Triple-porosity Model Research Articles

Impact of Inhomogeneous Deformation of Shale Matrix on Gas Depletion Behavior at Field Scale: A Modified Triple-Porosity Model

Impact of Inhomogeneous Deformation of Shale Matrix on Gas Depletion Behavior at Field Scale: A Modified Triple-Porosity Model

Studying the impact of pore sizes on gas flow and distribution in volatile carbonate reservoirs using a new triple-porosity model

Studying the impact of pore sizes on gas flow and distribution in volatile carbonate reservoirs using a new triple-porosity model

Granular activated carbon sound absorption predictions made using measured material parameters

Granular activated carbon (GAC) is hierarchical porosity material that yields better in low frequency sound absorption performance compared with many traditional porous materials due to the sorption effect created by nanometer-scale pores within the particles. In 2017, a triple porosity model accounting for the sorption effect in the micropores was proposed by Venegas et al. In the proposed model, some of input parameters (i.e., mesopore size and micropore effective diffusion coefficient) were fitted by matching the model to measured the surface impedance of a GAC stack; however, some fitted values are questionable from an inorganic material perspective. In the present work, the GAC material parameters, such as micro- and meso-pore sizes, were estimated from a standard isotherm measurement. The measurement results showed a standard Langmuir type isotherm behavior at different temperatures: i.e., 273.15 and 293.15 K. Thus, if the isotherms can be described with the Langmuir model, then the Langmuir constant and heat of adsorption can be estimated based on the isotherms. Finally, these parameters were used as the input to the GAC model and the absorption coefficient was calculated. The calculated result was also compared with the absorption coefficient measured following the E1050 standard.

An approximate analytical model for unconventional reservoir considering variable matrix blocks and simultaneous matrix depletion

In regard to unconventional oil reservoirs, the transient dual-porosity and triple-porosity models have been adopted to describe the fluid flow in the complex fracture network. It has been proven to cause inaccurate production evaluations because of the absence of matrix–macrofracture communication. In addition, most of the existing models are solved analytically based on Laplace transform and numerical inversion. Hence, an approximate analytical solution is derived directly in real-time space considering variable matrix blocks and simultaneous matrix depletion.To simplify the derivation, the simultaneous matrix depletion is divided into two parts: one part feeding the macrofractures and the other part feeding the microfractures. Then, a series of partial differential equations (PDEs) describing the transient flow and boundary conditions are constructed and solved analytically by integration. Finally, a relationship between oil rate and production time in real-time space is obtained.The new model is verified against classical analytical models. When the microfracture system and matrix–macrofracture communication is neglected, the result of the new model agrees with those obtained with the dual-porosity and triple-porosity model, respectively. Certainly, the new model also has an excellent agreement with the numerical model. The model is then applied to two actual tight oil wells completed in western Canada sedimentary basin. After identifying the flow regime, the solution suitably matches the field production data, and the model parameters are determined. Through these output parameters, we can accurately forecast the production and even estimate the petrophysical properties.

Analysis of gas storage and transport in Eagle Ford shale using pressure pulse decay measurements with He, Kr and CO2

