Triple Medium Physical Model of Post Fracturing High-Rank Coal Reservoir in Southern Qinshui Basin

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1 Journal of Earth Science, Vol. 26, No. 3, p , June 2015 ISSN X Printed in China DOI: /s z Triple Medium Physical Model of Post Fracturing High-Rank Coal Reservoir in Southern Qinshui Basin Shiqi Liu 1, Shuxun Sang* 2, Qipeng Zhu 2, Jiefang Zhang 2, Hefeng Gao 2, Huihu Liu 3, Lixing Lin 4 1. School of Safety Engineering, China University of Mining and Technology, Xuzhou , China 2. Key Laboratory of Coalbed Methane Resources and Reservoir Formation Process, Ministry of Education, School of Mineral Resource and Geoscience, China University of Mining and Technology, Xuzhou , China 3. School of Geoscience and Environment, Anhui University of Science and Technology, Huainan , China 4. Faculty of Engineering and Applied Science, University of Regina, Regina S4S0A2, Canada ABSTRACT: In this paper, influences on the reservoir permeability, the reservoir architecture and the fluid flow pattern caused by hydraulic fracturing are analyzed. Based on the structure and production fluid flow model of post fracturing high-rank coal reservoir, Warren-Root Model is improved. A new physical model that is more suitable for post fracturing high-rank coal reservoir is established. The results show that the width, the flow conductivity and the permeability of hydraulic s are much larger than natural s in coal bed reservoir. Hydraulic changes the flow pattern of gas and flow channel to wellbore, thus should be treated as an independent medium. Warrant-Root Model has some limitations and can t give a comprehensive interpretation of seepage mechanism in post fracturing high-rank coal reservoir. Modified Warrant-Root Model simplifies coal bed reservoir to an ideal system with hydraulic, orthogonal macroscopic and cuboid matrix. Hydraulic is double wing, vertical and symmetric to wellbore. Coal bed reservoir is divided into cuboids by hydraulic and further by macroscopic s. Flow behaviors in coal bed reservoir are simplified to three step flows of gas and two step flows of water. The swap mode of methane between coal matrix and macroscopic s is pseudo steady fluid channeling. The flow behaviors of methane to wellbore no longer follow Darcy s Law and are mainly affected by inertia force. The flow pattern of water follows Darcy s Law. The new physical model is more suitable for post fracturing high-rank coal reservoir. KEY WORDS: triple medium physical model, high-rank coal reservoir, hydraulic, seepage, southern Qinshui Basin. 0 INTRODUCTION Physical model is used to study the seepage mechanism, to provide necessary parameters to mathematical simulation, and to verify results of mathematical simulation and to propose new mathematical model (Liu, 2013; Chen, 2009; Zhang et al., 2003). Physical model of coal bed reservoir is the foundation of coal bed reservoir modeling (Liu, 2013; Chen, 2009; Zhang et al., 2003). Before coal bed reservoir modeling, geologic model should be idealized initially and physical model which can be depicted by mathematical formula should be established (Liu, 2013; Chen, 2009; Zhang et al., 2003). Interpretation of seepage mechanism given by physical model determines the accuracy of mathematical simulation to a great extent (Liu, 2013; Chen, 2009; Zhang et al., 2003). At present, scholars *Corresponding author: shuxunsang@163.com China University of Geosciences and Springer-Verlag Berlin Heidelberg 2015 Manuscript received June 25, Manuscript accepted October 26, mostly use Warren-Root Model for depicting pore- system, flow behaviors and flow laws in coal bed reservoir. Warren-Root Model is double medium physical model established for porous medium in oil-gas reservoir (Liu, 2013; Chen, 2009; Zhang and Tong, 2008; Fu and Qin, 2003). Warren-Root Model gives detailed and comprehensive interpretations to seepage mechanism in naturally d oil-gas reservoir (Xue, 2009; Zhang and Tong, 2008). Coal bed reservoir, especially the high-rank coal reservoir, is ternary pore- system formed by macro-, micro and pore (Liu, 2013; Chen, 2009; Fu and Qin, 2003; Zhang et al., 2003). Coal bed reservoir has greater aeolotropism and lower permeability, which is very different from naturally d oil-gas reservoir (Liu, 2013; Liu et al., 2012a; Chen, 2009; Fu and Qin, 2003; Zhang et al., 2003). Before exploitation, coal bed is always stimulated by hydraulic fracturing. Warren-Root Model has great distortion to depict seepage mechanism of post fracturing high-rank coal reservoir (Liu, 2013; Chen, 2009; Xue, 2009; Zhang and Tong, 2008; Zhang et al., 2003). Differences of composition and modality between hydraulic and natural, Liu, S. Q., Sang, S. X., Zhu, Q. P., et al., Triple Medium Physical Model of Post Fracturing High-Rank Coal Reservoir in Southern Qinshui Basin. Journal of Earth Science, 26(3): doi: /s z.

