Summary A mathematical formulation, applicable to both numerical simulation and transient well analysis, that describes the flow of gas in very tight (k8<0.1md) porous media and includes a dual-mechanism transport of gas is developed. Gas is assumed to be traveling under the influence of a concentration field and a pressure field. Transport through the concentration field is a Knudsen flow process and is modeled with Fick's law of diffusion. Transport through the pressure field is a laminar process and is modeled with Darcy's law (inertial/turbulent effects are ignored). The combination of these two flow mechanisms rigorously yields a composition-, pressure-, and saturation-dependent slippage factor. The pressure dependence arises from treating the gas as a real gas. The derived dynamic slippage is most applicable in reservoirs with permeabilities 0.01 md. The results indicate that in reservoirs of this type, differences between recoveries after 10 years of production with the dynamic-slip and constant-slip approaches were as great as 10%, depending on the initial gas saturation. If an economic production rate is considered, differences as great as 30% can be expected. Introduction lt has been estimated that 400 to 1,000 Tcf [11l.3×1012 to 28.3×1012 m3] of natural gas are trapped in formations designated as "tight sands" (k8<0.1 md). Also, another 300 to 2,700 Tcf [8.5×1012 to 76.5×1012 m3] of natural gas may be trapped in other low-permeability formations, such as Devonian shales and coal seams. The application of Darcy's law to gas flow in these low-permeability formations requires a correction for the Klinkenberg effect (gas slippage across the capillary walls of the pore channels). This correction takes the form of a slippage factor, b, in the Klinkenberg equation:Equation 1 Klinkenberg2 made the following observations:Fig. 1, 2, and 3** show that the apparent permeability is approximately a linear function of the reciprocal mean pressure. This linear function, however, is an approximation, as becomes evident from Tables 5, 6, and 7*** wherein the value of constant b increases with increasing pressure.Even with an idealized pore system, the factor b cannot be expected to be constant, as the theory of Kundt and Warburg cannot be applied to the flow of gas through a capillary if the mean free path is no longer small compared with the radius of the capillary (i.e., deviations to be expected at reduced pressures).This change in the factor b however, will not be discussed here in detail. Rose3 and, more recently, Sampath and Keighin4 conducted gas flow experiments in cores partially saturated with water. Their results show that the slope of the line ka vs. 1/p (i.e., the slippage effect) decreases with increasing water saturation. During depletion, a gas reservoir undergoes changes (both in time and location) in pressure and saturation. The effect of slippage, therefore, varies throughout the life of the reservoir. To date, no detailed theoretical or experimental investigation has been conducted regarding the dynamic behavior of gas slippage. This is surprising because of the large reserves of gas trapped in tight formations. We have developed a dynamic slippage model that is similar to the approach of Adzumi5 for slip through capillary tubes. This approach, based on simultaneous flow resulting from viscous (Darcian) and diffusion (Fickian) flow processes, yields a pressure-, composition-, and saturation-dependent slippage factor. In this way, it is possible to build the time- and space-dependent character of the slippage phenomenon into the gas-transport equation in porous media.

