (PNM) are applied to study the dynamic gas and water relative permeabilities ( k rg and k rw ) of hydrate-bearing porous media during the shear process. As such, the dynamic region extraction method of hydrate-bearing porous media under continuous shear is adopted by considering deformation in the vertical direction. The results show that k rw and k rg of hydrate-bearing porous media are influenced by the effect of disordered sand particle movement under axial strain. Declines in the critical pore structure factors (pore space connectivity, pore size, and throat size) contribute to the reduction in k rw and the increase in k rg . However, k rg decreases during the shear process at a high water saturation ( S w ) because of the high threshold pressure and flow channel blockage. In addition, the connate water saturation ( S wc ) continuously increases during the shear process. S wc is influenced by pore size, throat size, and flow channel blockage. Moreover, the preferential flow direction of k rg and k rw changes during the continuous shear process. The results of dynamic permeability evolution during the continuous shear process under triaxial stress provide a reference for pore-scale gas and water flow regulation analysis.

Summary In this paper, I present numerical results of gas/liquid flows in pipelines obtained from a new simulation code. One difference, with respect to other 1D fluid dynamic commercial simulation products, is the use of a compositional approach to the problem: This is rarely found in published articles about gas/liquid flow in the oil and gas industry. It is shown that the algorithm can calculate both pressure and material fast waves generated during the transportation of gas and liquid in pipes. The solution algorithm is based on the application of a two-fluid model to the mass, momentum, and energy conservation equations, which are solved using a mixed implicit-explicit integration schema. Closure equations for the calculation of interface stress are taken from literature articles. A dam-break simulation (i.e., a Riemann initial value problem) is presented as a severe test case for validation of the two-phase flow algorithm. Because the code is able to capture sharp and fast changes in the liquid holdup connected to the formation of pressure waves, it is applied to the simulation of slug flow without the use of steady-state “unit cell” models and slug tracking functions. In this context, the experimental results on pseudoslug formation in inclined pipes at high pressures, published by the Tulsa University Fluid Flow Project (TUFFP), are used to compare simulated results with experimental data. The last part is dedicated to the simulation of some cases taken from a classical flow-map of a fundamental article by Taitel and Dukler (1976) . At constant liquid superficial velocity, the formation of liquid slugs and their subsequent termination with the increase of gas flow rate is simulated with details never previously presented.

Summary Natural gas hydrate (NGH) is regarded as an important alternative future energy resource. In recent years, a few short-term production tests have been successfully conducted with both permafrost and marine sediments. However, long-term hydrate production performance and the potential geomechanical problems are not very clear. According to the available geological data at the Mallik site, a more realistic hydrate reservoir model that considers the heterogeneity of porosity, permeability, and hydrate saturation was developed and validated by reproducing the field depressurization test. The coupled multiphase and heat flow and geomechanical response induced by depressurization were fully investigated for long-term gas production from the validated hydrate reservoir model. The results indicate that long-term gas production through depressurization from a vertically heterogeneous hydrate reservoir is technically feasible, but the production efficiency is generally modest, with the low average gas production rate of 4.93 × 10 3 ST m 3 /d (ST represents the standard conditions) over a 1-year period. The hydrate dissociation region is significantly affected by the reservoir heterogeneity and reveals a heterogeneous dissociation front in the reservoir. The depressurization production results in significant increase of shear stress and vertical compaction in the hydrate reservoir. The response of shear stress indicates that the potential region of sand migration is mainly in the sand-dominant layer during gas production from the hydraulically heterogeneous hydrate reservoir (e.g., sand layers interbedded with clay layers). The maximum subsidence is approximately 78 mm and occurred at the 72nd day, whereas the final subsidence is slowly dropped to 63 mm after 1-year of depressurization production. The vertical subsidence is greatly dependent on the elastic properties and the permeability anisotropy. In particular, the maximum subsidence increased by approximately 81% when the ratio of permeability anisotropy was set at 5:1. Furthermore, the potential shear failure in the hydrate reservoir is strongly correlated to the in-situ stress state. For the normal fault stress regime, the greater the initial horizontal stress is, the less likely the hydrate reservoir is to undergo shear failure during depressurization production.