2 408 Shiqi Liu, Shuxun Sang, Qipeng Zhu, Jiefang Zhang, Hefeng Gao, Huihu Liu and Lixing Lin changes of flow pattern and flow level after hydraulic fracturing both have not been fully studied. The study of hydraulic has not been separated from that of natural and treated as an individual medium. The study of coal reservoir model has not been broken away from the model of double medium (matrix and cleat). Accordingly, physical model for interpretation of seepage mechanism and coal bed reservoir mathematical simulation has not been established (Xue, 2009; Zhang and Tong, 2008). The study of physical model of post fracturing high-rank coal reservoir in southern Qinshui Basin is of great importance to deeply understand of the flow mechanism and the regular pattern of gas and water, to guide the stimulation implement and to enrich the coal bed methane (CBM) exploitation mechanism in China. Taking the high-rank coal reservoir in southern Qinshui Basin as an example, structure model and flow pattern with and without hydraulic fracturing are compared in this paper. On the basis of structure model and flow model of post fracturing high-rank coal reservoir, Warren-Root Model is improved. New physical model that more is more suitable for post fracturing high-rank coal reservoir was established to help the establishment of coal bed reservoir mathematical model. 1 INFLUENCES ON THE HIGH-RANK COAL RE- SERVOIR CAUSED BY HYDRAULIC FRACTURING 1.1 Influences on the Reservoir Permeability Caused by Hydraulic Fracturing in Research Area s in No. 3 coal bed reservoir are non-developed and often filled by calcite and other minerals. The characteristics of macro-s are less favorable for the permeability of reservoir. Coal bed reservoir gives priority to micropores and transition pores, followed by macropores, and mesopores is non-developed. The characteristics of pores are favorable for gas adsorbing and less favorable for diffusion and seepage of gas. In a word, No. 3 coal bed reservoir in research area has low permeability. According to the well testing analysis data, variation of permeability in No. 3 coal bed reservoir is large, of the permeabilities in No. 3 coal bed reservoir are in the range of to μm 2 with the average of μm 2. There are 25.71% of CBM wells whose permeabilities are less than μm 2, and 51.43% of CBM wells whose permeabilities are μm 2, and 22.86% of CBM wells whose permeabilities are μm 2. So, No. 3 coal bed reservoir is low to middle permeability reservoir and low permeability reservoir is more developed (Table 1). Because of the lower permeability, before exploitation, coal bed is always stimulated by hydraulic fracturing (Li et al., 2013; Liu et al., 2013, 2012b; Meng et al., 2010; Ni et al., 2009). Development degree of the hydraulic in research area is much larger than the natural. According to results of the hydraulic fracturing monitoring and the numerical simulation, lengths of major hydraulic s are m, with the average of m. Widths of hydraulic s are m, with the average of m. Heights of hydraulic s can be regarded as reservoir thicknesses which are m, with the average of 6.42 m. However, widths of macro-s are less than m and macro-s are often filled by calcite and other minerals. According to results of numerical simulation and field engineering monitoring, after hydraulic fracturing, permeability of No. 3 coal bed reservoir has a great increase (Table 1). So, hydraulic has larger flow conductivity and permeability. Besides larger conductivity and permeability of hydraulic s, during hydraulic fracturing, part of natural s are stretched and opened that their permeability is