Detailed characterization of gas transport and storage in low-permeability and organic-rich shales is associated with an array of challenges due to the complex morphology of the pore space, representing a broad range of pore sizes, combined with the heterogeneous fabric of the shale matrix. These factors, and their interplay during gas transport and sorption, complicate a) the analysis of shale samples at the laboratory scale (∼ up to a ft. In length), and b) the prediction of natural gas production and carbon sequestration potential at larger scales.In this work, tandem experiments with inert (helium – He) and adsorbing (krypton - Kr and carbon dioxide - CO2) gases were performed and analyzed to develop an efficient workflow for characterizing and modeling transport and sorption at the laboratory scale. In particular, pressure pulse-decay (PPD) measurements were conducted on an Eagle Ford shale core sample at room temperature using He, Kr, and CO2. PPD measurements with He (a non-sorbing gas) were employed to probe the overall porosity, including natural fractures, microcracks, mesopores, and micropores. A triple-porosity model (TPM) was adopted to interpret the gas transport in the shale sample: The pore space is represented by three interacting continua, including macropores (larger fractures), mesopores (including microcracks), and micropores. To facilitate the application of the TPM, a modified analytical approach is introduced to extract effective transport parameters (in terms of the characteristic time for transport at relevant porosity levels) directly from the PPD measurements with He. To validate the modeling approach, model parameters extracted from two He PPD measurements are demonstrated to provide excellent agreement with a 3rd He PPD measurement performed at a higher pressure.The effective transport parameters, extracted from the He experiments, were subsequently converted for application to the Kr and CO2 PPD experiments, by accounting for relevant transport modes and differences in fluid properties. Excess adsorption isotherms were extracted from the equilibrium pressures of the Kr and CO2 PPD experiments using the He pore volume as a baseline. These adsorption isotherms were then integrated into the TPM to predict combined gas transport and sorption for Kr and CO2, with transport coefficients translated from the He measurements. The predictions for Kr and CO2 are demonstrated to be in excellent agreement with the experimental observations. This, in turn, demonstrates that the proposed analytical approach provides for an effective characterization of mass transfer rates in shales, that can be applied directly in a TPM representation of mass transfer and sorption.

Investigation of methane mass transfer and sorption in Marcellus shale under variable net-stress

Natural gas in shale exists as free and adsorbed gas, subject to prevailing pore pressures and stress conditions. Accordingly, to accurately estimate/predict the shale gas recovery potential, a central requirement is to represent gas transport and sorption behavior under varying stress conditions. The objective of this work is to facilitate the interpretation of laboratory-scale experiments, at relevant conditions, in an attempt to bridge the gap in scales between laboratory- and field-scale observations.We have conducted a series of high-pressure experiments on a full-diameter core sample from the Marcellus shale. These include gas loading (pressure-decay) and depletion (production) experiments with pure methane (CH4) at variable stress conditions to characterize transport and sorption behavior under reservoir-relevant conditions. We have formulated and applied a novel integral model for mass transfer and storage in multi-porosity shale systems that allows us to effectively investigate transport and sorption phenomena: We delineate gas transport by interpreting helium (He) pressure-decay experiments and demonstrate how to use the information gained to calculate the relevant transport coefficients of CH4 and other gases. A separate measurement of the CH4 sorption isotherm on a smaller sample (a shale cube) was interpreted and combined with the transport description to predict the production behavior of CH4 from the experiments with the full-diameter core.Our experiments demonstrate that the representation of sorption hysteresis is crucial for predicting and guiding shale gas production: At the end of both gas production experiments, approximately 20% of the initial gas in place remained in the core. Without accounting for sorption hysteresis, our modeling demonstrates that the CH4 production could be overestimated by 10%. We demonstrate that our integral, triple-porosity model provides an effective approach for the interpretation and prediction of gas transport and sorption behavior during loading and production experiments on shale cores under variable net-stress conditions.In summary, our work combines measurements and modeling of mass transfer and sorption in shales at different scales to validate a characterization approach that facilitates an improved understanding of shale gas production. Furthermore, the triple-porosity model utilized in our work defines a potential pathway for the translation of laboratory-scale experimentation to larger-scale applications.

P-wave anelasticity in hydrate-bearing sediments based on a triple-porosity model

P-wave anelasticity (attenuation and dispersion) of hydrate-bearing sediments depends on several factors, namely the properties of the mineral components, hydrate content and morphology, and fluid saturation. Anelasticity is analyzed with a triple-porosity model (stiff pores, clay micropores and hydrate micropores), by considering hydrate as an additional solid skeleton. We relate the hydrate volume ratio, porosity and radii of the hydrate inclusion and clay mineral to the P-wave velocity and attenuation. The model takes wave-induced local fluid flow (mesoscopic loss) at the grain contacts into account. The results are compared with those of a double-porosity and load-bearing models, and verified with well-log data from Offshore Drilling Program sites 1247B and 1250F, and data reported in Nankai Trough, Japan. Model results and data show a good agreement.

