Novel Approaches for the Simulation of Unconventional Reservoirs Bicheng Yan*, John E. Killough*, Yuhe Wang*, Yang Cao*; Texas A&M University

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1 SPE / URTeC Novel Approaches for the Simulation of Unconventional Reservoirs Bicheng Yan*, John E. Killough*, Yuhe Wang*, Yang Cao*; Texas A&M University Copyright 2013, Unconventional Resources Technology Conference (URTeC) This paper was prepared for presentation at the Unconventional Resources Technology Conference held in Denver, Colorado, USA, August The URTeC Technical Program Committee accepted this presentation on the basis of information contained in an abstract submitted by the author(s). The contents of this paper have not been reviewed by URTeC and URTeC does not warrant the accuracy, reliability, or timeliness of any information herein. All information is the responsibility of, and, is subject to corrections by the author(s). Any person or entity that relies on any information obtained from this paper does so at their own risk. The information herein does not necessarily reflect any position of URTeC. Any reproduction, distribution, or storage of any part of this paper without the written consent of URTeC is prohibited. Summary The development of shale plays in North America has achieved great success in satisfying increased energy demand. With the advances in experimental approaches, investigation of microstructures in organic-rich shale has identified several different pore types and the abundance of pores from the nanometer to the micron scale. Yet current modeling work for such reservoirs is mainly performed with dual porosity models based on Darcy s law. In addition, a great discrepancy between simulation results and production data persists. Because flow regimes in porous media are quite sensitive to pore size, the flow mechanisms in shale reservoirs are considerably more complex than Darcy flow and the feasibility of conventional models has been frequently challenged. This work presents an integration of realistic multi-porosity and multi-mechanistic treatments to resolve the conundrum of fluid flow in shale. Based on a unique reservoir simulator, a micro-scale multiple-porosity model for gas flow in shale reservoirs is presented in this paper. The model consists of three separate porosity systems: kerogen, inorganic minerals, and natural fractures. Inorganic and organic portions of the shale matrix are represented by sub-continua with different characteristics considering pore structures, fluid storage and flow mechanisms. In the kerogen gas desorption, diffusion and Darcy flow occur simultaneously. Through considering the different pore families in the kerogen, the effects of nanopores and microporosity are incorporated into the model. In addition, a novel gridding scheme has been specially designed to recognize the complex structures. To accomplish this, the grid incorporates randomly distributed kerogen in the shale matrix and different continua are tied to each other via arbitrary connectivities. Through changing the properties of both matrix and fracture, a unified concept of dynamic apparent permeability of shale matrix is proposed. The derived concept allows the design and function of the Micro-Scale Model to be extended to the reservoir scale model containing hydraulic fractures. The more realistic gas production forecasts using the workflow presented in this paper indicate significant differences from that of conventional models. The ability to more accurately simulate the complex flow mechanisms using the proposed techniques will allow operators to better predict and enhance ultimate recovery from shale reservoirs. Introduction The development of gas shale plays is much more difficult than that of conventional reservoirs, and horizontal well and hydraulic fracturing technologies are indispensable to obtain profitable production rates in shale gas reservoirs (King 2010). However, so far there is no acceptable theory system to sufficiently evaluate and forecast shale gas production (Passey et al. 2010), since there exist a lot of complexities and uncertainties for such kind of reservoirs. Geologically shale serves as both the source and reservoir rock for the natural gas in shale gas plays (Hill et al. 2007). Under microscopic view, many different porosity systems have been observed within organic-rich shale reservoirs, including inorganic minerals, kerogen, natural fractures and hydraulic fractures (Wang and Reed 2009). Those porosity systems are totally different with regards to porosity, permeability, wettability, gas storage and flow mechanisms (Yan et al. 2013), However, the connections between different porosity systems are yet not well understood (Andrade et al. 2011) and yet they have become a main challenge to characterizing gas flow in shale.