accreted. At the same time, parts of natural s are connected by hydraulic that reservoir permeability is also heightened. Although reservoir permeability at orientation with the least principal stress is much smaller than that at orientation with maximum principal stress, it is also much larger than the natural reservoir permeability. That means coal bed is also opened at orientation with least principal stress. Part of natural s are stretched and opened too that their permeability is increased. Different from the orientation with maximum principal stress, expanded range at orientation with least principal stress is smaller, hydraulic is shorter, and reservoir reconstructions are weaker. In conclusion, on the one hand, hydraulic has larger permeability than natural reservoir and contact area between hydraulic and macroscopic s is also much larger than contact area between macroscopic s and wellbore. After hydraulic fracturing, hydraulic becomes the most important medium for fluid flow. On the other hand, after hydraulic fracturing, permeability at orientation with maximum principal stress is much larger than that at orientation with least principal stress. Hydraulic mainly expands at orientation with maximum principal stress and not expands at orientation with least principal stress. 1.2 Influences on the Structure Model of High-Rank Coal Reservoir Caused by Hydraulic Fracturing According to the analysis above, conductivity and permeability of hydraulic are much larger than that of natural in No. 3 coal bed reservoir. Hydraulic should be considered when the macrostructure model of post Table 1 Permeability with and without hydraulic fracturing Reservoir permeability after hydraulic fracturing ( 10-3 μm 2 ) Reservoir permeability without hydraulic Orientation with maximum principal stress Orientation with least principal stress fracturing ( 10-3 μm 2 ) Maximum value Minimum value Average value

3 Triple Medium Physical Model of Post Fracturing High-Rank Coal Reservoir in Southern Qinshui Basin 409 fracturing high-rank coal reservoir is established. Structure models of exogenous s and cleats are the same as structure models without hydraulic fracturing. The reservoir respectively developed two groups of exogenic s and cleats. Exogenic s and cleats are controlled by palaeotectonic stress field. Cleats density of high-rank coal is much less than middle rank coal, however, this characteristic causes low permeability of high-rank coal reservoir (Fig. 1). So, macrostructure model of post fracturing high-rank coal reservoir is integration of macrostructure model of high-rank coal reservoir without hydraulic and characteristics of hydraulic. The reservoir mainly developed one group of hydraulic with the direction of NE50. The direction is controlled by modern tectonic stress field (Fig. 2). Hydraulic has larger flow conductivity and permeability than natural s. At the same time, hydraulic fracturing stretches and opens part of natural s that accretes the permeability of natural. Hydraulic connects part of natural s that increases the formation communication of natural s and the permeability of coal reservoir. Butt cleat Face cleat Dull coal Exogenous Bright coal Semi-bright coal Semi-dull coal Butt cleat Face cleat Exogenous Bright coal Semi-bright coal Semi-dull coal Figure 1. Macrostructure model of high-rank reservoir in research area. Butt cleat Face cleat Dull coal Bright coal Semi-bright coal Semi-dull coal Exogenous Hydraulic Butt cleat Face cleat Exogenous Bright coal Semi-bright coal Semi-dull coal Hydraulic Figure 2. Macrostructure model of post fracturing high-rank reservoir in research area.

