Single Porosity Model Research Articles

An Efficient Numerical Hybrid Model for Multiphase Flow in Deformable Fractured-Shale Reservoirs

Summary After hydraulic fracturing, a shale reservoir usually has multiscale fractures and becomes more stress-sensitive. In this work, an adaptive hybrid model is proposed to simulate hydromechanical coupling processes in such fractured-shale reservoirs during the production period (i.e., the hydraulic-fracturing process is not considered and cannot be simulated). In our hybrid model, the single-porosity model is applied in the region outside the stimulated reservoir volume (SRV), and the matrix and natural/induced fractures in the SRV region are modeled using a double-porosity model that can accurately simulate the matrix/fracture fluid exchange during the entire transient period. Meanwhile, the fluid flow in hydraulic fractures is modeled explicitly with the embedded-discrete-fracture model (EDFM), and a stabilized extended-finite-element-method (XFEM) formulation using the polynomial-pressure-projection (PPP) technique is applied to simulate mechanical processes. The developed stabilized XFEM formulation can avoid the displacement oscillation on hydraulic-fracture interfaces. Then a modified fixed-stress sequential-implicit method is applied to solve the hybrid model, in which mixed-space discretization [i.e., finite-volume method (FVM) for flow process and stabilized XFEM for geomechanics] is used. The robustness of the proposed model is demonstrated through several numerical examples. In conclusion, several key factors for gas exploitation are investigated, such as adsorption, Klinkenberg effect, capillary pressure, and fracture deformation. In this study, all the numerical examples are 2D, and the gravity effect is neglected in these simulations. In addition, we assume there is no oil phase in the shale reservoirs, thus the gas/water two-phase model is used to simulate the flow in these reservoirs.

Extended poromechanics for adsorption-induced swelling prediction in double porosity media: Modeling and experimental validation on activated carbon

Natural and synthesised porous media are generally composed of a double porosity: a microporosity where the fluid is trapped as an adsorbed phase and a meso or a macro porosity required to ensure the transport of fluids to and from the smaller pores. Zeolites, activated carbon, tight rocks, coal rocks, source rocks, cement paste or construction materials are among these materials.In nanometer-scale pores, the molecules of fluid are confined. This effect, denoted as molecular packing, induces that fluid-fluid and fluid-solid interactions sum at the pore scale and have significant consequences at the macroscale, such as instantaneous deformation, which are not predicted by classical poromechanics. If adsorption in nanopores induces instantaneous deformation at a higher scale, the matrix swelling may close the transport porosity, reducing the global permeability of the porous system. This is important for applications in petroleum oil and gas recovery, gas storage, separation, catalysis or drug delivery.This study aims at characterizing the influence of an adsorbed phase on the instantaneous deformation of micro-to-macro porous media presenting distinct and well-separated porosities. A new incremental poromechanical framework with varying porosity is proposed allowing the prediction of the swelling induced by adsorption without any fitting parameters. This model is validated by experimental comparison performed on a high micro and macro porous activated carbon. It is shown also that a single porosity model cannot predict the adsorption-induced strain evolution observed during the experiment. After validation, the double porosity model is used to discuss the evolution of the poromechanical properties under free and constraint swelling.

Comparison between single- and dual-porosity models for fluid transport in predicting lesion volume following saline-infused radiofrequency ablation

A recent study by Ooi and Ooi (EH Ooi, ET Ooi, Mass transport in biological tissues: Comparisons between single- and dual-porosity models in the context of saline-infused radiofrequency ablation, Applied Mathematical Modelling, 2017, 41, 271-284) has shown that single-porosity (SP) models for describing fluid transport in biological tissues significantly underestimate the fluid penetration depth when compared to dual-porosity (DP) models. This has raised some concerns on whether the SP model, when coupled with models of radiofrequency ablation (RFA) to simulate saline-infused RFA, could lead to an underestimation of the coagulation size. This paper compares the coagulation volumes obtained following saline-infused RFA predicted based on the SP and DP models for fluid transport. Results showed that the SP model predicted coagulation zones that are consistently 0.5 to 0.9 times smaller than that of DP model. This may be explained by the low permeability value of the tissue interstitial space, which causes the majority of the saline to flow through the vasculature. The absence of fluid flow tracking in the vasculature in the SP model meant that any flow of saline into the vasculature is treated as losses and do not contribute to the saline penetration depth of the tissue. Comparisons with experimental results from the literature revealed that the DP models predicted coagulation zone sizes that are closer to the experimental values than the SP models. This supports the hypothesis that the SP model is a poor choice for simulating the outcome of saline-infused RFA.