2 URTeC Previously we have investigated the influence of different flow mechanisms including Fickian diffusion, Darcy flow, Langmuir desorption within shale through a Micro-Scale Model (Yan et al. 2013). Within such tight porous medium, diffusion enhances gas flow in shale in comparison to that calculated with conventional dual porosity models, however, gas desorption significantly increases gas in place but with little improvement of the gas drainage capacity. A dynamic apparent permeability was proposed based on the Micro-Scale model, and it was concluded that this value is strongly related to Diffusion, Darcy flow, average matrix pressure and matrix permeability, but little influenced by desorption, matrix size and fracture permeability. These results were further applied in a macroscale reservoir model through an upscaling procedure. This paper is a continuation work of the previous one (Yan et al. 2013). It emphasizes the validation of the apparent permeability from the Micro-Scale Model and its application as well. A new algorithm specially designed for the matrix-fracture interaction with constant fracture pressure has been proposed to calculate this parameter, and through back calculation, good agreement between results from the Micro-Scale Model and those from a bulk matrix model applying dynamic apparent permeability has been achieved. Finally, an example based on the dynamic matrix permeability ratio has been used to upscale the Micro-Scale Model into a reservoir scale model. Methodology The distribution of kerogen within inorganic minerals and the size of natural fractures are all at the micro scale, thus it is reasonable to control the simulation model within micrometer size if subdivision of shale matrix is required. Based on petrophysical data, in the Micro-Scale Model three different pore systems are specifically considered: inorganic minerals, kerogen, and natural fractures. The natural fracture network serves as a pathway to connect the shale matrix to hydraulic fracture system and the wellbore. During gas production gas flows from matrix into the natural fracture network and the pressure within the network can be immediately depleted to the level of the bottomhole pressure. Therefore, in the Micro-Scale Model the natural fractures are located surrounding the matrix bulk and assumed as a constant pressure boundary. On the other hand, Curtis et al (2010) reports the pore geometry separation occurs in kerogen: the smaller pores penetrated the walls of the larger ones, besides, those smaller ones control most of the pore amount but larger pores contribute most of the pore volume. Flow regime in porous medium is very sensitive to pore-geometry. Therefore, the kerogen pore system is further subdivided into two different ones: kerogen with micropores (pore radii average on 100 nm) and kerogen with nanopores (pore radii average on 5nm). It is assumed that kerogen with nanopores can communicate with other pore systems only through kerogen with micropores. Therefore, in a 3-D Cartesian system six grids of kerogen with micropores surround a grid of kerogen with nanopores. The number of those kerogen grids is controlled by the Total Organic Carbon (TOC) from petrophysical data; because kerogen is usually dispersed within inorganic minerals, the locations of those kerogen grids are randomly distributed. A typical mesh map with TOC controlled at 7.0 wt% is shown on Fig. 1. In this figure, the cuboid is the matrix bulk, and those green grids are kerogen grids including kerogen with micropores and kerogen with nanopores, and the empty spaces in the matrix are actually inorganic grids for a better resolution. From the figure it can be observed that those kerogen grids are randomly dispersed in the inorganic minerals and show great connectivity, and this is consistent with those physical pictures, shown as Fig. 2 (Curtis et al. 2012) and thus should be a good approximation. In the Micro-Scale Model (Yan et al. 2013), Fickian diffusion and Langmuir desorption are considered to be the main physics in kerogen, and there is no Darcy flow for kerogen with nanopores; however, in inorganic minerals and natural fractures, Darcy flow is considered to be the only flow mechanism due to the larger pore scale in these pore systems. All those dynamics are coupled into a unique simulator, and the real gas properties are calculated through Peng-Robinson EOS. With the setup of the Micro-Scale model, a dynamic apparent permeability is calculated through Equation (1). Compared to our previous work, the K app in Equation (1) has a constant coefficient ω to consider the interaction between matrix and fracture. However, similar to previous apparent permeability, this one does not change with matrix size, fracture permeability, desorption, but significantly related with matrix average pressure, matrix permeability, Darcy flow and diffusion occurring in matrix. In Equation (2), K app is a harmonic average concept considering the weight from both matrix and fracture, so the impact of fracture permeability can be totally excluded even though it has neglectable influence on apparent permeability, and a matrix apparent permeability can be