4 410 Shiqi Liu, Shuxun Sang, Qipeng Zhu, Jiefang Zhang, Hefeng Gao, Huihu Liu and Lixing Lin Post fracturing high-rank coal reservoir has the same microstructure model with the high-rank coal reservoir without hydraulic fracturing: No. 3 coal bed reservoir universally develops three types of micro-fissure: shrinkage microfissure, static pressure micro-fissure and structure microfissure. Micro-fissure is the important passageway connecting pore and cleat. No. 3 coal reservoir universally develops ultramicros copic fissures which cut through part of gas pores. Intermolecular pore and residual gas pore are the main pores in No. 3 coal bed reservoir, followed by plant tissue pore and metamorphic gas pore, and some intergranular pore (Fig. 3) (Sang et al., 2009). 1.3 Influences on the Production Fluid Flow of High-Rank Coal Reservoir Caused by Hydraulic Fracturing According to the analysis above, after hydraulic fracturing, hydraulic becomes the most important flow channel to wellbore. Comparing with fluid supply capacity from hydraulic to wellbore, fluid supply capacity from macro- to wellbore can be ignored. According to diffusion and seepage regular pattern of methane in hydraulic, seepage pattern of methane in hydraulic is turbulent flow which is greatly different from seepage pattern in macro- (Figs. 4, 5). Seepage pattern of methane in hydraulic should be treated separately. In a word, hydraulic changes flow pattern of methane and passageway to wellbore. So, hydraulic should not be simply regarded as natural with larger permeability, however, hydraulic should be separated from natural and treated as an individual medium. Based on the fluid flow model in high-rank coal reservoir without hydraulic fracturing, methane goes through microbores, transition pores and ultramicroscopic fissures to mesopores/ macropores mainly with transition diffusion. Methane migrates from mesopores, macropores and micro-fissures to macros with transition diffusion, and laminar flow, transition flow (Fig. 4). Intergranular pore Fusinite Structural fissure Static pressure fissure Tekinite Shrinkage fissure Macrinite Plant tissue pore Corpocollinite 100 Residual gas pore Gas pore Ultramicroscopic fissure and intermolecular pore Figure 3. Microstructure model of high-rank reservoir in research area. Surface diffusion & knudsen diffusion & transition diffusion Microbore & transition pore Surface diffusion & knudsen diffusion & transition diffusion Ultramicroscopic fissure Transition diffusion Mesopore & macropore Transition diffusion & & transition flow Micro-fissure Transition diffusion & & transition flow Transition flow & turbulent flow Transition diffusion & & transition flow Figure 4. Flow model of methane in pore- system without hydraulic. Surface diffusion & knudsen diffusion & transition diffusion Transition flow & turbulent flow Microbore & transition pore Surface diffusion & knudsen diffusion & transition diffusion Ultramicroscopic fissure Transition diffusion Mesopore & macropore Transition diffusion & & transition flow Micro-fissure Transition diffusion & & transition flow Transition flow & turbulent flow Hydraulic turbulent flow Transition diffusion & & transition flow Figure 5. Flow model of methane in pore- system with hydraulic.

5 Triple Medium Physical Model of Post Fracturing High-Rank Coal Reservoir in Southern Qinshui Basin 411 Comparing with fluid flow model in high-rank coal reservoir without hydraulic fracturing, because that hydraulic is treated as an individual medium, methane goes through triple medium to wellbore and the flow pattern is three step flows (Fig. 5). Migration process of methane also has some changes. On the one hand, methane in macroscopic directly migrates to wellbore as transition flow, turbulent flow and (Fig. 5). On the other hand, because that hydraulic connects part of macroscopic, methane initially moves to hydraulic as transition flow, turbulent flow and, then migrates to wellbore as turbulent flow and through hydraulic (Fig. 5). Similarly, according to the fluid flow model in high-rank coal reservoir without hydraulic fracturing, seepage type of water is always laminar flow (Fig. 6). Water that is contained in mesopores, macropores and micro-fissures also migrates to macroscopic as laminar flow (Fig. 6). Comparing with fluid flow model in high-rank coal reservoir without hydraulic fracturing, water goes through double medium to wellbore which is two step flows (Fig. 7). Mesopore & macropore Micro-fissure Figure 6. Flow model of water in pore- system without hydraulic. Mesopore & macropore Micro-fissure Hydraulic Figure 7. Flow model of water in pore- system with hydraulic. 