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Technology Status Assessment Simulation of Shale Gas Reservoirs Incorporating Appropriate Pore Geometry and the Correct Physics of Capillarity and Fluid Transport The goals of this project are making available to the industry a shale gas simulator that captures all the relevant features to correctly simulate gas production, and water movement and production in shale-gas reservoirs. The selected pathway to this goal is to use commercial simulators for the basic framework and add new modules to incorporate the features needed for the shale-gas case. In the pre-project work a minimum complexity for the coupled pore and fracture system model has been identified. The conventional treatment of capillarity and fluid transport has also been found to be inadequate. This review first addresses the capacities of existing simulators in the light of the identified requirements. Then existing non-conventional approaches to capillarity and transport are reviewed.

Simulators Review The main commercial simulators available for simulation of shale gas reservoirs include CMG/GEM (Computer Modeling Group 2009), Eclipse/Eclipse 300 (Schlumberger 2009), COMET3 (Advanced Resources International Inc. 2010) and GCOMP (PHH Petroleum Consultants 2008). These simulators all model the reservoir as a 3D grid and simulate production by finite-difference solutions. Also available is PMTx (Phoenix Reservoir Software 2010), which provides an analytical modeling capacity for shale gas reservoirs that can be used as an auxiliary tool to supplement numerical simulators. Two widely used non-commercial simulators are UTCHEM (University of Texas 2000), which was developed for chemical flooding but provides insight for modeling shale gas flow, and PSU-COALCOMP (Penn State University), which was designed for coalbed methane simulation. VIP (Landmark) is not marketed, as shale gas simulator, although some operators may be using it for this purpose. CMG and ECLIPSE have integrated shale gas modules into their standard platforms; whereas other simulators such as GCOMP, PSU-COALCOMP, PMTx and COMET3 have been exclusively designed for unconventional reservoirs. The currently available simulators are successfully being used to produce history matches for gas production. Acceptable results (Cipolla et al., 2009a; Cipolla et al., 2009b; Rubin, 2010) involve considerable effort in reproducing complex hydraulic fracture networks by means of the gridding options available in commercial numerical simulators. Reservoir Model Structure Shale gas reservoirs are recognized as being comprised of four types of pore spaces: pores in the inorganic and organic regions of the rock, natural fractures and hydraulic fractures (Wang and Reed, 2009; Passey et al., 2010). Current studies based on sophisticated imaging methods (SEM images on ion milled samples) provide evidence of the existence of nano-meter scale pores imbedded within the organic (Kerogen) material present in the matrix (Wang and Reed, 2009; Ambrose et al., 2010; and Sondergeld et al., 2010). The matrix pore geometry at the least must account for water-wet, and or heterogeneous wettability pores in the inorganic matrix and hydrophobic pores in the organic matrix. The connectivity between these pore systems must be an adjustable variable. That is the matrix cannot be described by a single wettability. Additionally, fractures formed throughout the reservoir formation (natural fractures) and fractures induced by stimulation procedures (hydraulic fractures) must be independently treated. The natural fractures are most likely water-wet but the hydraulic-fracturing treatments might cut through zones of organic material, therefore wettability in the induced fractures needs to be fractionally wet. The connectivity between the fracture systems and the matrix system is again an adjustable parameter (Civan and Rasmussen, 2001). Available simulators do not seem to be set up to allow two matrix pore systems with different properties in a single grid block. Commercial systems provide for models that allow both fracture and pore systems but the current implementations do not seem to allow for the generality of model structure that shale gas reservoirs exhibit. Eclipse, CMG/GEM, UTCHEM, COMET and PSU-COALCOMP implement sub-gridding of dual porosity systems (Reeves and Pekot, 2001;Zhang et al., 2009). Matrix subdivision leads to a triple-porosity/dual-permeability approach where gas desorbs from the internal matrix block surfaces, then migrates by Darcy flow through micro-permeability in the matrix and finally in the fractures to the wellbore. Fluid Storage Gas storage in stimulated shale gas reservoirs is the sum of adsorbed/absorbed gas in the kerogen material and free gas stored in void spaces of the rock (inorganic matrix porosity, microfracture porosity, hydraulic fractures and