Summary Fracturing is the necessary means of tight oil development, and the most common fracturing fluid is slickwater. However, the Loess Plateau of the Ordos Basin in China is seriously short of water resources. Therefore, the tight oil development in this area by hydraulic fracturing is extremely costly and environmentally unfriendly. In this paper, a new method using supercritical carbon dioxide (CO 2 ) (ScCO 2 ) as the prefracturing energized fluid is applied in hydraulic fracturing. This method can give full play to the dual advantages of ScCO 2 characteristics and mixed-water fracturing technology while saving water resources at the same time. On the other hand, this method can reduce reservoir damage, change rock microstructure, and significantly increase oil production, which is a development method with broad application potential. In this work, the main mechanism, the system-energy enhancement, and flowback efficiency of ScCO 2 as the prefracturing energized fluid were investigated. First, the microscopic mechanism of ScCO 2 was studied, and the effects of ScCO 2 on pores and rock minerals were analyzed by nuclear-magnetic-resonance (NMR) test, X-ray-diffraction (XRD) analysis, and scanning-electron-microscope (SEM) experiments. Second, the high-pressure chamber-reaction experiment was conducted to study the interaction mechanism between ScCO 2 and live oil under formation conditions, and quantitively describe the change of high-pressure physical properties of live oil after ScCO 2 injection. Then, the numerical-simulation method was applied to analyze the distribution and existence state of ScCO 2 , as well as the changes of live-oil density, viscosity, and composition in different stages during the full-cycle fracturing process. Finally, four injection modes of ScCO 2 -injection core-laboratory experiments were designed to compare the performance of ScCO 2 and slickwater in terms of energy enhancement and flowback efficiency, then optimize the optimal CO 2 -injection mode and the optimal injection amount of CO 2 slug. The results show that ScCO 2 can dissolve calcite and clay minerals (illite and chlorite) to generate pores with sizes in the range of 0.1 to 10 µm, which is the main reason for the porosity and permeability increases. Besides, the generated secondary clay minerals and dispersion of previously cemented rock particles will block the pores. ScCO 2 injection increases the saturation pressure, expansion coefficient, volume coefficient, density, and compressibility of crude oil, which are the main mechanisms of energy increase and oil-production enhancement. After analyzing the four different injection-mode tests, the optimal one is to first inject CO 2 and then inject slickwater. The CO 2 slug has the optimal value, which is 0.5 pore volume (PV) in this paper. In this paper, the main mechanisms of using ScCO 2 as the prefracturing energized fluid are illuminated. Experimental studies have proved the pressure increase, production enhancement, and flowback potential of CO 2 prefracturing. The application of this method is of great significance to the protection of water resources and the improvement of the fracturing effect.

Summary Water-oil displacement is an important process that occurs in a shale matrix after hydraulic fracturing and in water-based enhanced oil recovery. Current understanding of this displacement process is limited because of the complicated pore structure and surface properties in shale. In this work, this process and its controlling factors are investigated through a comparative study of three shale samples that have different types of pore systems and wettability. An integrated method of imbibition and multiscale imaging was applied, and a modified oleic tracer that can better represent oil flow was used in imbibition testing and micro-computed tomography (CT) imaging. Scanning electron microscope (SEM) pore characterization was then performed under high magnification with guidance from the micro-CT images showing the changes caused by oil or water imbibition. New insights were obtained on the importance of both wettability and pore size effect on oil recovery and the distribution of residual oil after water-oil displacement. Connectivity of pores with different wettability is also discussed based on 3D analysis and SEM pore characterization. Collectively, these new findings improve the understanding of the complicated process of water-oil displacement and the role of influencing factors. Important implications for improved oil recovery strategy in shale are discussed for different types of reservoir rocks. The integrated imaging and imbibition technique provides a new path for further investigation of improved oil recovery in shale.

Summary Various unified gas flow (UGF) and apparent permeability models have been proposed to characterize the complex gas transport mechanisms in shale formations. However, such models are typically expressed as combinations of multiple gas flow mechanisms so that they cannot predict gas velocity profile. In this study, we develop a novel approach to predict the gas velocity profile in the entire Knudsen number (Kn) regime for circular and noncircular (i.e., square, rectangular, triangular and elliptical) nanochannels and investigate the effects of cross-sectional geometry on gas transport in nanochannels. To this end, a new UGF model is proposed to describe the gas flow behaviors in the entire Kn regime, considering the effects of gas slippage, bulk diffusion, Knudsen diffusion, surface diffusion, and cross-sectional geometry of flow channel. In addition, the boundary condition of the semianalytical second-order slip model applicable to various cross-sectional geometries is modified by adjusting the slip coefficients through the comparison between the proposed UGF model and the Navier-Stokes (N-S) equation with second-order slip boundary condition. As a result, the velocity profile of free gas in the entire Kn regime for the nanochannel with a specific cross section can be determined by solving the second-order slip model with adjusted slip coefficients via the finite element method. The results indicate that the geometry of the cross section has a significant influence on the mass flow rate and gas velocity profile in nanochannels. The predicted mass flow rates for the nanochannels with identical hydraulic diameter decrease with the cross-sectional geometry in the sequence as ellipse > equilateral triangle > rectangle > square > circle. However, the ranking of velocity profiles for such nanochannels, which is governed by the cross-sectional geometry, also varies with Kn. These findings indicate that the developed approach can predict the synergetic gas transport (i.e., gas slippage, bulk diffusion, Knudsen diffusion, and surface diffusion) and gas velocity profile in nanochannels with different cross-sectional geometries for a wide range of Kn, which gives insight into the characterization of gas flow behaviors in nanoporous shale.