A new coupled multiphysics model and partitioned time-stepping method for the triple-porosity-Stokes fluid flow model

This paper proposes a new coupled multiphysics model and decoupled finite element method for the realistic naturally fractured reservoir consisting of the triple-porosity medium combined with a free flow region. More specifically, the triple-porosity medium consists of three transmittable, interacting contiguous porous mediums with more-permeable macrofractures, less-permeable microfractures, and stagnant-matrix region, respectively, which is described by the dual-fracture-matrix equations. Moreover, the free fluid flow region is governed by the evolutionary Stokes equation. To couple the triple-porosity medium with the conduit region, five physically valid coupling conditions, are utilized to capture the interfacial phenomena efficiently. The variational formulation and the well-posedness of the model are reported. To lay a solid ground, a fully-implicit algorithm is proposed in a traditional format. On the other hand, based on the idea of partitioned time-stepping, the five interface conditions, and the mass exchange terms in the triple-porosity model, the second algorithm is decoupled into four levels. The decoupling technique allows a non-iterative splitting of the coupled problem into four parallel subproblems. The unconditional stability and optimal convergence analysis are derived for the partitioned time-stepping scheme. For the petroleum engineering applications, we design two numerical experiments and perform parameter sensitivity analysis, which shows the applicability and complicated flow characteristics of the triple-porosity-Stokes interface system.

Triple-Porosity and Dual-Permeability Productivity Prediction Model of CBM Wells Considering Complex Flow Regimes

The productivity evaluation of CBM wells can yield significant insights into exploring the patterns of CBM production, predicting the effectiveness of the CBM well and reservoir stimulation, optimizing the gas reservoir development program, and developing a reasonable production system, for the purpose of facilitating efficient development of CBM. In particular, to accurately evaluate CBM productivity, we should establish the corresponding mathematical model of fluid flow through porous media and productivity evaluation model based on a clear understanding of CBM occurrence states and mechanisms of its flow through porous media. After considering the effects of slip flow, Knudsen diffusion, surface diffusion, stress sensitivity, and matrix shrinkage on fluid mass transfer, we have put forward a triple-porosity and dual-permeability mathematical model to predict CBM productivity that incorporates matrix gas desorption, complex flow in matrix pores, and gas–water two-phase flow in a cleat system. In combination with reservoir characteristic parameters, a case study of Ma-26 well in the Mabidong block in the south of the Qinshui Basin, we carried out a numerical simulation of the productivity of a fractured CBM well and analyzed the effects (on production performance) of occurrence states, cleat system permeability, complex flow regimes in the matrix, Langmuir pressure, and Langmuir volume on production are provided. The results show that 1) in the initial drainage and production stage of CBM wells, both free gas and adsorbed gas are produced simultaneously, while adsorbed gas dominates the production in later stages; 2) the peak output and cumulative output of CBM wells increase significantly with the rise in cleat system permeability; 3) the increase of Langmuir pressure, volume, and matrix porosity are conducive to the increase of CBM production. The research has considerable reference value for work on mechanisms of CBM flow in porous media and post fracturing productivity evaluation of CBM and also provides a theoretical basis for fieldwork in CBM development.

Evaluating cementation factor for bioturbated sandstones, Bhuj Formation, Kachchh Basin, India: a novel approach using triple-porosity model