Investigation of distributed-porosity fields for urban flood modelling using single-porosity models

Porosity-based model rely on the assumption that an urban area can be compared to a porous medium, where the porosity is defined as the ratio between the actual area available to the flow, i.e. not occupied by buildings, and the total area of the considered urban environment. In classical single-porosity models, the resulting value of the porosity parameter is considered as constant and accounts essentially for the reduced water storage capacity and reduced space available for the flow. As a consequence, the source term involving the porosity parameter only accounts for a local head loss at the entrance and at the exit of the urban area. Therefore, the head losses occurring inside the urban area are accounted for using drag-type source terms. In the present work, we tested different definitions of the porosity parameter, showing the benefits of accounting for areas with distributed porosity based on the actual layout of buildings and streets. This formulation is still compatible with the basic idea of porosity-based model, i.e allowing for the use of coarse computational meshes instead of refined meshing of the urban area.

Solute Transport Properties of Fen Peat Differing in Organic Matter Content.

There is a limited understanding of solute transport properties of degraded peat soils as compared to mineral substrates. A lower organic matter (OM) content is often the result of peat degradation and mineralization following artificial drainage. In this study, we aimed at deducing changes in solute transport properties of peat soils differing in OM content. Miscible displacement experiments were conducted on 70 undisturbed soil columns with OM contents ranging from 11 to 86% w/w under saturated steady-state conditions using tritium and bromide as conservative tracers. Measured breakthrough curves (BTCs) were subjected to model analysis using three different approaches: single-porosity model (SPM), mobile-immobile model (MIM), and two-flow region model (TFRM). The results indicated that (i) nonequilibrium solute transport processes are common in peat soils; (ii) the TFRM improved predictions of BTCs with heavy tailing or two peaks; (iii) applied tracers, tritium and bromide, were retarded in peat soils with higher OM content; and (iv) pronounced preferential flow mainly occurred in peat soils with lower OM content. This type of strong preferential flow had a small ratio of measured to fitted pore water velocity and a greater ratio of velocities (/ > 3.0) in the fast and slow transport region as obtained from the TFRM. We conclude that shallow groundwater resources are more likely to become polluted in drained and degraded fen peats that are used for agricultural purposes.

Numerical simulation study on miscible EOR techniques for improving oil recovery in shale oil reservoirs

Shale formations in North America such as Bakken, Niobrara, and Eagle Ford have huge oil in place, 100–900 billion barrels of oil in Bakken only. However, the predicted primary recovery is still below 10%. Therefore, seeking for techniques to enhance oil recovery in these complex plays is inevitable. Although most of the previous studies in this area recommended that CO2 would be the best EOR technique to improve oil recovery in these formations, pilot tests showed that natural gases performance clearly exceeds CO2 performance in the field scale. In this paper, two different approaches have been integrated to investigate the feasibility of three different miscible gases which are CO2, lean gases, and rich gases. Firstly, numerical simulation methods of compositional models have been incorporated with local grid refinement of hydraulic fractures to mimic the performance of these miscible gases in shale reservoirs conditions. Implementation of a molecular diffusion model in the LS-LR-DK (logarithmically spaced, locally refined, and dual permeability) model has been also conducted. Secondly, different molar-diffusivity rates for miscible gases have been simulated to find the diffusivity level in the field scale by matching the performance for some EOR pilot tests which were conducted in Bakken formation of North Dakota, Montana, and South Saskatchewan. The simulated shale reservoirs scenarios confirmed that diffusion is the dominated flow among all flow regimes in these unconventional formations. Furthermore, the incremental oil recovery due to lean gases, rich gases, and CO2 gas injection confirms the predicted flow regime. The effect of diffusion implementation has been verified with both of single porosity and dual-permeability model cases. However, some of CO2 pilot tests showed a good match with the simulated cases which have low molar-diffusivity between the injected CO2 and the formation oil. Accordingly, the rich and lean gases have shown a better performance to enhance oil recovery in these tight formations. However, rich gases need long soaking periods, and lean gases need large volumes to be injected for more successful results. Furthermore, the number of huff-n-puff cycles has a little effect on the all injected gases performance; however, the soaking period has a significant effect. This research project demonstrated how to select the best type of miscible gases to enhance oil recovery in unconventional reservoirs according to the field-candidate conditions and operating parameters. Finally, the reasons beyond the success of natural gases and failure of CO2 in the pilot tests have been physically and numerically discussed.