2 PHYSICAL MODEL OF POST FRACTURING HIGH-RANK COAL RESERVOIR Physical model of coal bed reservoir contains reservoir model and flow model. Reservoir model describes major characteristics of media. Flow model describes flow behaviors of fluid in media (Chen, 2009; Zhang et al., 2003). Physical model can be described by mathematical model and serves reservoir modeling. Physical model in research area is established by idealizing characteristics of pores, natural s, hydraulic and flow pattern of the fluid. 2.1 Warren-Root Model At present, major physical model for coal bed reservoir modeling is Warren-Root Model. Warrant-Root Model simplifies double medium (matrix and natural s) reservoir to an ideal system with orthogonal macroscopic and cuboid matrix (Fig. 8) (Kong, 2010; Ge, 2003; Poollen and Jargon, 1969; Warren, 1964; Warren and Root, 1963). Coal bed reservoir was divided into cuboid by macroscopic s (Fig. 8) (Kong, 2010; Ge, 2003; Poollen and Jargon, 1969; Warren, 1964; Warren and Root, 1963). In Warren-Root Model, the orientation of macroscopic s is consistent with the orientation of major permeability. The width of macroscopic s is constant (Kong, 2010; Ge, 2003; Poollen and Jargon, 1969; Warren, 1964; Warren and Root, 1963). Macro network can be uniformly distributed or non-uniformly distributed. Non-uniformly distributed macro- network is used to study nonisotropy of macro- system and variation of permeability at a certain direction (Kong, 2010; Ge, 2003). is the major preserving space of methane. Methane adsorbs in microbores and transition pores in matrix (Xue, 2009; Fu et al., 2007). s are not only the major preserving spaces of water, but also the major seepage channel of water and gas (Xue, 2009; Fu et al., 2007). Only macro- supplies water and methane to wellbore. only supplies methane to macro- (Fig. 9) (Kong, 2010; Ge, 2003; Poollen and Jargon, 1969; Warren, 1964; Warren and Root, 1963). Warren-Root Model consists of double medium: matrix (pore and micro-fissure) and macro-. Flow level of methane is two step flows: matrix to macro- and macro- to wellbore. Flow level of water is single step flow: macro- to wellbore. The flow patterns of methane are desorption, diffusion and seepage. The flow pattern of water is only seepage. When mathematical model is established, Methane Figure 8. Warren-Root Model. Water

6 412 Shiqi Liu, Shuxun Sang, Qipeng Zhu, Jiefang Zhang, Hefeng Gao, Huihu Liu and Lixing Lin Kc Micro- Km Flow behavior of methane Kc Flow behavior of water Figure 9. Flow behaviors of Warren-Root Model. it is ordinarily considered that: desorbed methane migrates form matrix to macro- with ; methane migrates from macro- to wellbore with and laminar flow; water also flows from macro- to wellbore with laminar flow. follows Fick s Law of diffusion and laminar flow follows Darcy s Law. Fick s Law of diffusion and Darcy s Law can be expressed as Eq. (1) and Eq. (2) (Pang et al., 2009; Fu et al., 2007; Zhang et al., 2003). C J = Df x or 2 f 2 C C = D t x where, J is the diffusion velocity; D f is the coefficient of Fick C diffusion; is the concentration gradient at diffusion x direction; C is the concentration of methane. (1) K v = gradp (2) μ where, v is the flow velocity of fluid; K is the permeability of medium; μ is the viscosity of fluid; gradp is the gradient of seepage pressure Without regarding the diffusion of methane in matrix, Warren-Root Model can depict characteristics of high-rank coal reservoir without hydraulic fracturing well. However, it is not the case in post fracturing high-rank coal reservoir. Firstly, hydraulic becomes the most important medium for water and methane flowing to wellbore. Water and gas mainly flow to hydraulic from macro- and then flows to wellbore from hydraulic. Secondly, hydraulic changes flow levels of fluid. One more medium (hydraulic ) and one more flow behavior (macro- to hydraulic ) appear in flow model. Thirdly, the diffusion of methane in pore- system is not only. Methane mainly migrates as transition diffusion in microbores, transition pores and ultramicroscopic fissures, and changes from transition diffusion to in mesopores, macropores and micro-fissures that can be regard as. Methane just migrates with in macro-s and hydraulic. So, without regarding the diffusion of methane in matrix, diffusion pattern of methane can be regard as. Finally, flow patterns of methane in mesopores, macropores and micro-fissures are not only laminar flow but also transition flow. Methane flows in macro- with transition flow and turbulent flow, flows with turbulent flow in hydraulic. So, Darcy s Law is no longer suitable for the seepage of methane in macro- and hydraulic. Inertia force should be considered. Because of the difference of flow patterns in macro- and hydraulic, Warren-Root Model can t give a comprehensive interpretation of seepage mechanism in post fracturing high-rank coal reservoir. 