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1 SPE 6365 Beyond Dual-Porosity Modeling for the Simulation of Complex Flow Mechanisms in Shale Reservoirs Bicheng Yan, SPE, Yuhe Wang, SPE, John E. Killough, SPE, Texas A&M University Copyright 3, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Reservoir Simulation Symposium held in The Woodlands, Texas USA, 8 February 3. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 0 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright. Abstract The state of the art of modeling fluid flow in shale reservoirs is dominated by dual porosity models which divide the reservoirs into matrix blocks that significantly contribute to fluid storage and fracture networks which principally control flow capacity. However, recent extensive microscopic studies reveal that there exist massive micro- and nano- pore systems in shale matrices. Because of this, the actual flow mechanisms in shale reservoirs are considerably more complex than can be simulated by the conventional dual porosity models and Darcy s Law. Therefore, a model capturing multiple pore scales and flow can provide a better understanding of complex flow mechanisms occurring in these reservoirs. Through the use of a unique simulator this paper presents a micro-scale multiple-porosity model for fluid flow in shale reservoirs by capturing the dynamics occurring in three separate porosity systems: organic matter (mainly kerogen), inorganic matter, natural fractures. Inorganic and organic portions of shale matrix are treated as sub-blocks with different attributes, such as wettability and pore structures. In the organic matter or kerogen, gas desorption and diffusion are the dominant physics. Since the flow regimes are sensitive to pore size, the effects of nanopores and vugs in kerogen are incorporated into the simulator. The separate inorganic sub-blocks mainly contribute to the ability to better model dynamic water behavior. The multiple porosity model is built upon a unique tool for simulating general multiple porosity systems in which several porosity systems may be tied to each other through arbitrary transfer functions and connectivities. This new model allows us to better understand complex flow mechanisms and in turn is extended into the reservoir scale considering hydraulic fractures through upscaling techniques. Sensitivity studies on the contributions of the different flow mechanisms and kerogen properties give some insight as to their importance. Results also include a comparison of the conventional dual porosity treatment and show that significant differences in fluid distributions and dynamics are obtained with the improved multiple porosity simulation. Finally a case for reservoir-scale model covering organic matter, inorganic matter, natural fractures and hydraulic fractures is presented and will allow operators to better predict ultimate recovery from shale reservoirs. Introduction The development of unconventional resource plays in North America has achieved great success towards satisfy the growing energy demand. The organic shale formations which provide the basis of unconventional oil and gas production continue as an enigma as far as understanding production characteristics are concerned. Because of this many investigators have been inspired to establish suitable models to characterize fluid flow in shale encountering great challenges along the way. Shale is referred to as extraordinarily fine-grained sediments commonly showing fissility (Javadpour, 09). Loucks et al. (2) systematically classified nanometer to micrometer sized pores in the shale matrix into interparticle pores and intraparticle pores associated with mineral particles and organic-matter pores within kerogen. The organic matter has different physical properties from common rock constituents and could significantly affect gas storage and flow in shale. Curtis et al. () found that mostly kerogen is scattered in inorganic minerals, and pores within it are basically round in cross-section interestingly with numerous small pores residing on the interior walls of larger pores. Due to forming during the process of hydrocarbon generation, the pore networks in the organic matter in shale are mainly considered to be oil- or gas-wet (Wang et al., 09; Odusina et al., ). Experiments on Barnett Shale demonstrated that the both adsorbed gas and free gas stored in the shale matrix are linearly increased with TOC content (Jarvie, 04), and Javadpour (09) also theoretically proposed that beside free gas storage in shale, gas could also be adsorbed on the surface of kerogen and dissolved within it. Hill et al. (00)

2 2 SPE 6365 estimated that between and 85 percent of gas in shale might be stored as adsorbed gas. All those features make organic matter in shale unique and lead us to accept the proposal that the porosity systems in organic-rich shale could be separated into four types: inorganic bulk, organic matter, natural fractures, and hydraulic fractures (Wang et al., 09). Meanwhile, due to the extremely low permeability (nanodarcy scale) in the shale matrix, many investigators consider that Darcy flow is quite limited or even breaks down in shale with pore sizes in nanometer scale. For this reason the feasibility of conventional dual porosity/permeability models has been suspected. Instead, the flow mechanisms in tight formations have been re-investigated and many innovative methods have been proposed: the Dual-Mechanism Approach (Darcy flow and Fickian diffusion occur parallel in matrix) was introduced to characterize the gas flow in coal or shale formations through the dynamic gas slippage factor (Ertekin, et al., 986; Clarkson, et al., ); the concept of apparent permeability considering Knudsen diffusion, slippage flow and advection flow was first derived by Javadpour (09), and it was further applied to pore scale modeling for shale gas (Shabro et al., ; Shabro et al., 2); based on a unified Hagen-Poiseuille-type formula (Beskok and Karniadakis, 999), Civan et al () and Ziarani et al (2) proposed a method to calculate apparent permeability through the flow condition function (a function of Knudsen number) and the intrinsic permeability of porous medium. The validity of this latter model for different flow regimes still requires further confirmation. However, even with this greater detail these models may not be sufficient due to the use of an undivided shale matrix. Even with a proper connectivity between different pore systems there still remains little understanding of this aspect (Andrade et al., ). On the other hand, Hudson et al (, 2) did categorize the shale reservoir into organic porosity, inorganic porosity, natural fractures and hydraulic fractures, and explored several different tank models for connections between each pore system. Unfortunately, the modes to characterize the distribution of each continuum and the connections between those continua appear too regular to be realistic for shale reservoirs. Clearly, there remains a strong requirement to accurately model production from unconventional reservoirs based on detailed physics of the process and the interaction among to different porosities such that modeling uncertainty is reduced. Inspired by those predecessors and relying on the wide petrophysical knowledge about shale that is available in the literature, we consider that those conventional dual porosity/permeability models are not sufficient to describe those complex physics and dynamics. This paper establishes a micro-scale model of shale gas with five aspects: ) due to the importance of organic matter in shale, TOC (Total Organic Carbon, wt%) is an indispensable input parameter in the model; 2) the shale matrix bulk is now strictly separated into inorganic matrix and organic matrix, to further emphasize the organic matter in shale matrix, we consider the existence of two types of porosity system distinguished in pore size in kerogen: organic matter with vugs and organic matter with nanopores; 3) a well-designed algorithm which recognizes the random distribution and arbitrary connections between different continua is introduced; 4) complex mechanisms including Darcy flow, Fickian diffusion and desorption are optionally integrated into different continua in the model; 5) finally an upscaling approach to extend to the micro-scale model to a reservoir scale model has been proposed. To evaluate the impact of different mechanisms on the production of shale gas several cases studies are introduced. A comparison of the micro-scale model with the conventional dual porosity model demonstrates the differences between these two approaches. Finally, an example based on the upscaling approach demonstrates the utility of the method to extend simulations to the well and ultimately field scale. Model Description With the advances in experimental conditions, such as SEM, kerogen can be characterized as generally dispersed in inorganic minerals in the micrometer to nanometer scale. The width of natural fracture systems generally is less than 0.05 mm (King, ); therefore, the simulation scale should be limited to micrometers at most if subdivision of shale matrix is required. The validity of the micoscale model work must be well-established before applying any upscaling approaches. Curtis et al (2) stated that in the shale matrix small pores (radii in 3 to 6 nm) predominate in the amount of pores but those larger pores (radii in 0 nm) contribute most of the pore volume as shown in Figure (A) and (B). Moreover, due to the high porosities of up to 50% in kerogen (Passey et al., ) and the larger possible pore sizes in inorganic minerals (Loucks et al., 2), it is necessary to further separate the organic matrix grids into organic grids with vugs (average pore radii in 0 nm) and organic grids with nanopores (average pore radii in 5 nm). We further propose that the organic grids with nanopores could only connect to the organic grids with vugs. Any other porosity systems in shale should communicate with the organic matrix merely through those organic grids with vugs. This follows the observation from petrophysical data that in porous kerogen small pores penetrate the walls of larger pores as shown in Figure 2. Additional evidence indicates that the shale matrices are surrounded by natural fractures as pathways to connect with hydraulic fractures or the wellbore, and fractures are explicitly simulated with fine grids. Therefore, there exist four different continua in the micro-scale model: () Nano: organic matrix grid with nanopores with high porosity; (2) Vug: organic matrix grid with vugs with high porosity as well; (3) Inorg: inorganic matrix grid with very low porosity; (4) Frac: natural fracture grid surrounding shale matrix grids to communicate with induced fractures and the wellbore. A schematic of the mesh system is shown in Figure 3 (in this paper an organic matrix unit in the micro-scale model is composed of one Nano grid surrounded by six Vug grids on its six faces). To properly process the distribution of those