Unconventional multi-fractured analytical solution using dual porosity model

Five-region linear flow system proved to be a useful model to reproduce the flow behavior for multi-fractured horizontal wells in shale reservoirs. In earlier developments, the model was assumed single-porosity throughout all five regions. However, assumption of single porosity system for stimulated region may promote errors in pressure transient analysis. So by adopting the existing mathematical models for naturally fractured reservoirs (dual-porosity system), one can apply the dual-porosity nature of flow in the stimulated reservoir volume (SRV). In this study the analytical solution for single-porosity model is reproduced and compared with numerical solution. Then the five-region model of previous studies is modified by implementing the dual porosity behavior in Laplace domain and compared to single-porosity solution using the same reservoir properties. Furthermore, a series of type-curves is constructed in this study using dimensionless properties, such as matrix-fracture capacity ratio and storativity ratio, hydraulic fracture conductivity, and hydraulic fracture half-length. Theses curves could provide valuable information to characterize the multi-fractured complex systems.

Dynamics and wave dispersion of strongly heterogeneous fluid-saturated porous media

The paper deals with the homogenization approach to the modelling dynamics and wave dispersion of fluid-saturated periodic media. At the mesoscopic scale, the medium is described by the Biot model which is characterized by large contrasts in material properties of two mesoscopic constituents periodically distributed in the two porosities, called the matrix and the channels. By virtue of the homogenization, this contrast is related to the scale parameter which is subject of the asymptotic analysis. In the matrix, the material is much less permeable than in the channels, while the channels are much more compliant than the matrix. We analyze numerically properties of such a material using the homogenized double porosity model developed recently in [1]. The wave dispersion responses obtained using the double porosity model are compared with the analogous responses of a more standard homogenized model without the large contrast assumption (the single porosity model). The double porosity model exhibits much more important dispersion than the single porosity model.

Some remarks on single- and double-porosity modeling of coupled chemo-hydro-mechanical processes in clays

Active clays are known to possess an aggregated structure, which justifies the use of double-porosity models to reproduce their behavior. Simulation of chemo-mechanical processes requires instead the introduction of a relevant number of coupled mechanical and transport laws. It follows that double porosity models for coupled chemo-hydro-mechanical require a relevant number of parameters, which are twice those needed by single porosity models. The aim of this work is to evaluate the consequences of using single- and double-porosity frameworks to simulate the transient chemo-mechanical processes in active clays, showing how models based on simple microstructural considerations can help in performing simulations which are a reasonable trade-off between simplicity and accuracy. In particular with single porosity models, it might be necessary introducing parameters having a doubtful meaning to describe adsorption–desorption processes. This type of assumption is not required by double porosity models. While for compacted clays these conclusions are corroborated with microstructural observations, the same hold also when reproducing the behavior of an active clay at a remolded condition. In this latter case the delay of swelling with respect to desalinization, typical of remolded conditions, was satisfactorily reproduced only with double porosity models.