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pores in the organic matter) (Ambrose et al., 2010; Rahmanian et al., 2010; Aguilera, 2010). Commonly, the gas adsorbed/absorbed by the rock matrix is specified by a Langmuir isotherm. When the simulation involves compositional analysis the Langmuir isotherm is replaced by the Extended Langmuir Isotherm (Ruthven 1984; Arri et al. 1992). Straightforward calculations (see for example Ambrose et al., 2010), show that for organic pores on the nano-meter size scale the volume occupied by the adsorbed gas significantly reduces the volume available for free gas, so that gas storage is not a simple linear sum of adsorbed state gas and gas in a pressure independent free gas volume. In addition, pore volume changes due to rock compressibility need to be accounted for (Kang et al., 2010). PMTx takes into account porosity and permeability as functions of pressure (stress). Beyond that, PSU-COALCOMP (Siriwardane et al., 2006), COMET3 (Kuuskraa et al., 1992), ECLIPSE and CMG have shrinking/swelling capabilities to account for rock volume variations due to sorption during production of methane or CO2 injection (enhanced recovery) (Hower, 2003; Siriwardane et al., 2006). Geomechanical modeling packages (such as VISAGE) independently simulate in-situ stress distribution, stress sensitive permeability and porosity changes. Reservoir simulators and geomechanical modeling platforms can be coupled (Du et al., 2009). To be exact though storage has to be explicitly divided among the four pore types each with different storage pressure dependence. This would require modification of the currently available simulators. Fluid Transport Absolute Permeability Gas transport in a generic nano-porous material is an open research topic. For single-phase fluids the transport mechanism is a function of pressure and temperature. As pressure reduces it transforms from Darcy (viscosity controlled flow) to free molecular flow (Karniadakis, 2005). Transport in pores outside of the Darcy regime is generally treated as Knudsen diffusion (Karniadakis, 2005). Adsorbed gas on the surface of organic pores is released into the organic pores. This modifies the distribution of gas in the organic pores, and the effective pore size so the permeability of the organic porous media is a complex function of pressure. There is no explicit inclusion of Knudsen diffusion in the available simulation packages. Flow in the fractures can be accurately described by Darcy law (Wang and Reed, 2009)for relatively slow flow and the Forchheimer equation when the flow is rapid and thus involves inertial effect owing to convective acceleration. Relative Permeability Two issues are of concern with relative permeability curves. One is need for different curves in organic pores, inorganic pores, and two kinds of fractures because of difference in wettability. The other is rate dependence because of its effect on deviation of fluid saturation from equilibrium. ECLIPSE, CMG/GEM and UTCHEM allow different relative permeability data for different locations within the porous system geometry, accounting for anisotropy, different wettabilities and heterogeneity capabilities of the simulation tool. Proper definition of the simulation problem exhibits a relative permeability data set for each porous medium. Then, for a fractured medium relative permeability data for both system; fracture and matrix are required. Relative permeability data is usually available as input data. Nevertheless numerical simulators allow construction of relative permeability curves by means of Corey-type correlations (CMG presents a user-friendly application for relative permeability curve design). Additionally, scanning modules result in hysteresis relative permeability curves in case saturation path exhibits any change during the simulation (displacement history). In typical simulators irreducible water and gas saturations are constants that enter only through the relative permeability curves. Because of the small pore size, capillary forces can dominate fluid transport in shale gas reservoirs; this standard approach does not capture the effects of flow controlled by capillary forces. This is seen in standard laboratory measurements of ordinary rocks where multi-phase flow is stopped when water is no longer being produced from the sample. The sample is then centrifuged and the water saturation is reduced due to capillary drainage. That is flow rate dependent relative permeability curves need to be introduced to correctly model the gas and water transport. Relative permeability curves are actually dynamic functions of both space and time (Tyagi et al., 2007). In tight reservoirs such as shale gas the assumption of the existence of a steady-state saturation at which relative permeability curves are evaluated is likely never attained. In such case, relative permeabilities cannot be assumed as unique functions of saturation. They may be rate dependent. Non-equilibrium formulation for capillarity