3 SPE different matrix grids, a rigorous Monte Carlo Algorithm is implemented: with the same size for each matrix grid, the number of the organic grids depends on the properties of each medium in the shale matrix and the TOC content of the shale from petrophysical data, shown as Equation (). Through the computed organic grid number, those organic grids (including Vug grids and Nano grids) and inorganic grids are randomly distributed within the shale matrix bulk. A shale matrix mesh map workable for simulation is shown in Figure 6. 0 %.. Among the four different continua listed above, gas adsorption is assumed to only occur in organic grids (kerogen), and any pressure drop within the kerogen could induce gas molecules desorbed from the kergen surface; therefore, the desorption process could actually increase the gas accumulation within the organic grids in this model. This phenomenon is taken into account in the simulator used in this work through terms of Langmuir isothermal function as Equation (2) (Cui, 09; Civan, et al., ; Shabro, et al., ; Freeman, et al., 2):. 2 _ Because Nano grids can only connect to Vug grids as previously assumed, there are likely to be seven different connections in total, shown as following, () Vug Vug ; (2) Vug Nano ; (3) Vug Inorg ; (4) Vug Frac ; (5) Inorg Inorg ; (6) Inorg Frac ; (7) Frac Frac. In those different connections, diffusion and Darcy flow could be conditionally considered based on the actual flow mechanisms. In kerogen there are many nanopores with small sizes very close to the size of methane molecule, and some investigators applied Knudsen number to define the flow regimes and concluded that under such circumstances conventional Darcy s law has been problematic (Javadpour et al., 07). For that reason we assume that free gas or desorbed gas flows across the connection between organic matter with nanopores and organic matter with vugs only through Fickian diffusion, and both Fickian diffusion and Darcy flow coexist in the connections between organic grids with vug; however, there is only Darcy flow in any other connections elsewhere. From these assumptions it follows that a general formula of the mass balance equation for a single phase single component isothermal system can be written as follows,. 3 The first term in Equation (3) refers to the flux due to only Fickian diffusion, only Darcy flow or both mechanisms acting in parallel (Ertekin, et al., 986). The right hand side represents the accumulation of compressed gas in all of the grids as well as the accumulation of desorbed gas in organic grid blocks. In our simulator, Equation (3) is solved by a fully implicit iterative algorithm. Real gas properties are computed as a function of pressure under isothermal conditions through the Peng-Robinson equation of state in the model. There are natural fracture grids surrounding those matrix grids and set as a constant pressure boundary for the whole system. Therefore, gas in the shale matrix will spontaneously flow into the natural fracture system until the average pressure in the matrix decreases to the same level of that in natural fracture system. Because the fracture grids are explicitly described in this model, the fracture permeability is related to fracture aperture as cubic law (Pruess, 982; Hoteit et al., 06),.. 4 Sensitivity Analysis The dimensions of the micro-scale system are 482 µm 482 µm 92 µm divided into 50 grids 50 grids grids, in total 27,500 grids. Generally, the length of each matrix cub is µm and the fracture aperture is µm. The TOC value is typically 2.50%, and other media properties are presented in Table below. Note that the mesh data, TOC content and data in Table are used in the following parts of this section as the default if not specified. Based on Equation () the organic grid number is 5243 (the ratio of the Vug grid number to the Nano grid number is constantly 6:). Because the gas mass within such a fine scale model is in the magnitude of - kg, the drainage process is very short and at the later period of the drainage process the gas in place is an important constraint on gas drainage rate. Therefore, to better compare the significance of difference mechanisms on gas flow, a parameter analogous to Productivity Index is defined here, which is now called as Gas Drainage Capacity into the Fracture System,... 5