Mass transport in biological tissues: Comparisons between single- and dual-porosity models in the context of saline-infused Radiofrequency Ablation

Conventional method for modelling mass transport in biological tissues is based on the single-porosity (SP) model, which assumes a homogeneous pressure and concentration in the vasculature. Over the years, the dual-porosity (DP) model, which was originally derived for describing water flow in fractured rocks, has seen an increase in its application to describe flow in biological tissues. In DP models, two porous continua (the interstitium and the vasculature) co-exist within the same space. Flows in both continua are modelled explicitly, which allows for a more accurate representation of the hydraulic interaction between the interstitium and the vasculature. This raises the question on the validity and accuracy of the SP model for describing saline transport in biological tissues. This paper seeks to answer this question by performing a comparative study on the numerical predictions obtained using the SP and DP models in the context of saline-infused radiofrequency ablation (RFA). The results suggest that the SP model has a tendency to underestimate the saline penetration depth inside the tissue. Results from the present study are applicable only in the context of saline-infused radiofrequency ablation. They should not be generalized to other medical and biological applications, as comparison between the SP and DP models for these applications may yield observations that are different from those in the present study.

Simulation of the Impact of Fracturing-Fluid-Induced Formation Damage in Shale Gas Reservoirs

Summary The unconventional gas resources from tight and shale gas reservoirs have received great attention in the past decade and have become the focus of the petroleum industry. Shale gas reservoirs have specific characteristics, such as tight reservoir rock with nanodarcy permeability. Multistage hydraulic fracturing is required for such low-permeability reservoirs to create very complex fracture networks and therefore to connect effectively a huge reservoir volume to the wellbore. During hydraulic fracturing, an enormous amount of water is injected into the formation, where only 25–60% is reproduced during flowback and a long production period. A major concern with hydraulic fracturing is the water-blocking effect in tight formations caused by the high capillary pressure and the presence of water-sensitive clays. High water saturation in the invaded zone near the fracture face may reduce gas relative permeability greatly and may impede gas production. In this paper, we consider the numerical techniques to simulate during hydraulic fracturing the water invasion or formation damage and its impact on the gas production in shale gas reservoirs. Two-phase-flow simulations are considered in a large stimulated reservoir volume (SRV) containing extremely low-permeability tight matrix and multiscale fracture networks including primary hydraulic fractures, induced secondary fractures, and natural fractures. To simulate the water-blocking phenomenon, it is usually required to explicitly discretize the fracture network and use very fine meshes around the fractures. On the one hand, the commonly used single-porosity model is not suitable for this kind of problem, because a large number of gridblocks is required to simulate the fracture network and fracture–matrix interaction. On the other hand, a dual-porosity (DP) model may also be not applicable, because of the long transient duration with large block sizes of ultralow-permeability matrix. In this paper, we study the applicability of the MINC (multiple interacting continuum) method, and use a hybrid approach between matrix and fractures to correctly simulate the fracturing-fluid invasion and its backflow during hydraulic fracturing. This approach allows us to quantify the fracturing water invasion and its formation-damage effect in the whole SRV.

A comprehensive numerical analysis of the hydraulic behavior of a permeable pavement

The increasing frequency of flooding events in urban catchments related to an increase in impervious surfaces highlights the inadequacy of traditional urban drainage systems. Low Impact Development (LID) techniques have proven to be a viable and effective alternative by reducing stormwater runoff and increasing the infiltration and evapotranspiration capacity of urban areas. However, the lack of adequate modeling tools represents a barrier in designing and constructing such systems. This paper investigates the suitability of a mechanistic model, HYDRUS-1D, to correctly describe the hydraulic behavior of permeable pavement installed at the University of Calabria. Two different scenarios of describing the hydraulic behavior of the permeable pavement system were analyzed: the first one uses a single-porosity model for all layers of the permeable pavement; the second one uses a dual-porosity model for the base and sub-base layers. Measured and modeled month-long hydrographs were compared using the Nash-Sutcliffe efficiency (NSE) index. A Global Sensitivity Analysis (GSA) followed by a Monte Carlo filtering highlighted the influence of the wear layer on the hydraulic behavior of the pavement and identified the ranges of parameters generating behavioral solutions. Reduced ranges were then used in the calibration procedure conducted with the metaheuristic Particle swarm optimization (PSO) algorithm for the estimation of hydraulic parameters. The best fit value for the first scenario was NSE=0.43; for the second scenario, it was NSE=0.81, indicating that the dual-porosity approach is more appropriate for describing the variably-saturated flow in the base and sub-base layers. Estimated parameters were validated using an independent, month-long set of measurements, resulting in NSE values of 0.43 and 0.86 for the first and second scenarios, respectively. The improvement in correspondence between measured and modeled hydrographs confirmed the reliability of the combination of GSA and PSO in dealing with highly dimensional optimization problems. Obtained results have demonstrated that PSO, due to its easiness of implementation and effectiveness, can represent a new and viable alternative to traditional optimization algorithms for the inverse estimation of unsaturated hydraulic properties. Finally, the results confirmed the suitability and the accuracy of HYDRUS-1D in correctly describing the hydraulic behavior of permeable pavements.