Summary In-situ evaluation of fracture tortuosity (i.e., pore geometry complexity and roughness) and preferential orientation is crucial for fluid flow simulation and production forecast in subsurface water and hydrocarbon reservoirs. This is particularly significant for naturally fractured reservoirs or postacid fracturing because of the strong permeability anisotropy. However, such downhole in-situ characterization remains a challenge. This study presents a new method for evaluating fracture tortuosity and preferential orientation based on the pulsed field gradient (PFG) nuclear magnetic resonance (NMR) technique. Such an approach provides diffusion tortuosity, τ d , defined as the ratio of bulk fluid diffusion coefficient to the restricted diffusion coefficient in the porous media. In the PFG NMR technique, the magnetic field gradient can be applied in different directions, and therefore anisotropy in diffusion coefficient and τ d can be evaluated. Three 3D printed samples, characterized by well controlled variable fracture tortuosity, one fractured sandstone, and three acidized carbonate samples with wormhole were used in this study. PFG NMR measurements were performed using both 2- and 12-MHz NMR instruments to obtain τ d in the three different principal directions. The results obtained from the NMR measurements were compared with fracture tortuosity and preferential orientation determined from the microcomputed tomography (micro-CT) images of the samples. The results showed that τ d increases as the fracture tortuosity and pore geometry complexity increases, showing good agreement with the image-based geometric tortuosity values. Moreover, the lowest τ d values were found to coincide with the preferential direction of fracture surfaces and wormhole body for a given sample, whereas the maximum τ d values correspond to the nonconnected pathway directions. These results suggest that the implantation of directional restricted diffusion measurements on the NMR well logging tools would offer a possibility of probing tortuosity and determining preferential fluid flow direction via direct downhole measurements.

Summary The relative permeability ( k r ) and capillary pressure ( P c ) are essential components to predict the gas and water flow in hydrate-bearing reservoirs. In this study, we analyze the dynamic gas and water relative permeability ( k rg and k rw ) during the continuous creep process of hydrate-bearing sand (HBS) under conditions of thermal-stimulated hydrate dissociation using computed tomography (CT) and the pore network model (PNM). The dynamic sample region extraction method for CT images is adopted by considering the deformation of HBS in the vertical direction. The pore structure of the HBS was visualized and reconstructed by CT scanning. The 3D pore network is built after image processing; then, gas and water flow processes are analyzed by the PNM. The results show that k rw is highly consistent with two main pore structure factors: the pore space size and connectivity variation. k rg is greatly affected by an increasing number of narrow flow channels in the HBS during the creep process. In addition, the irreducible water saturation ( S wir ) during the creep process is mainly affected by the joint effect of the pore size, throat size, and pore space connectivity. The preferential flow directions of the gas and water change from vertical to horizontal along with the progression of creep.

Summary Reservoir depletion is known to reduce the porosity and permeability of stress-sensitive reservoir rocks. The effect may substantially hinder the productivity index (PI) of producing wells. This study presents analytical solutions for the time-dependent and steady-state well PIs, respectively, of a bounded, disk-shaped, elastic reservoir with no-flow and constant-pressure conditions at the outer boundary. A combination of Green's functions, the Laplace transform method, and the perturbation technique is used to solve the governing nonlinear partial differential equations of the considered coupled problems of flow and geomechanics. Dimensional analyses based on the Buckingham Π theorem are conducted to identify the dimensionless parameters groups of each problem and to express the resulting analytical solutions in the dimensionless form. In addition, necessary corrections to an existing error in the reported Green's functions for the induced strain field of a ring-shaped pressure source within an elastic half-space ( Segall 1992 ) are made. The corrected Green's functions are used to obtain the strain induced by the pore fluid pressure distribution within a depleting disked-shaped reservoir. Consequently, a corrected permeability variation model compared to our previously published, time-independent solution for rate-dependent PI ( Zhang and Mehrabian 2021a ) is presented. Finally, a mechanistically rigorous formulation of the permeability modulus parameter that commonly appears in the pertinent literature is suggested. In addition to the in-house developed finite-difference solutions, the presented analytical solutions are verified against results from the finite-element simulation of the same problems using COMSOL® Multiphysics (2018). The obtained rate-dependent PI of the reservoir is controlled by four dimensionless parameters, namely, the dimensionless rock bulk modulus, the Biot-Willis effective stress coefficient, Poisson's ratio, and rock initial porosity. The pore fluid pressure solution is shown to asymptotically approach the corresponding flow-only solution for large values of the dimensionless rock bulk modulus. Parametric analysis of the solution suggests that the well productivity loss has a reverse relationship with the dimensionless bulk modulus and initial porosity of the rock, whereas a direct relationship is identified with Biot-Willis effective stress coefficient and Poisson's ratio. Compared to the reservoir with a constant-pressure outer boundary, the PI of a reservoir with a no-flow condition at the outer boundary is shown to be more significantly hindered by the stress sensitivity of the reservoir rock.