4 4 SPE 6365 Table Description of medium properties for the micro-scale modeling Medium Type Frac Inorg Vug Nano Media Density(g/cc) Media Porosity(fraction) Media Permeability(mD) Media Pressure (MPa) Media Temperature(K) Note the density of inorganic bulk and organic matter in shale is estimated from Sigal. Effect of Desorption: To evaluate the effect of the gas desorption in kerogen on gas flow in shale, diffusion coefficients are temporarily set to zero causing Darcy flow to be the only flow mechanism. The Langmuir pressure for both Vug and Nano grids are taken as 500 psi (Hudson et al., 2), and with different Langmuir volume of methane in kerogen the adsorption isotherm curve can be changed significantly causing the corresponding Adsorbed Gas Weight Percentage (hereafter referred to as AGWP ) to vary. To reasonably analyze the effect of desorption, the AGWP value should be controlled within a realistic range. All parameters in Table are applied here and Table 2 lists the Langmuir adsorption parameter of different organic grids for five different cases. Table 2 Adsorption parameters for each case to evaluate desorption in shale (no diffusion) Case NO. in Vug in Vug in Nano in Nano AGWP (scf/ton) (psi) (scf/ton) (psi) (%) Figure 4 compares the cumulative gas rate curves for the five cases. We could see that at the early period of the gas drainage process there is little difference among those cases because free gas in the porosity initially mainly supports the gas drainage, however, at the later period of time the effect of desorption in kerogen becomes significant so that the cumulative gas rate could increase with increasing AGWP. Using Case without desorption as a base case, the increase of the ultimate cumulative gas rate into the natural fracture system for Case 2 to Case 5 could be.3%, 3.47%, 6.62% and 9.77% respectively. Figure 5 exhibits the change of average pressure in the matrix bulk with time. The effect of desorption helps to maintain the pressure within the matrix bulk but not substantially. It is worth noting that since in this model it is assumed that there is no Darcy flow within the Organic Nano grids and with here diffusion nullified as well, the average pressure will not decline to the level in the fracture grids during the period simulated. Figure 6 compares the curves of gas drainage capacity (defined in Equation 5) with time in a semi-log plot for the five cases, and through calculation we find that during the range of 0 to seconds, on average 90% of total producible gas is drained into fracture system. Desorption only improves gas drainage capacity maximally about 6.7% (in Case 5: AGWP = 27.2%). Therefore, desorption increases gas drainage capacity during the later times but its influence is not considerable; the main contribution of desorption to gas flow in shale is that it increases the cumulative gas rate from shale after pressure starts depletion. This is caused by the adsorption model applied here and the way it affects the gas flow in shale. As part of accumulation term and with the same unit as gas density, in Equation (2) and (3) should be evaluated in a time or pressure scale similar to gas density, which is, _ _... 6 Equation (6) implies that as pressure decreases with producing time, the effect of desorption on gas accumulation in kerogen increases significantly with given properties in the system and pressure drop. Effect of Diffusion: To better evaluate the effect of diffusion, the Langmuir adsorption parameters are now set to zero so that only free gas resides in shale matrix. The mesh system and the parameters listed in Table are still used here. According to Hoteit et al. (06), the diffusion coefficient in gas phase is in the range of m 2 /sec, so the gas diffusion coefficients of organic grids are here set in the range of -8 to -4 m 2 /sec to conduct the sensitivity analysis. In a fashion similar to the analysis of desorption process, if the diffusion coefficient in the Nano grids is zero, gas within those grids cannot be drained out and the average pressure in the matrix cannot reach the pressure in the fracture system outside. Table 3 enumerates the diffusion coefficients in organic grids for five cases. Note that diffusion is hypothesized to only occur in kerogen. Table 3 Diffusion coefficients for each case to evaluate diffusion in kerogen (no desorption)

5 SPE Case NO. Dv (Diffusion Coefficient in Vug ) Dn (Diffusion Coefficient in Nano ) (m 2 /sec) (m 2 /sec) Figure 7 shows the relationship of cumulative gas rate into the fracture system with time. The comparison shows that there is little difference in the ultimate cumulative gas rate for those cases considering diffusion. The greater the diffusion coefficients the faster the cumulative rate curves reach the peak level. As previously claimed, without considering diffusion the gas stored in Nano grids can never be produced. Comparing to the ultimate cumulative rate of Case 7 to, there is a significant decrease of about 5% on average of that in Case 6 (base case) which neglects diffusion in kerogen. In Figure 8, the above observations could be further confirmed: diffusion could accelerate the pressure drop within the matrix bulk, and Case 6 consequentially maintains a little higher average pressure because of more gas left in those Nano grids. Finally, in Figure 9 we could conclude that diffusion could greatly increase the gas drainage capacity into fracture system, especially at the later time of production or at a lower average pressure in shale matrix. Comparison with Dual Porosity Model: With the same mesh system as above, a Dual Porosity Model with homogeneous matrix grids is established to compare with the Micro-Scale Model considering diffusion and desorption, and still keep the initial pressure in matrix bulk at 7.2 MPa, pressure in fracture system constant at 8.6 MPa and temperature in the system constant at Kelvin. Table 4 to 6 lists the parameters related to each medium in each case. Figure shows the cumulative gas rate flowing into natural fracture system for each case. With the same gas in place, the Micro-Scale Model only considering diffusion could reach the cumulative rate plateau much earlier than Dual Porosity Model, and the ultimate gas recovery is almost the same. The Micro-Scale Model considering both diffusion and desorption could have on average 2.0% more ultimate cumulative gas rate than those of another two cases. The deviations of these three curves also indicate that Darcy flow, diffusion and desorption occur sequentially in our model. In Figure, the two Micro- Scale Models cost almost half of the time to decrease the average pressure in the matrix bulk to the pressure in fracture system comparing to the conventional Dual Porosity Model, and the desorption in kerogen could to some extent maintain the pressure in the matrix bulk. Figure 2 exhibits the curves of gas drainage capacity changing with time for the three models, and it is very clear that through diffusion the Micro-Scale Model could maintain a much greater gas drainage capacity than the Dual Porosity Model, and desorption actually has little or even no effect to increase this parameter. Table 4 Parameters for Dual Porosity Model (AGWP: 0.00%) Medium Type Natural Fracture Shale Matrix Media Density(g/cc) Media Porosity(fraction) % (keeping the same pore volume) Media Permeability(mD) Media Diffusivity (m 2 /sec) Table 5 Parameters for the Micro-Scale Model considering diffusion (AGWP: 0.00%) Medium Type Frac Inorg Vug Nano Media Density(g/cc) Media Porosity(fraction) %.0% 25.0% Media Permeability(mD) Media Diffusivity (m 2 /sec) Table 6 Parameters for the Micro-Scale Model considering diffusion and desorption (AGWP: 8.36%) Medium Type Frac Inorg Vug Nano Media Density(g/cc) Media Porosity(fraction) %.0% 25.0% Media Permeability(mD) Media Diffusivity (m 2 /sec) Langmuir Volume(scf/ton) Langmuir Pressure(psi) Effect of Organic Grids (Kerogen) Distribution in Shale Matrix: To obtain an obvious effect of random distribution for