Modelling of water and gas flow through an excavation damaged zone in the Callovo-Oxfordian argillites in the framework of a single porosity model

Abstract The excavation damaged zone (EDZ) of the Callovo-Oxfordian argillites can be regarded as a double-porosity media consisting of blocks of undisturbed argillites separated by cracks generated by shear or traction stresses. However, owing to hardware limitations, most of the hydraulic-gas simulations undertaken on large scales are based on an equivalent-porous-media model of the EDZ, where the fractures are not explicitly represented. The aim of this study is to improve the equivalent-porous-media model's consistency with the double-porosity flow behaviours shown by experimental data while keeping the same level of simplification. The new model has been developed through a performance assessment (PA)-like approach in two steps: a phenomenological model including explicit fractures has been designed in accordance with the actual geometrical and hydraulic understanding of the EDZ; then, the properties of the simplified model have been calibrated to comply with the hydraulic behaviour of the explicit-fracture model. This methodological approach has been used on an access gallery parallel to the main horizontal stress axis. The new equivalent-porous-media model differs from the previous one on the following three main points: the gallery EDZ has an anisotropic intrinsic permeability that is lower than previously; the same retention law is used as the undisturbed host rock; and there is a higher relative permeability for gas and water than previously.

General Multi-Porosity simulation for fractured reservoir modeling

In the area of fractured reservoir modeling, conventional Dual Porosity Models is challenged to flexibly simulate more than two porosity systems and it is also difficult to capture the transient fluid transfer between matrix and fracture. This work aims to solve those problems in fractured reservoir simulation. The newly introduced Multi-Porosity Model honors any number of porosity types with different properties, such as permeability, porosity and wettability thus achieving significant improvements over conventional Dual-Porosity Models. Arbitrary connections for intra-porosity flow and inter-porosity flow are incorporated into the design to allow for the convenient transformation between Multi-Porosity and Multi-Permeability formulations. The addition of a flexible subdivision in each porosity system has allowed us to characterize the transient flow for inter-porosity flow. Due to the low permeability in the matrix, transient flow between matrix and fracture dominates, and thus matrix spatial subdivision is necessary to accurately capture the dynamics. The formulation is designed to allow the proposed scheme to be generalized. To quantify the improvements available with the new formulation, several typical Multi-Porosity Models are compared with Fine-Grid Single-Porosity Models. Consistent results have been obtained with those similar cases from literature, and the robustness and efficiency of the model is validated. Besides, the extra matrix subdivision is proven to accurately capture the transient fluid transfer between matrix and fracture.