Summary Most simulators currently use the advection/diffusion model (ADM), where the total flux comprises Darcian advection and Fickian diffusion. However, significant errors can arise, especially for modeling diffusion processes in fractured unconventional reservoirs, if diffusion is modeled by the conventional Fick’s law using molar concentration. Hence, we propose an improved multicomponent diffusion model for fractured reservoirs to better quantify the multiphase multicomponent transport across the fracture/matrix interface. We first give a modified formulation of the Maxwell-Stefan (MS) equation to model the multicomponent diffusion driven by the chemical potential gradients. A physics-based modification is proposed for the ADM in fractured reservoirs, where fracture, matrix, and their interface are represented by three different yet interconnected flow domains to honor the flux continuity at the fracture/matrix interface. The added interface using a more representative fluid saturation and composition of the interface can hence better capture the transient mass fluxes between fracture and matrix. The proposed approach is also implemented in an in-house compositional simulator. The multicomponent diffusion model is validated with both intraphase and interphase diffusion experiments. Then, the improved model for fracture/matrix interaction is compared with a fine-grid model. The proposed multiple interacting continua (MINC) model with three continua (MINC3) can better match the fine-grid model’s result than the double-porosity (DP) model, which only obtains a fair match at an early time. Then, we simulate a gas huff ‘n’ puff (HnP) well in the Permian Basin to investigate the effect of diffusion within the fractured tight oil reservoir. The simulation reveals that diffusion has a minor effect on the performance of depletion when oil is the dominant phase. For gas HnP, the simulation neglecting diffusion will underestimate the oil recovery factor (RF) but overestimate the gas rate. The DP approach tends to overestimate the RF of heavy components but leads to a similar cumulative oil RF compared with MINC3. With the diffusion included in the simulation, gas HnP performance becomes more sensitive to the soaking time than the model without diffusion. Although increasing the soaking time will lead to a higher RF after considering diffusion, the incremental oil is not sufficiently large to justify a prolonged soaking time.

Summary As part of studying miscible gas injection (GI) in a major field within the Green Canyon protraction area in the Gulf of Mexico (GOM), asphaltene-formation risk was identified as a key factor affecting a potential GI project. The industry has not conducted many experiments to quantify the effect of asphaltenes on reservoir and well performance under GI conditions. In this paper we discuss a novel laboratory test for evaluating the asphaltene effect on permeability. The goals of the study were to define the asphaltene-precipitation envelope using blends of reservoir fluid and injection gas, and measure permeability reduction caused by asphaltene precipitation in a core under GI. To properly analyze the effect of GI, a suite of fluid-characterization studies was conducted, including restored-oil samples, compositional analysis, constant composition expansion (CCE), and differential vaporization. Miscibility conditions were defined through slimtube-displacement tests. Gas solubility was determined through swelling tests complemented by asphaltene-onset-pressure (AOP) testing. The unique procedure was developed to estimate the effect of asphaltene deposition on core permeability. The 1-ft-long core was saturated with the live-oil and GI mixture at a pressure greater than the AOP, and then pressure was depleted to a pressure slightly greater than the bubblepoint. Several cycles of charging and depletion were conducted to mimic continuous flow of oil along the path of injected gas and thereby to observe the accumulation of asphaltene on the rock surface. The test results indicated that during this cyclic asphaltene-deposition process, the core permeability to the live mixture decreased in the first few cycles but appeared to stabilize after Cycle 5. The deposited asphaltenes were analyzed further through environmental scanning electron microscopy (ESEM), and their deposition was confirmed by mass balance before and after the tests. Finally, a relationship was established between permeability reduction and asphaltene precipitation. The results from the asphaltene-deposition experiment show that for the sample, fluids, and conditions used, permeability is impaired as asphaltene flocculates and begins to coat the grain surfaces. This impairment reaches a plateau at approximately 40% of the initial permeability. Distribution of asphaltene along the core was measured at the end by segmenting the core and conducting solvent extraction on each segment. Our recommendation is numerical modeling of these test results and using this model to forecast the magnitude of the permeability impairment in a reservoir setting during miscible GI.