6 6 SPE 6365 organic grids, here TOC content in shale matrix is set constant at 7.0% (constant number of organic grids). However, the dimensions of the system are still 482 µm 482 µm 92 µm divided into 50 grids 50 grids grids, with fracture aperture µm and matrix cub length µm; in the system the temperature is constant at Kelvin, the initial pressure in the matrix bulk is 7.2 MPa and the pressure in natural fracture system maintains at 8.6 MPa. Other parameters related to each medium are from Table 6, but because of the lower TOC content here, the AGWP is now decreased to about 5.8%. Five mesh systems (Case to 5) with different kerogen random distribution (different random seed for each case) are generated and coupled into the simulator. Figure 3 to 5 respectively show the cumulative gas rates into the natural fracture system, the average pressure in the matrix bulk and the gas drainage capacity for the five cases, we could observe that those five series of curves is completely overlapped, besides, through calculation the maximum differences between the five cases for the three different plots are respectively 0.9%, % and 0.3%, which could be almost neglected in engineering. Therefore, it is concluded that the random distribution modes of kerogen with a given TOC value cannot impact the global gas flow behavior in shale. Figure 6 is a sample matrix grids map in each layer for Case. The organic grids (white grids) are randomly distributed within the inorganic grids (black grids), and in space it is like a cluster of kerogen evenly distributed within the inorganic minerals. Moreover, a pressure map for the matrix bulk corresponding to this mesh map is shown in Figure 7. Through comparison of the two maps, we could find that the pressure map could perfectly match with the distribution of organic grids, and in the pressure maps of 4, 5 and 6 layer matrices, which are actually the inner part of the matrix bulk in a 3-D view, the pressure within organic grids (shallow red) are on average lower than that of inorganic grids (dark red) because of the well developed and connected kerogen system compared to inorganic minerals nearby. However, in pressure maps of other layer matrices which are the outer part the shale matrix, the pressure in organic grids is much higher than that in inorganic grids, and here we consider that it is partly because of the desorption effect in kerogen and partly because of the poor connectivity of kerogen at the tail end of the kerogen cluster compared to that of the inner organic grids. Effect of TOC Content in Shale Matrix: Here we use typical TOC values 3.00% (Case 6), 6.00% (Case 7) and 2.00% (Case 8) to show the difference of simulation results. Still we keep the dimensions the system 482 µm 482 µm 92 µm divided into 50 grids 50 grids grids, with fracture aperture µm and matrix cub length µm; in the system the temperature is constant at Kelvin, the initial pressure in the matrix bulk is 7.2 MPa and the pressure in natural fracture system maintains at 8.6 MPa. Besides, the parameters in Table 6 for each medium are still applied. Under the initial condition in the system, the AGWP in shale matrix are respectively.09%, 5.00% and 8.2% for the three cases with an increase trend in TOC content. Figure 8 to show those curves of the cumulative gas rate, average pressure within the matrix bulk and gas drainage capacity into the fracture system versus time for Case 6 to 8. From those curves, we could observe that higher TOC content in shale matrix will lead to greater ultimate cumulative gas production, lower speed to decrease the average pressure in matrix bulk and significantly higher gas drainage capacity. Kerogen has considerable gas adsorption capacity and much higher porosity than that of inorganic minerals. In consequence, an increase in TOC could directly bring more gas in place to sustain higher gas drainage rate. Case 7 (6.00% TOC) and Case 8 (2% TOC) could respectively ultimately release.4 and 2. times more gas into the fracture system than Case 6 (3.00% TOC). Meanwhile, because of greater gas in place for cases with higher TOC content, to keep mass conservative the average pressure in matrix bulk stay a little higher (Figure 9). Moreover, diffusion could only occur in organic matrix and thus an increase in TOC value will magnify the gas drainage capacity due to the significantly increasing effect of diffusion in kerogen, which is exhibited in Figure. Apparent Permeability The comprehensive work above is still limited in micro-scale simulation for qualitative analysis. It could not be used for reservoir scale simulation unless it is upscaled. Besides, our observation so far is within the range of a matrix bulk subdivided by tens of thousands of gridblocks surrounded by natural fracture grids outside, therefore, it is a transient behavior we could observe. To make the work friendly to commercial simulators, we calculate the apparent permeability (, shown in Equation 7) for the system similar to Darcian permeability, which is now approximated as an average behavior within the matrix bulk (pseudo steady state) considering the different mechanisms coupled in the model above,.. 7 In this part, TOC content in shale matrix is set constant as.0%. The dimensions of the model are divided into 32 grids 32 grids 32 grids, with 5268 organic grids and 32,678 grids in total. Organic grids are randomly distributed within matrix and fracture grids are encircling the matrix cubic bulk. Fracture aperture is constantly set as µm, but the size of matrix grid is varied from µm to m. Initial pressure in matrix is set as 7.2 MPa, and pressure in natural fracture is 8.6 MPa, with temperature Kelvin everywhere in the system. Medium properties are from Table 6, but diffusion coefficients or