Summary One primary goal of any enhanced recovery project is to maximize the ability of the fluids to flow through a porous medium (i.e., the reservoir). This paper discusses the effect of capillary number, a dimensionless group describing the ratio of viscous to capillary forces, on two-phase (oil-water) relative permeability curves. Specifically, a series of steady-state relative permeability measurements were carried out to determine whether the capillary number causes changes in the two-phase permeabilities or whether one of its constituents, such as flow velocity, fluid viscosity, or interfacial tension (IFT), is the controlling variable. For the core tests, run in fired Berea sandstone, a Soltrol 170™ oil/calcium chloride (CaCl2) brine/isopropyl alcohol (IPA)/glycerin system was used. Alcohol was the IFT reducer and glycerin was the wetting-phase viscosifier. The nonwetting-phase (oil) relative permeability showed little correlation with the capillary number. As IFT decreased below 5.50 dyne/cm [5.50 N/m], the oil permeability increased dramatically. Conversely, as the water viscosity increased, the oil demonstrated less ability to flow. For the wetting-phase (water) relative permeability, the opposite capillary number effect was shown. For both the tension decrease and the viscosity increase (i.e., a capillary number increase) the water permeability increased. However, the water increase was not as great as the increase in the oil curves with an IFT decrease. No velocity effects were noted within the range studied. Other properties relating to relative permeabilities were also investigated. Both the residual oil saturation (ROS) and the imbibition-drainage hysteresis were found to decrease with an increase in the capillary number. The irreducible water saturation was a function of IFT tension only. A relative permeability model was developed from the experimental data, based on fluid saturations, IFT, fluid viscosities, and the residual saturations, by using regression analysis. Both phases were modeled for both the imbibition and the drainage processes. These models demonstrated similar or better fits with experimental data of other water- and oil-wet systems, when compared with existing relative permeability models. The applicability of these regression models was tested with the aid of a two-phase reservoir simulator. Introduction As world oil reserves dwindle, the need to develop EOR techniques to maximize recovery is of great importance. Methods such as chemical flooding, miscible flooding, and thermal recovery involve altering the mobility and/or the IFT between the displacing the displaced fluids. Recovery efficiency was found to be dependent on the capillary number, defined asEquation 1 The viscous forces were defined as the fluid viscosity, flow velocity, and the flow path length. Capillary forces vary with the fluid IFT and the pore geometry of the medium.1 Taber defined the capillary number in terms of the pressure drop between two points, the flow length, and the IFT.2Equation 2 He concluded that as this ratio increased to a value of 5 psi/ft/dyne/cm [0.2 kPa/m/N/m] the ROS was reduced significantly. By decreasing the IFT by using surface-active agents, or by decreasing the path length by altering the field geometry, the capillary number could be increased. Others have shown similar results. Melrose and Brandner,3 for example, indicated that as the capillary number rose to a value of 10–4, the microscopic displacement efficiency, which accounts for the residual saturations to both oil and water, increased. The effects of the capillary number on the recovery of residual oil are given by Chatzis and Morrow4 and by other authors5 (Fig. 1). Few studies, however, have shown the effect of the capillary number on the two-phase flow between the residuals. The variables within this group have been researched, but their combined effect on relative permeabilities has been largely ignored. Several authors have noted that the viscosity ratio of oil and water alters the oil relative permeability but has little effect on that of water.6–8 Few or no changes by fluid flow velocity were observed, provided that no boundary effects were present during the core tests.9–11

Summary This paper describes the mathematical and numerical developments for a series of finite-difference models that simulate the simultaneous flow of water and gas through dual-porosity coal seams during the degasification process. Models for unstimulated and hydraulically stimulated degasification wells are included in this series. The hydraulically stimulated wells are assumed to be intercepted by a single infinite- or finite-conductivity vertical fracture. Introduction Unconventional natural gas has been defined as pipeline- quality (high-Btu-content) gas produced from resources other than those historically exploited by the oil and gas industry. These unconventional gas resources include geopressured aquifers, tight sands (koo less than 0.1 md), Devonian shales, and coal seams. The potential of unconventional gas, broken down by each resource, is presented in Table 1. In addition to the pricing incentives associated with unconventional natural gas (unconventional gas prices are unregulated under Sec. 107 of the 1978 Natural Gas Policy Act), several geographic and economic factors make the future of gas production from coal seams quite promising.1.Many producible coal seams are in the eastern U.S., close to established pipelines and markets. 2.Most major domestic coal seams are thought to have been discovered before or during the industrial revolution (see Fig. 1). These seams are well characterized; therefore, exploration costs would be minimal. 3.Many major domestic coal seams are shallow (depths less dm 1,000 ft [300 ml). Therefore, drilling costs would be minimal. 