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The assumption of instantaneous capillary equilibrium (correct for conventional reservoirs) is used in conventional simulators. For tight-gas sand and shale-gas reservoirs the assumption of instantaneous capillary equilibrium is an inadequate approximation because redistribution of fluid phases in tight formations is a slow process. Andrade et al. (2010) used a theoretical approach to investigate the effect of relaxing this condition for a core flood and found it significant. Available shale gas simulators in general all assume instantaneous capillary equilibrium.

Theoretical Review Capillarity Tyagi et al. (2007) show that the relative permeability and capillary pressure curves cannot be assumed functions of phase saturations alone and these curves are functions of both space and time. When fluid conditions in porous media are varied, the fluid adjusts its distribution throughout the porous media accordingly until a new steady-state is attained. Barenblatt et al. (2003) emphasize that transition and redistribution from one equilibrium-state to another equilibrium-state does not occur instantaneously and may in fact require a substantial amount of time. The redistribution time representing the characteristic time-scale of this process to take place effectively varies with the saturation of the wetting fluid. Its value is zero at zero saturation and approaches infinity as saturation approaches unity.

The relaxation time concept reasonably describes the transition through the meta-stable states. However, its quantification has been implemented in various ways. Barenblatt et al. (1995) assumed that the relaxation time is a function of the reciprocal-capillary pressure derivative. However, Barenblatt et al. (2003) used a constant value for the relaxation time. Silin and Patzek (2004) assumed that the relaxation time is a function of instantaneous saturation, becoming zero at the irreducible water saturation and infinity at the residual oil saturation. Multivariate power-law type correlations were also recommended and demonstrated for correlation of the relaxation time (Downar-Zapolski et al., 1996; Badur and Banaszkiewicz, 1998; Civan, 2006; Michael and Civan, 2006).

Alternatively, Gupta and Civan (1994) and Rasmussen and Civan (1998) presented approaches based on the kinetics description of the fluid redistribution processes at three stages, namely the matrix, matrix-fracture interface, and fracture media, each described by separate rate equations with different process kinetics. Gallego et al. (2006) demonstrated the validity of this approach by means of experimental data.

Fluid Transport Recent publications discuss the relevant importance of Knudsen diffusion in the shale permeability (Freeman et al., 2010; Wang and Reed, 2009). Florence et al. (2007) discuss a theoretical model to calculate the intrinsic permeability of formation from the apparent permeability using a correction as a function of the dimensionless Knudsen number (Freeman et al., 2010; Rahmanian et al., 2010). Complexity of Knudsen diffusion and slip flow have been coupled resulting in Darcys law-type formulations (Javadpour ,2009; Florence et al., 2007; Civan, 2010). This particular kind of formulation can be easily implemented in any numerical simulator capable of Darcys flow modeling. Essentially, derivations presented by Javadpour (2009), Florence et al. (2007)and Civan (2010) come from reviewing the Hagen-Poiseuille-model. Kang et al. (2010) discuss models of transport in nanometer scale adsorbing media and find that transport in the adsorbed phase is significant and provides a separate additional term in the total transport equation. Apparent permeability is not only a property of the rock; as it is the intrinsic (true) permeability, but it is also function of properties of flowing gas at specified pressure and temperature (Javadpour, 2009). Civan (2010) remarks and improves critical deficiencies of previous models to correlate intrinsic and apparent permeability by means of a more accurate and practical approximation

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