Cementation factor has a crucial role in evaluating volumetric reserves for heterogeneous clastic reservoir. Bioturbation is a prominent source of heterogeneity existing in hydrocarbon-bearing formation across the world. The effect of bioturbation on the petrophysical properties of the clastic has not been comprehensively understood yet, especially its effect on cementation factor estimation. The precise description of such properties is beneficial in developing better volumetric estimates and optimizing field development planning. The present work discusses an approach to characterize cementation factor in bioturbated clastic Bhuj Formation, Kachchh Basin, India. In order to ascertain the cementation exponent for bioturbated media, an improved triple-porosity model is proposed by quantifying the total porous volume into three components, namely matrix 1, matrix 2 and bioturbated region. An equivalent resistance model is then developed by identifying the series and parallel relation between the two matrix components and the burrow. The experimental observations of electrical response indicated large variation in resistivity in vertical cores compared to horizontal cores. The decreased resistivity is due to the vertically aligned burrow which due to their enhanced porosity provides less tortuous path for current to flow. The triple-porosity model is validated with different porosity value of matrix 1, matrix 2 and burrow, and a cementation factor of 2.8 for higher bioturbated samples and 3 for lower bioturbated samples is obtained. This validates the previous understanding of enhanced flow and storage property and thereby produces a consistent way to evaluate total cementation factor. The correct estimation of cementation factor helps in precise evaluation of water saturation in bioturbated reservoirs.

Improved triple porosity model for calculating porosity exponent of fractured-vuggy reservoirs based on Maxwell-Garnett mixing rule and anisotropic conductivity analysis

Porosity exponent (m) is a key parameter for calculating reservoir oil and gas saturation and evaluating reservoir effectiveness; the development of matrix pores, vug pores, and fractures makes the m response regularity of fractured-vuggy reservoirs unclear, which makes the accurate calculation of saturation difficult. By applying Maxwell-Garnett mixing rule to vuggy reservoirs and conductivity tensor analysis to fractured reservoirs, an improved Triple Porosity Model considering fracture dip angle is established. The newly improved Triple Porosity Model clarifies the response regularity of m to the matrix pores, vug pores, fracture pores, and fracture angles. Based on the improved Triple Porosity Model, the response regularity chart of m is further established. The findings show that: (1) m increases with the increase of fracture dip angle (θ) and the development of vugs; (2) m increases with the development of high-angle fractures and decreases with the development of low-angle fractures; (3) in fractured reservoirs, the fracture dip angle of 33° is the critical dip angle that determines the relationship between m and matrix porosity exponent (mb); (4) an increase in matrix porosity will weaken the influence of vugs, fractures, and fracture dip angle on m, which will eventually make m converge to mb. The field application of fractured-vuggy reservoirs shows that the water saturation calculated by the improved Triple Porosity Model is better in agreement with the core analysis results.

Identification of watered-out zones in carbonate reservoirs using resistivity curve reconstruction based on reservoir classification

The KT–II layer in the Zananor Oilfield, Caspian Basin, Kazakhstan, contains carbonate reservoirs of various types. The complex pore structure of the reservoirs have made it difficult to identify watered-out zones with traditional logging interpretation methods. This study classifies the reservoirs on the basis of core analysis and establishes an identification model for watered-out layers in the field to effectively improve the interpretation accuracy. Thin section analysis shows that there are three types of pores in the reservoirs, i.e., the matrix pore, fracture and dissolution vug. A triple porosity model is used to calculate the porosities of the reservoirs and the results are combined with core analysis to classify the reservoirs into the fractured, matrix pore, fracture-pore as well as composite types. A classification standard is also proposed. There are differences in resistivity logging responses from the reservoirs of different types before and after watering-out. The pre–watering-out resistivities are reconstructed using generalized neural network for different types of reservoirs. The watered-out layers can be effectively identified according to the difference in resistivity curves before and after watering-out. The results show that the watered-out layers identified with the method are consistent with measured data, thus serving as a reference for the evaluation of watered-out layers in the study area.