A MIXED-FRACTAL FLOW MODEL FOR STIMULATED FRACTURED VERTICAL WELLS IN TIGHT OIL RESERVOIRS

Stimulated reservoir volume (SRV) with large fracture networks can be generated near hydraulic fractured vertical wells (HFVWs) in tight oil reservoirs. Statistics show that natural microfractures and fracture networks stimulated by SRV were self-similar in statistical sense. Currently, various analytical models have been presented to study pressure behaviors of HFVWs in tight oil reservoirs. However, most of the existing models did not take the distribution and self-similarity of fractures into consideration. To account for stimulated characteristic and self-similarity of fractures in tight oil reservoirs, a mixed-fractal flow model was presented. In this model, there are two distinct regions, stimulated region and unstimulated region. Dual-porosity model and single porosity model were used to model stimulated and unstimulated regions, respectively. Fractal geometry is employed to describe fractal permeability and porosity relationship (FPPR) in tight oil reservoirs. Solutions for the mixed-fractal flow model were derived in the Laplace domain and were validated among range of the reservoir parameters. The pressure transient behavior and production rate derivative were used to analyze flow regimes. The type curves show that the fluid flow in HFVWs can be divided into six main flow periods. Finally, effect of fractal parameters and SRV size on flow periods were also discussed. The results show that the SRV size and fractal parameters of fracture network have great effect on the former periods and fractal parameters of matrix mainly influence the later flow periods.

Ion adsorption and diffusion in smectite: Molecular, pore, and continuum scale views

Clay-rich media have been proposed as engineered barrier materials or host rocks for high level radioactive waste repositories in several countries. Hence, a detailed understanding of adsorption and diffusion in these materials is needed, not only for radioactive contaminants, but also for predominant earth metals, which can affect radionuclide speciation and diffusion. The prediction of adsorption and diffusion in clay-rich media, however, is complicated by the similarity between the width of clay nanopores and the thickness of the electrical double layer (EDL) at charged clay mineral–water interfaces. Because of this similarity, the distinction between ‘bulk liquid’ water and ‘surface’ water (i.e., EDL water) in clayey media can be ambiguous. Hence, the goal of this study was to examine the ability of existing pore scale conceptual models (single porosity models) to link molecular and macroscopic scale data on adsorption and diffusion in compacted smectite. Macroscopic scale measurements of the adsorption and diffusion of calcium, bromide, and tritiated water in Na-montmorillonite were modeled using a multi-component reactive transport approach while testing a variety of conceptual models of pore scale properties (adsorption and diffusion in individual pores). Molecular dynamics (MD) simulations were carried out under conditions similar to those of our macroscopic scale diffusion experiments to help constrain the pore scale models. Our results indicate that single porosity models cannot be simultaneously consistent with our MD simulation results and our macroscopic scale diffusion data. A dual porosity model, which allows for the existence of a significant fraction of bulk liquid water—even at conditions where the average pore width is only a few nanometers—may be required to describe both pore scale and macroscopic scale data.

Evaluation of different soil water potential by field capacity threshold in combination with a triggered irrigation module

Irrigation efficiency improvement requires optimization of its parameters like irrigation scheduling, threshold and amount of water usage. If these parameters are not satisfactorily optimized, negative consequences for the plant-soil system can occur with decreased yield and hence economic viability of the agricultural production. Numerical modelling represents an efficient, i.e. simple and fast method for optimizing and testing different irrigation scenarios. In this study HYDRUS-1D model assuming single- and dual-porosity systems was used to evaluate a triggered irrigation module for irrigation scheduling in maize/soybean cropping trials. Irrigation treatment consisted of two irrigation regimes (A2 = 60-100% field capacity (FC) and A3 = 80-100% FC) and control plot (A1) without irrigation. The model showed a very good fit to the measured data with satisfactory model efficiency values of 0.77, 0.69, and 0.93 (single-porosity model) and 0.84, 0.67, and 0.92 (dual-porosity model) for A1, A2, and A3 plots, respectively. The single-porosity model gave a slightly better fit in the irrigated plots while the dual-porosity model gave better performance in the control plot. This inconsistency between the two approaches is due to the manual irrigation triggering and uncertainty in field data timing collection. Using the triggered irrigation module provided more irrigation events during maize and soybean crop rotation and consequently increased cumulative amounts of irrigated water. However, that increase resulted in more water available in the root zone during high evapotranspiration period. The HYDRUS code can be used to optimize irrigation threshold values further by assuming different scenarios (e.g. different irrigation threshold or scheduling) or a different crop.