7 SPE Langmuir Parameters are respectively nullified to analyze the effect of diffusion, desorption and Darcy flow on apparent permeability in Equation (7). Three series of cases with different matrix size are simulated through the micro-scale model, and the results are plotted in Figure 2 and Figure 22. In Figure 2, at the early period of pressure drop, the apparent permeability of those different cases are almost overlapped because of the domination of Darcy flow in the system; gradually those cases considering diffusion would maintain a much higher than the cases neglecting diffusion which finally decline to the level of the intrinsic permeability (50 nanodarcies) within the Vug or Inorg grids. On the other hand, desorption could not affect the apparent permeability at all because there is no difference between cases considering desorption and diffusion and cases considering diffusion. Besides, it is obvious that matrix size could not change the apparent permeability in any cases plotted, which sets a solid foundation to extend the previous micro-scale model to a reservoir model later. In Figure 22, the apparent permeability ratio of cases considering diffusion (and desorption) to cases only considering Darcy flow increases with the average pressure in the matrix cub bulk decreasing, and it is comparable to the results of the tube model considering Knudsen diffusion, advection and slip flow from Javadpour (09). Meanwhile, it further demonstrates that desorption has neglectable effect on the apparent permeability through the comparison of the two cases in Figure 22. To exclude the likelihood that the apparent permeability is dominated by the fixed natural fracture permeability above, here the effect of fracture permeability on the apparent permeability is analyzed. Based on the smallest model (matrix grid size: µm and fracture grid size: µm) when evaluating the apparent permeability considering diffusion, Darcy flow and desorption just now, here the fracture permeability is changed from md to 8.44 D with any parameters else in the system the same. The result of the apparent permeability is shown in Figure 23. As shown in the figure, with five fracture permeabilities in significantly different magnitudes, the curves for apparent permeabilities versus pressure have no difference and are overlapped together. Therefore, the permeability from Equation (7) is virtually the average permeability for the total matrix bulk including inorganic and organic grids and it does account the shape factor effect for matrix because the matrix size cannot change it at all. Upscaling with a Triple-Permeability Simulation For the results of the above modeling effort to be useful, the dynamic apparent permeability is further upscaled to a realistic single well model in a commercial simulator (Coats, et al., 03) with multiple fractures are shown in Figure 24. As shown in the figure, the well is approximately 5000 feet long with five hydraulic fractures distributed each 00 feet along the well s length. The width of the simulation model is 00 feet with a constant reservoir thickness of 500 feet. The first level grid is a three-dimensional system with blocks in the x-direction, 60 blocks in the y-direction, and blocks in the z-direction for a total of 8,000 cells. Local grid refinement is further utilized to better capture the hydraulic fractures by reducing the grid in the y-direction to approximately 5 feet at the fracture locations as shown in Figure 25. Three separate porosity systems are simulated here fracture including hydraulic and natural fractures, organic matrix (kerogen), and finally inorganic matrix. Since the hydraulic fractures and the natural fractures exist at separate grid locations, a single porosity type is used for those fractures. Static permeabilities in the matrix are varied over a range of 50 to 2500 nanodarcies as described below. To capture the dynamic permeability effect of Figure 2, pressure-dependent modifications are made to a case which causes the apparent matrix permeability to vary with average matrix block pressures similar to that shown in Figure 2. Desorption in kerogen is treated using the technique of Seidle and Arri (CIM/SPE 90-8, 990). Parameters for the desorption are the same as those discussed above to yield an AGWP about %. The well is simulated with a maximum rate of MMSCF/d and a minimum bottomhole pressure of 247 psia (8.6MPa). Initial reservoir properties are 5% water saturation and an initial reservoir pressure of 2495 psia (7.2MPa). Gas properties are derived from correlations for a dry gas. The porosity of the natural fractures is limited to the refined grid area of the stimulated reservoir volume as shown in Figure 24. Similarly the hydraulic fracture is confined to a single set of grid blocks extending from the well with a fracture half-length of feet. Hydraulic fracture permeability and porosity are set to 500md and 0.9 respectively while for the natural fractures values of,000 nanodarcies and 0.02 are used for the permeability and porosity. Simulations are performed with a triple permeability model in which all fractures, inorganic, and organic porosity systems are allowed to flow among themselves and between different porosity types. This is different from a MINC or multiple-porosity model in which only the fluids in the fractures are allowed to flow in the fracture network. The well is produced for years with the results shown in Figures Figure 26 shows the results of three different simulations. The black line represents the case in which the apparent permeability of the matrix is dynamically modified with average matrix block pressure as described above. The green line represents the case for a static apparent permeability of 500 nanodarcies (lower limit) and the red line represents the static case for 2500 nanodarcies (upper limit). The results in Figure 26 indicate that, as expected, the dynamic permeability case falls between the maximum and minimum static permeability cases. The dynamic results are closer to the minimum static case due to the rapid falloff in the apparent permeability with average matrix pressure as shown in Figure 2 from the micro-scale model.

8 8 SPE 6365 Figure 27 shows the additional results of a low permeability (50 nanodarcies, intrinsic permeability in shale matrix), nondiffusive case. Also presented is a triple porosity case with dynamic apparent permeability in which only the fracture fluids are allowed to flow among other fractures. The blue line for the 50nd matrix permeability is slightly higher than the triple porosity (not permeability) results shown in pink. This indicates that even without diffusive flow, intra-matrix flow has some contribution to the production. The results for the triple porosity case in Figure 27 show much lower gas production when compared to the triple permeability cases indicating that intra-matrix flow is an important part of the mechanism that must be captured when diffusion in organic matter is considered in the transport process. The results of Figure 27 tend to indicate that given certain characteristics of the shale matrix, it might be possible to simulate the gas production process simply by using a static permeability intermediate to the maximum and minimum static values. Unfortunately, this does not appear to be the case as shown in Figure 28 in which a single static value cannot model the entire time period of the simulation. Simulation times to achieve these results were moderate taking only a few minutes of CPU time per year simulation. Conclusions This research proposes a micro-scale model with natural fractures and shale matrix subdivided into three random distributed continua and considering Darcy flow, Fickian diffusion and desorption in kerogen. With a considerable adsorbed gas weight percentage in shale matrix, gas desorption from kerogen could provide more gas in place and sustain a much greater cumulative gas rate and slightly higher average matrix pressure, however, it could little improve the gas drainage capacity (similar to productivity index) and not influence the apparent permeability defined in this paper. Diffusion cannot be neglected and is crucial to produce gas in those nanopores in kerogen, and it is fairly effective to enhance the gas drainage capacity and the apparent permeability as well. Darcy flow, diffusion and desorption occur sequentially in our model and the latter two mechanisms are strengthened at the later time or lower average pressure in the matrix bulk because Darcy flow and free gas release dominate the early period. The difference of the Micro-Scale Model and conventional Dual Porosity Model with the same pore volume is significant: the former takes into diffusion and desorption so that the system should be more producible and the pressure drop should be much faster. With a constant TOC content in shale, different random even distribution of kerogen could have actually neglectable difference in the global gas flow behavior from shale matrix bulk to the natural fractures. The pressure map within the matrix bulk could be perfectly matched with matrix grids distribution. Besides, higher TOC content in shale could effectively increase gas in place due to more adsorbed gas and free gas and also magnify the role of diffusion in kerogen. The relationship of apparent permeability with pressure is independent of the matrix size and the fracture permeability, which implies the apparent permeability is an average property for the matrix bulk, and thus provides reliable base for upscaling the micro-scale model. The ratio of apparent permeability considering diffusion, Darcy flow and desorption to apparent permeability only considering Darcy flow increases with the decrease of average pressure in matrix bulk. Upscaling to the well scale with multiple fractures shows results which indicate that a triple permeability model allowing intra-matrix flow is required to adequately simulate the gas recovery observed in the micro-scale models and a dynamic apparent permeability in matrix should be indispensable. Recommendations The mesh scheme in the micro-model for this paper is still limited since an upper limit for the TOC content exists, but it is sufficiently persuasive for the usage in a realistic TOC range and in this paper. Furthermore, multiphase flow simulation and refinement of the upscaling workflow for well and field scale simulation should be the focus of the next step in this project. Acknowledgements The authors wish to thank The Crisman Institute at Texas A&M University for funding this project.