3 URTeC obtained. For a better compatibility with the current simulator, a ratio of matrix apparent permeability to the matrix intrinsic permeability is used to tune the matrix-fracture transmissibility. Besides, the result from the Micro-Scale Model with matrix extensively discretized is treated as an accurate solution. To validate the matrix apparent permeability ratio, a bulk matrix model is established without any discretization (single matrix grid) but keeps all basic input parameters the same as the Micro-Scale Model, and the combinational effect of Diffusion, Darcy flow, and transient interaction between matrix and fracture is considered through the matrix apparent permeability ratio. Finally an approximate solution is obtained and further compared with the accurate solution. Through repeatedly adjusting the ω coefficient, the approximate solution finally reaches closest to the accurate solution with an optimum ω. q f dmf mf Kapp (1) ( Pm P f ) A K app m mapp f mf f mf Kmapp K f (2) W K W K Diffusion and Darcy flow are considered to in a similar way because both of them could be treated as pressure difference related terms in the mass balance equation for isothermal cases; therefore, it should be straightforward and effective to start with cases considering Darcy flow only to obtain a reasonable ω, and then apply it to cases with Darcy flow and Diffusion. Here desorption is not taken into account since we already know that it would not influence the apparent permeability in Equation (2). Results Analysis Case Considering Darcy Flow Only In this case, the only flow mechanism in the model is Darcy flow. The dimensions of the Micro-Scale Model are 242 μm 242 μm 242 μm divided into 26 grids 26 grids 26 grids, in total grids (note here matrix grids are ). For comparison, the dimensions of the bulk matrix model are 242 μm 242 μm 242 μm divided into 3 grids 3 grids 3 grids(note here matrix grids are 1 1 1). The basic parameters are shown in Table 1. It should be noted that in this case, fracture grids are single layered surrounding the matrix bulk as a constant pressure boundary. Through a lot of repeated calculation, it is concluded that 2 / 2is the best choice for ω. Based on the results from the Micro-Scale Model, the dynamic matrix apparent permeability ratio is shown as Fig. 3. With the dynamic curve applied in the bulk matrix model, the gas amount in matrix, average matrix pressure and gas recovery with time are all calculated and compared with the accurate solution from the Micro-Scale Model. Because the model size and the simulation time scale are extremely small, dimension analysis is conducted here, and those dimensionless variables definition can be referred in the Nomenclature Part. As shown in Fig. 4 to 6, compared to the accurate solution the relative errors of the approximated solution with regards to gas in matrix, average matrix pressure and gas recovery are separately %, % and %. Those results are fairly acceptable for compressible gas flow and significant, because the matrix bulk model reduces 70 times of the simulation time compared to the Micro-Scale Model but without sacrificing too much accuracy. Case Considering Darcy Flow and Fickian Diffusion Our previous work has shown that in the Micro-Scale Model, those kerogen grids are actually evenly distributed within matrix and different random distributions of kerogen grids with a constant TOC value cannot influence the global behavior of matrix-fracture interaction(yan et al. 2013). Moreover, Fickian diffusion is similar to Darcy flow. Therefore, the method to calculate the matrix apparent permeability ratio in the case considering only Darcy flow is also applicable to the Micro-Scale Model considering Darcy flow and Fickian diffusion, the only point neglected here is the desorption occurring in kerogen, it should be fine right now because desorption has little to do with the apparent permeability. In this case, TOC is controlled at 10.0 wt%, and the dimensions of the Micro-Scale Model are still 242 μm 242 μm 242 μm divided into 26 grids 26 grids 26 grids, in total grids. For comparison, the dimensions of the bulk matrix model are 242 μm 242 μm 242 μm divided into 3 grids 3 grids 3 grids. In the Micro-Scale Model four different continua are included while in the bulk matrix model there are only two medium types. The basic parameters in this case are shown in Table 2.1, 2.2 and 3. To keep the pore volume in matrix equal in the two different models, the matrix porosity in the bulk matrix model is averaged at