A composite model of hydraulic fractured horizontal well with stimulated reservoir volume in tight oil & gas reservoir

Due to the low porosity and permeability, multiple hydraulic fracturing is applied in tight oil & gas reservoir. A composite model of multiple fractured horizontal well is built with considering the stimulated reservoir volume (SRV), where the reservoir is divided into three main areas including fractures, stimulated reservoir volume and unstimulated reservoir. The dimension of fracture is reduced based on the discrete fracture model (DFM) to improve the computational efficiency, the stimulated reservoir volume follows the dual permeability model, and the unstimulated reservoir obeys to the single porosity model. The composite model is solved using the finite element method and verified by the classic analytical solution in dual porosity reservoir. The result shows that there are five main flow regimes for the multi-fractured horizontal well (MFHW) in the composite model including linear flow around the hydraulic fractures, pseudo-steady flow of transition area, inter-porosity flow period, radial flow of unstimulated reservoir and the outer boundary pseudo-steady flow. The bigger the size of SRV is, the later the pseudo-steady flow of transition area arrived, so according to the arrival time of pressure wave to the SRV outer boundary, namely the pseudo-steady flow of transition area appeared, the size of SRV can be determined; and the smaller main hydraulic fracture permeability is, the later the time of pseudo-steady flow of transition area arrived.

Compositional Modelling of the Diffusion Effect on EOR Process in Fractured Shale-Oil Reservoirs by Gasflooding

Gas injection is considered as an effective recovery process that has been widely used in the worldwide oil industry. There are limited pilot field projects conducted on enhanced-oil-recovery (EOR) process by gas injection in shale-oil reservoirs. Although numerous studies have been conducted on gas injection in tight gas or oil reservoirs, the main recovery mechanism in shale-oil reservoirs is not well-understood. Diffusion plays an important role in the oil-recovery process in fractured-shale reservoirs. Most of the current studies on diffusion are performed in such a way that the producing pressure is equal to the initial reservoir pressure or core pressure; thus, the convective displacement is eliminated or minimized. One of the challenges is to evaluate the role of diffusion in field-scale displacements in the presence of viscous flow. This paper discusses the role of diffusion in improving oil recovery in fractured shale-oil reservoirs. Hoteit and Firoozabadi (2009) investigated the diffusion effect on recovery performance in a fractured gas/condensate reservoir. Their simulation results showed that molecular diffusion has a significant effect on gas recovery if the reservoir pressure is below the minimum miscible pressure. Modelling of the diffusion effect on ultimate oil recovery in extensively fractured shale reservoirs is crucial to the development of these marginal shale-oil or -gas projects. Evaluation of the recovery contribution from diffusion will provide important insights into the recovery mechanisms in intensely fractured shale-gas/oil reservoirs. Currently, a majority of the diffusion models were developed on the basis of the single porosity model that demands tremendous grid refinement in intensely fractured shale-oil reservoirs. The grid refinement is necessary for surrounding the fracture intersections, which makes the system become computationally expensive. In this paper, the matrix/matrix and matrix/fracture diffusion is coupled in a dual-permeability model to overcome the drawback of the single-porosity model. The simulation results demonstrate that the EOR by gas injection in the Eagle Ford shale-oil reservoir will benefit from matrix/matrix and matrix/fracture molecular diffusion.

Slug Test in a Large Dip Angle Fracture Zone: Model and Field Experiment

A single-porosity model is developed to deal with a fracture zone slug test in a large dip angle by assuming the fracture zone causes a downward regional flow. For the oscillatory response, a larger dip angle causes larger amplitude while introduces little impact on period. The effective water length, an important parameter necessary for analyzing the oscillatory response, is proven to be independent of the dip angle and can be evaluated using the available horizontal formation methods. The dip angle effect is more pronounced for a larger storage coefficient. An empirical relationship is developed to evaluate the limiting dip angle, below which the dip angle effect is negligible. Field data analysis of a slug test in a 47° dip angle fracture zone indicates that neglecting the dip angle can result in a 27% transmissivity over estimation and a 53% storage coefficient under estimation.