9 SPE Nomenclature AGWP = Adsorbed Gas Weight Percentage, wt%; = total contact area between the matrix bulk and the fracture system, m 2 ; = gas compressibility, /Pa; D = diffusion coefficient, m 2 /second; = nodal distance between the matrix bulk and the fracture system, m; Frac = natural fracture grid; = the gravitational acceleration vector, m 2 /s; Inorg = inorganic matrix grid; = media permeability, m 2 ; = apparent permeability within matrix, m 2 or nanodarcy; = fracture permeability, m 2 ; = gas molar weight, g/mol; = number of matrix grids, number; Nano = organic grid with nanopores; = pressure, Pa; = constant pressure in fracture system, Pa; = Langmuir pressure, Pa; = average pressure within the matrix bulk (inorganic grids and organic grids in total), Pa; = the mass of gas adsorbed on unit volume of media, kg/m 3 ; = total rate flowing from matrix system into fracture system, kg/s; = pore radii of porous media, m; = temperature, Kelvin; = Total Organic Carbon, wt%; = time, seconds; = medium bulk volume, m 3 ; = Langmuir volume, m 3 /kg; = the molar volume of gas at standard temperature and pressure (273.5 K and.325 Pa); Vug = organic grid with vugs; = distance in the gravitational direction, m; = real gas deviation factor; = fracture aperture, m; = density, kg/m 3 ; = gas density at reservoir conditions, kg/m 3 ; _ = gas density at standard temperature and pressure (273.5 K and.325 Pa), kg/m 3 ; = average gas density in the micro model (fracture and matrix), kg/m 3 ; = the skeleton density of the porous media, kg/m 3 ; = gas viscosity, Pa s; = average gas viscosity in the micro model (fracture and matrix), Pa S; = the porosity of the porous media, fraction; References Andrade, J., Civan, F., Devegowda, D., Sigal, R. F.. Design and examination of requirements for a rigorous shale-gas reservoir simulator compared to current shale gas simulators. SPE 4440, paper presented at the SPE North American Unconventional Gas Conference and Exhibition held in the Woodlands, Texas, June 4-6. Beskok, A., Karniadakis, G. E A model for flows in channels, pipes, and ducts at micro and nano scales. Microscale Thermophys Eng. 3(), 43-77(999). Civan, F.. Effective correlation of apparent gas permeability in tight porous media, Transport in Porous Media, Vol.82: Civan, F., Rai, C. S., Sondergeld, C. H.. Shale-gas permeability and diffusivity inferred by improved formulation of relevant retention and transport mechanisms, Transport in Porous Media, Vol. 86(3): Clarkson, C. R., Ertekin, T.. A new model for shale gas matrix flow using the dynamic-slippage concept. AAPG

10 SPE 6365 Hedberg Conference, Austin, Texas, December 5-. Cui, X., Bustin, A.M., Bustin, R., 09. Measurement of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications. Geofluids 9, (09). Coats, B. K., et al, 03. A Generalized Wellbore and Surface Facility Model Fully Coupled to a Reservoir Simulator, SPE presented at the SPE Reservoir Simulation Symposium, February 3-5, 03, Houston, Texas. Curtis, M.E., Ambrose, R. J., Sondergeld, C. H., Rai, C. S.. Structural characterization of gas shales on the micro- and nano-scales. SPE-37693, paper presented at the Canadia Unconventional Resources & International Petroleum Conference held in Calgary, Alberta, Canada, SPE, October 9-2. Curtis, M. E., Sondergeld C. H., Ambrose, R. J., Rai, C. S. 2. Microstructural investigation of gas shales in two and three dimensions using nanometer-scale resolution imaging, AAPG Bulletin, 96, p Ertekin, T., King, G. R., Schwerer, F. C Dynamic gas slippage: a unique dual-mechanism approach to the flow of gas in tight formations. SPE Formation Evaluation, (): Paper SPE 45-PA doi:.28/45-pa. Freeman, C. M., Moridis, G. J., Michael, G. E., Blasingame, T. A. 2. Measurement, modeling, and diagnostics of flowing gas composition changes in shale gas wells. SPE-5339, paper presented at the SPE Latin American and Caribbean Petroleum Engineering Conference held in Mexico City, Mexico, SPE, April 6-8. King G. E.. Thirty years of gas shale fracturing: what have we learned? SPE 33456, paper presented at the SPE Annual Technical Conference and Exhitions held in Florence, Italy, September Hill D. G., Nelson, C. R. 00. Gas productive fractured shales: an overview and update. Gas TIPS 6(3): 4-3. Hoteit, H., Firoozabadi, A. 06. Numerical modeling of diffusion in fractured media for gas injection and recycling schemes. SPE-3292, paper presented at the SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, SPE, September Hudson, J., Civan, F., Michel, V. G., Devegowda, D., Sigal, R. 2. Modeling multiple-porosity transport in gas-bearing shale formations. SPE-53535, paper presented at the SPE Latin American and Caribbean Petroleum Engineering Conference held in Mexico City, Mexico, SPE, April 6-8. Hudson, J.. Quad-porosity model for description of gas transport in shale-gas reservoirs. Master s thesis, Oklahoma U., Norman, Oklahoma,. Javadpour, F., Fisher, D., and Unworth, M. 07. Nanoscale gas flow in shale sediments. J. of Canadian Petroleum Tech., 46(), Javadpour, F. Nanopores and apparent permeability of gas flow in mudrocks (shales and siltstone). 09. J. of Canadian Petroleum Tech., v. 48, pp 6-2. Jarvie, D. 04. Evaluation of hydrocarbon generation and storage in Barnett Shale, Fort Worth Basin, Texas: The University of Texas at Austin, Bureau of Economic Geology/PTTC, 6p. Loucks, R.G., Reed R. M., Ruppel S. C., Hammes, U. 2. Spectrum of pore types and networks in mudrocks and a descriptive classification for matrix-relatedd mudrocks pores, AAPG Bulletin, 96, p Odusina, E., Sondergeld, C. H., Rai, C. S.. An NMR study on shale wettability. SPE-4737, paper presented at the Canadia Unconventional Resources & International Petroleum Conference held in Calgary, Alberta, Canada, SPE, November 5-7. Passey, Q.R., Bohacs, K.M., Esch, W.L., Klimentidis, R., and Sinha, S.. From the oil-prone source rock to gasproducting shale reservoir-geological and petrophysical characterization of unconventional shale gas reservoirs. SPE-3350, paper presented at the International Oil and Gas Conference and Exhibition held in Beijing, China, SPE, June 8-. Pruess, K GMINC Amesh generator for flow simulations in fractured reservoirs, Lawrence Berkeley Laboratory Report LBL-5227, Berkeley, CA.