4 URTeC Based on the results from the Micro-Scale Model, the dynamic apparent permeability is calculated with ω equal to 2 / 2, and the matrix apparent permeability ratio is plotted in Fig. 7. After that the curve is assigned as a coefficient to the shale matrix permeability in the bulk matrix model. Finally the results of these two different models in terms of dimensionless variables are plotted in Fig. 8 to 10. Compared to the Micro-Scale Model, the relative errors of the bulk matrix model with regards to gas in place, average matrix pressure and gas recovery are separately %, % and %, which should be very good results. The last two cases are not comparable in terms of gas recovery, because the case considering Darcy flow only cost one third longer time to reach the ultimate gas recovery level, which cannot be observed in a dimensionless time scale here. Macro-Scale Modeling Considering Darcy Flow, Fickian Diffusion Through the validation of the matrix apparent permeability ratio before, a Macro-Scale Model with hydraulic fractures was established. The matrix apparent permeability ratio is taken into account through the use of a variable permeability based on the matrix pressure which allows both diffusion and Darcy flow to be considered in the Macro-Scale Model. The basic parameters are shown in Table 4. The dual-porosity Macro-Scale Model is shown in Figure 11. This model is based on a simple 3x3x3 system of matrix blocks surrounded by a fracture system. Initially, the pressure in the fracture system is lowered such to about one-half of the original pressure in the matrix block causing gas to drain from these blocks. Results of three different simulations at the macro-scale are shown in Figure 12. As shown in this figure, the use of the enhanced variable permeability model appears to differentiate the model from fixed permeability models. As expected, variable permeability results in drainage intermediate to the maximum apparent permeability ratio and the absolute matrix permeability validating that the results of the Micro-Scale Model can be upscaled efficiently in this manner. Conclusions In this paper, a coefficient considering the interaction between matrix and fracture has been introduced into the matrix apparent permeability. Through a back calculation algorithm, the matrix apparent permeability has been validated and it can provide high accuracy. Further, in the Micro-Scale Model considering random distribution of kerogen and diffusion in kerogen, the matrix apparent permeability can again provide good results. Finally, the Micro-Scale Model can be upscaled through the variable matrix apparent permeability ratio effectively. Acknowledgments The authors wish to thank The Crisman Institute at Texas A&M University for funding this research work. Nomenclature Dimensionless Average Matrix Pressure = Average Matrix Pressure / Initial Matrix Pressure; Dimensionless Gas Amount in Matrix = Gas in Matrix / Original Gas in Matrix; Dimensionless Time = Time Step in Simulation / Time for the Whole Simulation; Gas Recovery = Cumulative Gas Rate / Original Gas in Matrix; A = Total contact area between the matrix bulk and the fracture system, m 2 ; mf d mf = Nodal distance between the matrix bulk and the fracture system, m; K app = Apparent permeability, m 2 or nanodarcy; K mapp = Matrix apparent permeability totally excluding the influence of fracture, m 2 or nanodarcy; K m = Matrix intrinsic permeability, m 2 or nanodarcy; P m = Average pressure within the matrix bulk, Pa; P f = Constant pressure within the fractures surrounding the matrix bulk, Pa; q f = Total rate flowing from matrix system into fracture system, kg/s; TOC = Total Organic Carbon, wt%; W f = Weight of fracture system for harmonic average; W m = Weight of matrix for harmonic average; = Average gas density in the micro model (fracture and matrix), kg/m 3 ; mf = Porosity of the porous media, fraction;