A novel triple-porosity model for fractured-vuggy reservoirs based on Maxwell-Garnett mixing rule

Under the new energy pattern, the petrophysical properties of carbonate reservoirs are still the research focus in the petroleum industry. Compared with conventional reservoirs, the calculation of water saturation is more complicated for carbonate reservoirs. One of the main challenges is that the accurate calculation of the porosity exponent of the reservoirs is influenced by the development of fractures and vugs. The existing triple-porosity model provides a way to calculate the porosity exponents; however, the existing model still has some problems: (1) The conduction theory adopted to establish the model varies from the actual conductivity process of the reservoir; (2) The model is deduced from the effective medium theory and regional empirical formula without considering the fracture shapes, thus it is not applicable for the carbonate reservoirs with fractures developed. Therefore, this paper proposed a novel triple-porosity model to calculate the porosity exponents by applying the Maxwell-Garnett mixing rule to the fractured-vuggy reservoir. This novel model can calculate the porosity exponents of reservoirs with the joint development of the vugs (non-connected vugs), fractures (fractures and connected vugs), and matrix pores. From the results of the novel model, the more developed the vugs, the greater the porosity exponents, and the more developed the fractures, the smaller the porosity exponent. Therefore, the porosity exponents of the reservoir can reflect the combined influence of the vugs, fractures and matrix pores. In order to effectively calculate the water saturation through this model, a method based on the binary processing of the Full-bore Formation Micro-Imager (FMI) logs was further proposed to calculate the vug porosity and fracture porosity. The field application demonstrated that the novel triple-porosity model can accurately calculate the water saturation of the fractured-vuggy reservoirs and provide guidance to the actual production.

Characterization of shale using Helium and Argon at high pressures

In order to estimate the shale gas in place and the eventual recovery during shale gas operations, one of the key requirements is to accurately characterize the shale's petrophysical and transport properties such as porosity, permeability, diffusivity, and storage capacity. Despite the many efforts reported in the technical literature aiming to provide an improved understanding of the complex pore structures and the associated fluid flow in gas shales, a complete characterization of organic-rich shale samples still poses a big challenge. In this work, we have characterized mass transfer and sorption in shale at different length scales using Helium (He) and Argon (Ar) as probe gases. Thermogravimetric analysis (TGA) with a shale cube of ~1 cm3 in size and gas expansion experiments with a full-diameter core (3.5” in diameter) were used to measure sorption kinetics/isotherms and mass transfer, respectively. Both samples are from the same depth/location in the Marcellus shale formation. The TGA steady-state technique was initially used to generate excess sorption isotherms for Ar, while dynamic TGA experiments were used to study its sorption kinetics. The TGA experiments demonstrate that Ar, which has a similar sorption potential as Methane, but is generally assumed to be inert, adsorbs onto the surfaces of the mesoporous and microporous regions of the shale samples according to a Langmuir-type behavior. Helium expansion experiments, on the full-diameter core, were used to measure the overall porosity, on the basis that He is a non-sorbing and inert gas as compared to Ar. The He expansion experiments, furthermore, allow us to delineate the mass transfer of gas across the inherent hierarchy of pore sizes, including macropores (macro- and micro-cracks), mesopores and micropores. Similar expansion experiments were also performed with Ar to study the combined impact of mass transfer and sorption. A triple-porosity model (TPM) was utilized to interpret the He expansion experiments with the shale core and to extract (estimate) relevant transport parameters. We report and compare here the diffusivities and permeabilities of the whole core for both He and Ar, as calculated from the modeling and fitting of the experimental data. On the premise that the shale cube is representative of the matrix region of the core, the Ar sorption kinetics from the cube experiments were subsequently combined with the transport parameters extracted from the He experiments to predict the behavior of the Ar expansion test with the full-diameter core. An excellent agreement is observed between the model predictions and the experimental data. The experimental observations and their interpretation indicate that one must be cautious when using Ar to estimate the true porosity and permeability of shales. In addition, we demonstrate that He and Ar probe gases, when used in tandem, can be employed effectively as a tool to characterize shales in terms of mass transfer and sorption dynamics across scales.