11 SPE 6365 Seidle, J. P., and Arri, L. E., Use of Conventional Reservoir Simulation Models for Coalbed Methane Simulation, SPE/CIM 90-8, presented at the CIM International Technical Meeting, Calgary, June -3, 990. Shabro, V., Torres-Verdin, C., and Javadpour, F.. Numerical simulation of shale-gas production: from pore-scale modeling of slip-flow, Knudsen diffusion, and Langmuir desorption to reservoir modeling of compressible fluid. SPE 44355, paper presented at the North American Unconventional Gas Conference and Exhibition in the Woodlands, Texas, USA, 4-6 June. Shabro, V., Torres-Verdin, C., and Sepehrnoori, K. 2. Forecasting gas production in organic shale with the combined numerical simulation of gas diffusion in kerogen, Langmuir desorption from kerogen surfaces, and advection in nanopores. SPE-59259, paper presented at the Annual Technical Conference and Exhibition held in San Antonio, Texas, USA, October 8-. Sigal, R. F. A note on the intrisince porosity of organic material in shale gas reservoir rocks. Swami V., Settari, A. T. 2. A pore scale gas flow model for shale gas reservoir. SPE-55756, paper presented at the Americas Unconventional Resources Conference held in Pittsburgh, Pennsylvania, USA, SPE, June 5-7. Wang, F.P., and Reed, R.M. Pore networks and fluid flow in gas shales. 09. SPE-24253, paper presented at the Annual Technical Conference and Exhibition, SPE, October 4-7. Ziarani, A. S., Aguilera, R. 2. Knudsen s permeability correction for tight porous media, Transport in Porous Media, Vol.9:

12 2 SPE 6365 Figure (A) Pore-size distribution estimated from the Horn River reconstruction indicating that small pores dominate in number; (B) Volumetric contribution of the same pores with peak at 2.0. (Curtise et al., 2) Figure 2 BSE images of a region of kerogen with varying pore sizes. Smaller pores can be seen in the inner walls of larger pores. (Curtise et al., ) Figure 3 Schematic of Micro-Scale Multiple Porosity Model: it is a grid system for instance, with one Organic Matrix Unit randomly distributed in shale matrix core surrounded by natural fracture grid.

13 SPE x - Cumulative Gas Drainage Mass into Natural Fracture System Versus Time 7 Cumulative Gas Drainage Mass, kg Case : AGWP = 0.00% Case 2: AGWP = 6.35% Case 3: AGWP =.28% Case 4: AGWP = 23.85% Case 5: AGWP = 27.2% AGWP = Adsorbed Gas Weight Percentage Figure 4 Cumulative gas rate curves for five cases with different adsorbed gas weight percentage..8 x 7 Average Pressure in the Matrix Bulk Versus Time Average Pressure in the Matrix Bulk : Pa Case : AGWP = 0.00 % Case 2 : AGWP = 6.35 % Case 3 : AGWP =.28 % Case 4 : AGWP = % Case 5 : AGWP = 27.2 % Initial Pressure in Matrix Constant Pressure in Fracture Figure 5 Average pressure curves for five cases with different adsorbed gas weight percentage. -3 Gas Drainage Capacity into Natural Fracture System Versus Time Gas Gas Drainage Capacity, kg / s / Pa Case : AGWP = 0.00% Case 2 : AGWP = 6.35% Case 3 : AGWP =.28% Case 4 : AGWP = 23.85% Case 5 : AGWP = 27.2% Gas Drainage Capacity = Gas Drainage Rate / (Average Pressure in Matrix - Pressure in Nature Fracture) Figure 6 Gas drainage capacity curves for five cases with different adsorbed gas weight percentage.

14 4 SPE x - Cumulative Gas Drainage Mass into Natural Fracture System Versus Time 7 Cumulative Gas Drainage Mass, kg Case 6: Dv = 0.0 m2/sec, Dn = 0.0 m2/sec Case 7: Dv = 7.09e-7 m2/sec, Dn = 4.43e-8 m2/sec Case 8: Dv = 7.09e-6 m2/sec, Dn = 4.43e-7 m2/sec Case 9: Dv = 7.09e-5 m2/sec, Dn = 4.43e-6 m2/sec Case : Dv = 7.09e-4 m2/sec, Dn = 4.43e-5 m2/sec Figure 7 Cumulative gas rate curves of five cases with different diffusion coefficients in kerogen..8 x 7 Average Pressure in the Matrix Bulk Versus Time.7 Average Pressure in the Matrix Bulk : Pa Case 6: Dv = 0.0 m2/sec, Dn = 0.0 m2/sec Case 7: Dv = 7.09e-7 m2/sec, Dn = 4.43e-8 m2/sec Case 8: Dv = 7.09e-6 m2/sec, Dn = 4.43e-7 m2/sec Case 9: Dv = 7.09e-5 m2/sec, Dn = 4.43e-6 m2/sec Case : Dv = 7.09e-4 m2/sec, Dn = 4.43e-5 m2/sec Inital Pressure in Matrix Constant Pressure in Fracture Figure 8 Average pressure curves for five cases with different diffusion coefficients in kerogen. 3.5 x -4 Gas Drainage Capacity into Natural Fracture System Versus Time Gas Drainage Capacity = Gas Drainage Rate / (Average Pressure in Matrix - Pressure in Natural Fracture) Gas Drainage Capacity, kg / s / Pa Case 6: Dv = 0.0 m2/sec, Dn = 0.0 m2/sec Case 7: Dv = 7.09e-7 m2/sec, Dn = 4.43e-8 m2/sec Case 8: Dv = 7.09e-6 m2/sec, Dn = 4.43e-7 m2/sec Case 9: Dv = 7.09e-5 m2/sec, Dn = 4.43e-6 m2/sec Case : Dv = 7.09e-4 m2/sec, Dn = 4.43e-5 m2/sec Figure 9 Gas drainage capacity curves for five cases with different diffusion coefficients in kerogen.

15 SPE x - Cumulative Gas Drainage Mass into Natural Fracture System Versus Time 7 Cumulative Gas Drainage Mass, kg Diffusion starts working! Desorption initiates to maintain high level rate! Dual Porosity Model Micro-Scale Model Considering Diffusion Micro-Scale Model Considering Diffusion and Desorption Figure Cumulative gas rate curves to compare Micro-Scale Model with conventional Dual Porosity Model..8 x 7 Average Pressure in the Matrix Bulk Versus Time.7 Average Pressure in the Matrix Bulk : Pa Dual Porosity Model Micro-Scale Model Considering Diffusion Micro-Scale Model Considering Diffusion and Desorption Initial Pressure in Matrix Constant Pressure in the Fracture Figure Average pressure curves to compare Micro-Scale Model with conventional Dual Porosity Model. 3.5 x -4 Gas Drainage Capacity into Natural Fracture System Versus Time Gas Gas Drainage Capacity, kg / s / Pa Dual Porosity Model Micro-Scale Model Considering Diffusion Micro-Scale Model Considering Diffusion and Desorption Gas Drainage Capacity = Gas Drainage Rate / (Average Pressure in Matrix - Pressure in Natural Fracture) Figure 2 Gas drainage capacity curves to compare Micro-Scale Model with conventional Dual Porosity Model.