5 URTeC = Average gas viscosity in the micro model (fracture and matrix), Pa S; mf ω = Coefficient considering the interaction between matrix and fracture; References Andrade, J., Civan, F., Devegowda, D. et al Design and Examination of Requirements for a Rigorous Shale-Gas Reservoir Simulator Compared to Current Shale-Gas Simulator. Paper presented at the North American Unconventional Gas Conference and Exhibition, The Woodlands, Texas, USA. Society of Petroleum Engineers SPE MS. DOI: / ms. Curtis, M.E., Ambrose, R.J., and Sondergeld, C.H Structural Characterization of Gas Shales on the Micro- and Nano- Scales. Paper presented at the Canadian Unconventional Resources and International Petroleum Conference, Calgary, Alberta, Canada. Society of Petroleum Engineers SPE MS. DOI: / ms. Curtis, M.E., Sondergeld, C.H., Ambrose, R.J. et al Microstructural Investigation of Gas Shales in Two and Three Dimensions Using Nanometer-Scale Resolution Imaging. AAPG Bull. 96 (4): DOI: / Hill, R.J., Jarvie, D.M., Zumberge, J. et al Oil and Gas Geochemistry and Petroleum Systems of the Fort Worth Basin. AAPG Bull. 91 (4): DOI: DOI: / King, G.E Thirty Years of Gas Shale Fracturing: What Have We Learned? Paper presented at the SPE Annual Technical Conference and Exhibition, Florence, Italy. Society of Petroleum Engineers SPE MS. DOI: / ms. Passey, Q.R., Bohacs, K., Esch, W.L. et al From Oil-Prone Source Rock to Gas-Producing Shale Reservoir Geologic and Petrophysical Characterization of Unconventional Shale-Gas Reservoirs. Paper presented at the International Oil and Gas Conference and Exhibition in China, Beijing, China. Society of Petroleum Engineers SPE MS. DOI: / ms. Wang, F.P. and Reed, R.M Pore Networks and Fluid Flow in Gas Shales. Paper presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana. Society of Petroleum Engineers SPE MS. DOI: / ms. Yan, B., Wang, Y., and Killough, J Beyond Dual-Porosity Modeling for the Simulation of Complex Flow Mechanisms in Shale Reservoirs. Paper presented at the 2013 SPE Reservoir Simulation Symposium, The Woodlands, TX, USA. Society of Petroleum Engineers SPE MS. DOI: / ms. Table 1 Basic parameters for cases considering Darcy flow only Micro-Scale Model Bulk Matrix Model K f (md) Fracture Porosity Fracture Aperture (µm) 1 1 K m (nd) Matrix Porosity Matrix Grid Size (µm) Matrix Grid NO. in 3-D Initial matrix pressure (MPa) Pressure in fracture (MPa) Temperature in model (Celsius) Table 2.1 Basic medium parameters for Micro-Scale Model Medium Type Fracture Inorganic matrix Kerogen-micropores Kerogen- nanopores Medium density (g/cc) Porosity Permeability (md) Diffusivity (m 2 /sec) Grid NO

6 URTeC Table 2.2 Other basic parameters for micro-scale model Micro-Scale Model Fracture Aperture (µm) 1 Matrix Grid Size (µm) 10 Matrix Grid NO. in 3-D Initial matrix pressure (MPa) 17.2 Pressure in fracture (Mpa) 8.6 Temperature in model (Celsius) 100 Table 3 Basic parameters for bulk matrix model Bulk Matrix Model K f (md) 84.4 Fracture Porosity 1.0 Fracture Aperture (µm) 1 K m (nd) 50 Matrix Porosity Matrix Grid Size (µm) 10 Matrix Grid NO. in 3-D Initial matrix pressure (MPa) 17.2 Pressure in fracture (MPa) 8.6 Temperature in model (Celsius) 100 Table 4 Basic parameters for Macro-Scale model Macro-Scale Model K f (md) 84.4 Fracture Porosity 1.0 Fracture Aperture (µm) 1 K m (nd) 50 Matrix Porosity Initial matrix pressure (psi) 2494 Pressure in fracture (psi) 1247 Temperature in model (Celsius) 100 Fig.1 Sample Micro-Model with TOC = 7.0 wt% (a) (b) (c) Fig.2 Reconstruction of the Horn River sample (a) a 3-D matirx, (b) kerogen, (c) pores. (Curtis et al. 2012)

7 URTeC Fig. 3 Matrix apparent permeability ratio from model considering Darcy flow only Fig. 4 Dimensionless analysis of residual gas in matrix with time Fig. 5 Dimensionless analysis of average matrix pressure with time

8 URTeC Fig. 6 Dimensionless analysis of gas recovery with time Fig. 7 Matrix apparent permeability ratio from model considering Darcy flow and Fickian Diffusion Fig. 8 Dimensionless analysis of residual gas in matrix with time

9 URTeC Fig. 9 Dimensionless analysis of average matrix pressure with time Fig. 10 Dimensionless analysis of gas recovery with time

10 URTeC Fig. 11 Macro-Model used for validation of variable permeability Fig. 12 Matrix pressures for Macro-Model showing effect of variable permeability