2.2 Modified Warren-Root Model In order to satisfy high-rank coal reservoir modeling, Warren-Root Model is improved and physical model of post fracturing high-rank coal in southern Qinshui Basin is established, based on the structure model and flow model of post fracturing high-rank coal reservoir Reservoir model According to the analysis above, hydraulic should be treated as an individual medium in post fracturing high-rank coal reservoir. Hydraulic in No. 3 coal bed reservoir is vertical, just extends in coal bed and is symmetric to wellbore. Hydraulic mainly extends at orientation with maximum principal stress and less extends at orientation with least principal stress. Only considering major hydraulic, coal bed reservoir is simplified to an ideal system with hydraulic, orthogonal macroscopic and cuboid matrix. Coal bed reservoir was divided into cuboids by hydraulic and further by macroscopic s (Fig. 10). Hydraulic is double wing, vertical, symmetric to wellbore and points to wellbore. The direction of hydraulic is in accordance with major permeability. Suppose that the width of hydraulic is a constant. The direction of macro- also is also in accordance with major permeability. Also suppose that the width of macro- is a constant. network can be uniform distribution or non-uniform distribution. is major preserving space of methane. Methane adsorbs in microbores and transition pores in matrix. s are not only major preserving spaces of water, but also major seepage channel of water and gas. Hydraulic is the major seepage channel of water and methane to wellbore Flow model Based on the modified Warren-Root reservoir model, flow model is established by flow patterns of post fracturing high-rank coal reservoir in southern Qinshui Basin. Without regarding the migration of methane in matrix, methane undergoes triple medium to wellbore which is three step flows. In physical model, triple medium means matrix (pore and micro-fissure), macro- and hydraulic. Water undergoes double medium to wellbore which is two step flows. In physical model, double medium means macro and hydraulic. Suppose that only hydraulic supplies water and methane to wellbore. and macro- don t supply water and methane to wellbore and matrix only supplies methane to macro- (Fig. 11). According to the flow patterns of post high-rank coal reservoir, in matrix, methane mainly migrates as transition diffusion in micropores, transition pores and ultramicroscopic fissures. Methane mainly flows as and laminar flow in mesopores and macropores. No. 3 coal bed reservoir in

7 Triple Medium Physical Model of Post Fracturing High-Rank Coal Reservoir in Southern Qinshui Basin 413 research area gives priority to micropores, transition pores, ultramicroscopic fissures and micro-fissures. Macropore and mesopore is non-development. So, diffusion pattern of methane in matrix can be regarded as transition diffusion which means that desorption methane in micropores and transition pores migrates as transition diffusion in matrix. Coefficient of transition diffusion can be expressed as Eq. (3) (Pang et al., 2009) = + (3) D D D P f k where, D P is the coefficient of transition diffusion; D k is 1 8RT the coefficient of Knudsen diffusion, Dk = r, and r 3 πm is the pore diameter/ width, R is the universal gas constant, T is the absolute temperature, M is the molar mass of methane. Without regarding the migration of methane in matrix, desorption methane in matrix mainly diffuses and flows to Hydraulic Methane Water Figure 10. Modified Warren-Root Model. Kf Hydraulic Kc Micro- Km Flow behavior of methane Kf Kc Hydraulic Flow behavior of water Figure 11. Flow behaviors of modified Warren-Root Model. macro-s through micro-fissures. The swap mode of methane between matrix and macro-s can be regarded as and laminar flow, and gives priority to laminar flow. Because that seepage pattern is laminar flow, and laminar flow belongs to time invariant seepage, the swap mode of methane between matrix and macro-s can be regarded as pseudo steady fluid channeling. Pseudo steady fluid channeling can be expressed by Barenblatt s equation of fluid channeling (Eq. (4)) (Kong, 2010; Ge, 2003). Methane migrates from macro- into hydraulic by Fick diffusion and transition flow (Fig. 12). Methane migrates from hydraulic into wellbore as and turbulent flow (Fig. 12). During diffusion process of methane to wellbore, diffusion follows Fick s Law of diffusion expressed by Eq. (1). Seepage of methane no