16 6 SPE x - Cumulative Gas Drainage Mass into Natural Fracture System Versus Time Cumulative Gas Drainage Mass, kg Case : Random Kerogen Distribution Case 2: Random Kerogen Distribution Case 3: Random Kerogen Distribution Case 4: Random Kerogen Distribution Case 5: Random Kerogen Distribution Figure 3 Cumulative gas rate curves for five cases with different kerogen distribution modes..8 x 7 Average Pressure in the Matrix Bulk Versus Time.7 Average Pressure in the Matrix Bulk : Pa Case : Random Kerogen Distribution Case 2: Random Kerogen Distribution Case 3: Random Kerogen Distribution Case 4: Random Kerogen Distribution Case 5: Random Kerogen Distribution Initial Pressure in Matrix Constant Pressure in the Fracture Figure 4 Average pressure curves for five cases with different kerogen distribution modes. 3.5 x -4 Gas Drainage Capacity into Natural Fracture System Versus Time Gas Drainage Capacity : kg / s / Pa Gas Drainage Capacity = Gas Drainage Rate / (Average Pressure in Matrix - Pressure in Natural Fracture) Case : Random Kerogen Distribution Case 2: Random Kerogen Distribution Case 3: Random Kerogen Distribution Case 4: Random Kerogen Distribution Case 5: Random Kerogen Distribution Figure 5 Gas drainage capacity curves for five cases with different kerogen distribution modes.

17 SPE st Matrix Layer 2nd Matrix Layer 3rd Matrix Layer th Matrix Layer 40 5th Matrix Layer 40 6th Matrix Layer th Matrix Layer 40 8th Matrix Layer 40 9th Matrix Layer Figure 6 Matrix grids map distribution for 9 layers of matrix in Case with TOC value 7.0%. Note that in vertical direction there are layers of grids with the fracture grids contacted to the six outer faces of matrix bulk and not exhibited in this map. Those white grids represent the organic grids, and the crosses in the map are caused by the the organic matrix units (Figure 3); those black grids are the inorganic minerals within shale matrix bulk. st Matrix Layer x 7 2nd Matrix Layer x 7 3rd Matrix Layer x th Matrix Layer x 7 5th Matrix Layer x 7 6th Matrix Layer x th Matrix Layer x 7 8th Matrix Layer x 7 9th Matrix Layer x Figure 7 Pressure map for 9 layers of matrix in vertical direction in Case with TOC value 7.0%, corresponding to the matrix mesh map in Figure 6, and the time step is.0-4 seconds, when it is still at an early depletion period.

18 8 SPE x - Cumulative Gas Drainage Mass into Natural Fracture System Versus Time 7 Cumulative Gas Drainage Mass, kg Case 6 : TOC = 3.00 % Case 7 : TOC = 6.00 % Case 8 : TOC = 2.00 % Figure 8 Cumulative gas rate curves for three cases with different TOC value..8 x 7 Average Pressure in the Matrix Bulk Versus Time Average Pressure in the Matrix Bulk : Pa Case 6 : TOC = 3.00 % Case 7 : TOC = 6.00 % Case 8 : TOC = 2.00 % Initial Pressure in Matrix Constant Pressure in the Fracture Figure 9 Average pressure curves for three cases with different TOC value. x -4 Gas Drainage Capacity into Natural Fracture System Versus Time 3 Gas Drainage Capacity, kg / s / Pa Gas Drainage Capacity = Gas Drainage Rate / (Average Pressure in Matrix - Pressure in Natural Fracture) Case 6 : TOC = 3.00 % Case 7 : TOC = 6.00 % Case 8 : TOC = 2.00 % Figure Gas drainage capacity curves for three cases with different TOC value.

19 SPE Apparent permeability, nanodarcy Apparent Permeability Versus Pressure Matrix Size:.0e-5m, Diffusion & Darcy Flow Matrix Size:.0e-5m, Darcy Flow Matrix Size:.0e-5m, Diffusion & Darcy Flow & Desorption Matrix Size:.0e-4m, Diffusion & Darcy Flow Matrix Size:.0e-4m, Darcy Flow Matrix Size:.0e-4m, Diffusion & Darcy Flow & Desorption Matrix Size:.0e-3m, Diffusion & Darcy Flow Matrix Size:.0e-3m, Darcy Flow Matrix Size:.0e-3m, Diffusion & Darcy Flow & Desorption Matrix Size:.0e-2m, Diffusion & Darcy Flow Matrix Size:.0e-2m, Darcy Flow Matrix Size:.0e-2m, Diffusion & Darcy Flow & Desorption Matrix Size:.0e-m, Diffusion & Darcy Flow Matrix Size:.0e-m, Darcy Flow Matrix Size:.0e-m, Diffusion & Darcy Flow & Desorption Matrix Size:.0m, Diffusion & Darcy Flow Matrix Size:.0m, Darcy Flow Matrix Size:.0m, Diffusion & Darcy Flow & Desorption Intrinsic Permeability in Shale Matrix: 50 nanodarcies Deviation because of diffusion! Pressure : MPa Figure 2 Apparent permeability as a function of pressure with different matrix grids size. 8 Apparent Permeability Ratio as a Function of Average Pressure in Matrix Bulk Ratio of Apparent Permeability(Diffusion and Darcy Flow) to Apparent Permeability (Darcy Flow Only) Ratio of Apparent Permeability (Diffusion, Darcy Flow and Desorption) to Apparent Permeability (Darcy Flow Only) 7 6 Apparent Permeability Ratio Pressure : MPa Figure 22 Apparent permeability ratio (base case: Darcy flow only) as a function of pressure.

20 SPE Apparent Permeability(Considering diffusion, Darcy flow and Desorption) Versus Pressure Apparent permeability, nanodarcy K f = md K f = 8.44 md K f = 84.4 md K f = 844 md K f = 8.44 md Pressure : MPa Figure 23 Apparent permeability as a function of pressure with different fracture permeability. Results shows that fracture permeability cannot influence the dynamic apparent permeability since all curves are overlapped together. Figure 24 Single Horizontal well with multiple fractures used for upscaled triple permeability simulations.

21 SPE Figure 25 Upscaled triple permeability simulation model showing fine grid detail. Figure 26 Comparison of different matrix treatments for single horizontal well case.