A transient two-phase flow model for production prediction of tight gas wells with fracturing fluid-induced formation damage

A major concern with hydraulic fracturing in tight formation is the fracturing fluid-induced formation damage (FFIFD) for the high capillary pressure and the presence of water-sensitive clays. Analytical and semi-analytical models are good choices for formation damage evaluation comparing to computationally expensive numerical simulations, particularly in early times when there is limited information about the formation properties. However, the effects of FFIFD and two-phase flow are not addressed in many analytical models. This paper presents a semi-analytical model for this problem with the consideration of both FFIFD and two-phase flow. First, the physical model and mathematical fundamentals of the model are presented. The triple-porosity model is modified to capture the formation damage caused by fracturing fluid. A low permeability fracturing fluid invasion layer (FFIL) is used to characterize leakoff caused clay swelling and polymer adsorption in the matrix pores, and two-phase flow is assumed in the fractures to capture the choking effects. The analytical solution is obtained in the Laplace domain, and a successive iteration is used to update the dynamic parameters by coupling the flowing material balance equations. Then, the commercial numerical simulator Eclipse is used to validate the precision of the semi-analytical model, and several synthetical cases are presented to study the effects of two-phase flow, and the permeability and width of FFIL on gas production rate. Finally, a field case is provided to test the application of the proposed model. The main contribution of this paper is the provision of a simple yet versatile semi-analytical model for production prediction and analysis with the consideration of fracture networks, FFIFD, and two-phase flow. It serves as a good tool for making production prediction and production data analysis for hydraulically fractured tight gas wells.

Quasi-Analytical Model of the Transient Behavior Pressure in an Oil Reservoir Made Up of Three Porous Media Considering the Fractional Time Derivative

The present work proposes a new model to capture high heterogeneity of single phase flow in naturally fractured vuggy reservoirs. The model considers a three porous media reservoir; namely, fractured system, vugular system and matrix; the case of an infinite reservoir is considered in a full-penetrating wellbore. Furthermore, the model relaxes classic hypotheses considering that matrix permeability has a significant impact on the pressure deficit from the wellbore, reaching the triple permeability and triple porosity model wich allows the wellbore to be fed by all the porous media and not exclusively by the fractured system; where it is considered a pseudostable interporous flow. In addition, it is considered the anomalous flow phenomenon from the pressure of each independent porous medium and as a whole, through the temporal fractional derivative of Caputo type; the resulting phenomenon is studied for orders in the fractional derivatives in (0, 2), known as superdiffusive and subdiffusive phenomena. Synthetic results highlight the effect of anomalous flows throughout the entire transient behavior considering a significant permeability in the matrix and it is contrasted with the effect of an almost negligible matrix permeability. The model is solved analytically in the Laplace space, incorporating the Tartaglia–Cardano equations.

A Quadruple-Porosity Model for Consistent Petrophysical Evaluation of Naturally Fractured Vuggy Reservoirs

SummarySeveral dual- and triple-porosity models have been proposed for quantifying the porosity exponent (m) in multiporosity reservoirs. Total porosity (ϕ) is usually portioned into the matrix (ϕb) and vuggy porosity, which includes separate vugs (SVGs) and connected vugs (CVGs). As a result, in their majority, the existing petrophysical models were developed and applied mostly without any distinction between the various types of CVGs despite their specific pore geometries, which critically determine the properties of the rock/fluid systems. For instance, unlike otherwise CVGs, natural fractures (NFs) and microcracks that have low pore-aspect-ratio values are highly compressible; this can cause their closure and lead to increasing m values.In this paper, we proposed a quadruple-porosity model that accounts for NFs (ϕ2 or ϕf) and CVGs (ϕc), in addition to ϕb and SVGs (ϕnc) separately, as distinct input variables to ensure accurate determination of m in composite reservoirs. The approach was based on the volume-model method and rules of electric-resistance networks in porous media. Computed water-saturation values used to validate the model show significant improvement and close agreement with the laboratory measurements, demonstrating the applicability of the proposed model for accurate prediction of m in naturally fractured vuggy reservoirs.New correlations that consider the pore-type diversity were generated using a plot of ϕ vs. m, obtained with the proposed quadruple-porosity model. The procedure involved sorting the ϕ/m scattering points using pore-type mixing and relative abundance of specific porosity. It allowed defining consistent ϕ/m relationships, with determination coefficients of 0.7 to 0.9. This suggests that m varies with the pore-structure types; this was further demonstrated with a rock-frame flexibility factor (γ) used as a proxy to cluster the scattering points. The established correlations can alternatively be applied to reasonably predict m using detailed prior knowledge of pore-type description.