long follows Darcy s Law during flow process. The influence of inertial force should be considered. The seepage can be expressed by binomial expression of non-linear fluid flow (Eq. (5)) (Kong, 2010; Ge, 2003). α Km q = ( Pm Pf ) (4) μ where, q is the rate of fluid channeling of methane between matrix and macro-facture; α is the form factor between matrix and macro-facture; K m is the permeability of matrix; P m is the pressure of matrix; P f is the pressure of macro-. dp μ 2 = v+βρv (5) dx K where, β is the factor of non-darcy flow; ρ is the density of fluid. Water in pores and micro-fissures of coal bed reservoir is often ignored because of the small amount. Water mostly occurs in macro-s. Water initially flows to hydraulic from macro-s, then flows to wellbore from hydraulic. Seepage patterns of water in macro- and hydraulic are both laminar flow and follow Darcy s Law (Eq. (2)) (Fig. 12). Methane Pseudosteady Fluid channeling Macroscopic Transition flow Hydraulic Transition flow Water Macroscopic Hydraulic Figure 12. Flow model of modified Warren-Root Model. According to the analysis above, flow model is established. (1) Methane undergoes triple medium to wellbore. Swap mode of methane between matrix and macro-s is pseudo steady fluid channeling and follows Barenblatt s equation of fluid channeling. Methane migrates from macros into hydraulic as and transition flow, and migrates from hydraulic to wellbore as and turbulent flow. follows Fick s Law of diffusion and seepage can be expressed by binomial expression of non-linear fluid flow (Fig. 12). (2) Water first flows to hydraulic from macros as laminar flow, then flows to wellbore from hydraulic as laminar flow. Seepage pattern of water follows Darcy s Law (Fig. 12). In conclusion, based on the Warren-Root Model, hydrau-

8 414 Shiqi Liu, Shuxun Sang, Qipeng Zhu, Jiefang Zhang, Hefeng Gao, Huihu Liu and Lixing Lin lic is treated as an individual medium according to the characteristics of structure and exploitation reality. The join of hydraulic gives good interpretations to the changes of flow patterns from macro-s to hydraulic and the great differences of water and gas production rate between post fracturing CBM wells and und CBM wells. So, modified Warren-Root Model is more suitable for post fracturing high-rank coal reservoir. According to modified Warren- Root Model, mathematical model of high-rank coal reservoir using for reservoir simulation study of southern Qinshui Basin can be established. 3 CONCLUSIONS (1) Hydraulic is the major flow channel for migration of water and methane to wellbore in southern Qinshui Basin. The amount of fluid supplied by macro-s to wellbore can be ignored. Flow patterns of methane in hydraulic are different from macro-s. Hydraulic should be treated as an individual medium. (2) Post fracturing high-rank coal reservoir in research area mainly develops one group of hydraulic with high permeability and high flow conductivity. Flow behaviors of methane and water make hydraulic as a type of individual medium. Methane goes through triple medium which is three step flows. Water undergoes double medium which is two step flows. Methane migrates from hydraulic into wellbore as and turbulent flow. Water flows from hydraulic to wellbore as laminar flow. (3) Warren-Root Model can depict characteristics of high-rank coal reservoir without hydraulic fracturing, but can t give a comprehensive interpretation of seepage mechanism in post fracturing high-rank coal reservoir well. Warren-Root Model is improved on basis of structure and flow model of post fracturing high-rank coal reservoir. Coal bed reservoir is simplified to an ideal system with hydraulic, orthogonal macroscopic and cuboid matrix. Coal bed reservoir was divided into cuboids by hydraulic and further by macroscopic s. Hydraulic is double wing, vertical and symmetric to wellbore. Swap mode of methane between matrix and macro- is pseudo steady fluid channeling and follows Barenblatt s equation of fluid channeling. Seepage of methane no long follows Darcy s Law and can be expressed by binomial expression of non-linear fluid flow. Seepage of water follows Darcy s Law. Modified Warren-Root Model can give a comprehensive interpretation of seepage mechanism in post fracturing high-rank coal reservoir. ACKNOWLEDGMENTS This study was supported by the National Natural Science Foundation of China (Nos , , , , and ), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), and Jiangsu Planned Projects for Postdoctoral Research Funds (No B). We thank Mengxi Li and Lilong Wang from the Shanxi CBM Branch of Huabei Oilfield Company for their supports. 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