From double to triple porosity modelling of bentonite pellet mixtures

The present work analyses the hydro-mechanical behaviour of bentonite pellet mixtures using a macroscopic overlapping continua approach based on a triple porosity model. Two macrostructural functional levels are considered (inter-pellet pore space and void space between the clay aggregates inside the pellets) as well as a microstructural level (corresponding to the space inside the aggregates). This triple porosity approach reveals that, when assuming a double porosity model, the intrinsic permeability, the tortuosity and the degree of saturation of the single macrostructural level under consideration are the average values of the state functions of the adopted triple porosity model, but are not state functions themselves.The analysis also illustrates that, when assuming the same liquid pressure for the two macrostructural levels of the triple porosity model, it is relatively easy to expand upon the calculation procedures initially developed for a double porosity model to include a triple porosity model.When evaluating the applicability of the model, quality results were obtained, comparable to those of a triple porosity model, for both open and closed bentonite pellet mixtures. The results are better than those obtained with a double porosity model, since the state functions have a stronger physic base when using a triple porosity approach. Encouraging results are also obtained when analysing the overall swelling of a bentonite block and a mixture of bentonite pellets, using the same parameters for both materials. Therefore, given its capacity for relatively simple incorporation in a double porosity models, the model offers an interesting tool for researchers working on improving the characterisation of bentonite pellet mixtures.

A Multi-Scale Modeling of Confined Fluid: from Nanopore to Unconventional Reservoir Simulation

Tight oil and shale gas reservoirs have a significant part of their pore volume occupied by micro (below 2 nm) and mesopores (between 2 and 50 nm). This kind of environment creates strong interaction forces in the confined fluid with pore walls and then changes dramatically the fluid phase behavior. An important work has therefore to be done on thermodynamic modeling of the confined fluid and on developing upscaling methodology of the pore size distribution for large scale reservoir simulations. Firstly, the comparison between molecular simulation results and commonly used modified equation of state (EOS) in the literature highlighted the model of flash with capillary pressure and critical temperature and pressure shift as the best one to model confined fluid behavior. Then, fine grid matrix/fracture simulations have been built and performed for different pore size distributions. The study has shown that the pore size distribution has an important impact on reservoir production and this impact is highly dependent on the volume fraction of nanopores inside the matrix. Afterwards, coarse grid upscaling models have then been performed on the same synthetic case and compared to the reference fine grid results. The commonly used upscaling methodology of dual porosity model with average pore radius for the pore size distribution is unable to match the fine grid results. A new triple porosity model considering fracture, small pores and large pores with their own capillary pressure and EOS, together with MINC (Multiple Interacting Continua) approach, has shown very good agreement with the reference fine grid results. Finally a large scale stimulated reservoir volume with different pore size distribution inside the matrix has been built using the upscaling method developed here.

A new triple-porosity multiscale fractal model for gas transport in fractured shale gas reservoirs

A new triple-porosity model is proposed based on the fractal properties, multiscale flow properties, multiple transport mechanisms and multilayer adsorption/desorption in organic matter pores (OMP), inorganic matter pores (IMP), and fracture network (FN). This model is validated by field gas production data and the key factors affecting gas production are explored. Results show that gas flow is of temporal and spatial multiscale. Shale gas is extracted firstly from hydraulic fractures, then FN and IMP, finally OMP. More adsorbed gases are desorbed and surface diffusion is enhanced when gas pressure decreases. Slip flow is the dominate gas transport mechanism in OMP and IMP. The surface diffusion in OMP and the Knudsen diffusion in IMP are not ignorable contributors to gas production. The OMP contributes 21% of gas production in the later stage. This new triple-porosity model is more accurate than single-porosity and dual-porosity models in gas recovery.