4.Drilling, completion, and stimulation technology borrowed from the natural gas industry have been well developed. 5.The gas from coal seams is generally sweet, requiring only dewatering, metering, and compression facilities at the surface. In addition, there are other incentives for producing gas from coal seams when the seam in question is minable:mining safety can be increased;mining rates can be increased; andmining costs, especially for ventilation systems, can be reduced. Coal Gas Coal gas is a byproduct of the physical and chemical reactions associated with the coalification process (the process by which vegetable matter is converted to coal). process by which vegetable matter is converted to coal). Consequently, coal seams are different from conventional gas reservoirs because the coal acts as both the source rock and the reservoir rock for the gas. Approximately 46 Mscf [1300 std m ] of gas are evolved during the formation of 1 ton [0. 907 Mg] of coal. Coal gas is composed primarily of methane and CO2, with trace amounts of higher-molecular-weight hydrocarbons and other gases-such as oxygen, nitrogen, and helium. Table 2 lists the compositions of gases from several domestic coal seams. Samples of gases from virgin coal seams yield calorific values that range from 900 to 1075 Btu/scf [34 x 10 to 40 x 10 kj/M ]; this makes these gases commercially profitable with little processing. Gas from gob (previously mined areas) may contain 25 to 60 vol % air and generally needs processing to upgrade it to commercial quality. Coal Seams as Natural Gas Reservoirs Pore Structures. Coal seams are characterized by a Pore Structures. Coal seams are characterized by a dualporosity nature: they contain both a micropore (primary porosity) and macropore (secondary porosity) system. The porosity) and macropore (secondary porosity) system. The micropores have a diameter ranging from 5 to 10 k [0.5 to 1.0 mn] and exist in the coal matrix between the seam's cleat (uniformly spaced natural fractures). Because of the dimensions of the micropores, the micropore system is inaccessible to water, The macropore system is made up of the volume occupied by the cleat. The fracture spacing is very uniform and ranges from a fraction of an inch to several inches. Two types of cleat are present in coal: the face and butt cleat. The face cleat is continuous throughout the seam while the butt cleat in many cases is discontinuous, ending at an intersection with the face cleat. Generally, the face and butt cleats intersect at right angles. The dimensions of the macropores may vary from aperture widths on the order of angstroms to microns. There do not appear to be any transitory pores between the two systems. SPEFE p. 165

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Summary A parametric study is conducted to investigate the effects of reservoir properties on gas drainage efficiency. It is found that when a coal seam is opened to production, the gas desorption and production rates increase to a maximum value and then decline. The magnitude of the early desorption peak was found to be a function of (1) the ability of the micropore matrix to supply gas to the macropore system, and (2) the coal seam's conductivity to water. The desorbing gas was observed to create a localized, high-gas-saturation bank in the area enclosed by the pressure transient. The gas bank provided an internal pressure maintenance to the reservoir, while it decreased the relative permeability to brine. This created a competing effect with respect to water production. Because water removal strongly influences the pressure decline and, consequently, the desorption rate, a unique production mechanism was observed. The study explored the interference effects on gas and water flow in multiple-well systems. It was found that the pressure drawdown caused by the multiple wells enhanced the desorption of gas into the macropore system and caused a positive interference effect on the gas flow rate. The water rate, however, encountered the more conventional negative interference effect. Introduction During the metamorphosis of organic material to coal, vast quantities of methane gas are produced and retained by the coal. It has been estimated that during the formation of 1 ton [0.9 Mg] of coal, up to 46 Mscf [1303 std m3] of gas is produced. In a study comparing the anthracitic coalbeds of northern Pennsylvania with the bituminous coalbeds of southern Illinois, Darton found that most mature coal contains between 20 and 100 scf [0.566 and 2.832 std m3] of methane per ton. With the onset of energy conservation, much attention has been given to unconventional gas resources. Unconventional natural gas can be defined as gas produced from resources other than those historically exploited by the oil and gas industry. Unconventional gas resources include tight gas formations, eastern gas shales, coal seams, and geopressured aquifers. Estimates of technically recoverable gas contained in domestic coalbeds range from 300 × 10 12 to 800 × 10 12 Scf [8495 × 10 9 to 22 653 × 109 M3]. This gas is high-quality and requires little or no processing before transmission. Reservoir characteristics of coalbeds are quite complicated, which makes mathematical modeling a challenge. The coal matrix is heterogeneous and characterized by two distinct porosity systems: macropores and micropores. The macropores (commonly known as cleat in the coal industry) constitute the cracks and fissures inherent in all coals. The cleat system is composed of two major components: the face cleat and butt cleat. The face cleat is continuous throughout the reservoir and is capable of draining large areas, the butt cleat, on the other hand, is discontinuous usually terminating at an intersection with the face cleat (see Fig. 1). Butt cleats contact a much smaller area of the reservoir and thus are limited in their drainage capacities. The micropore system consists of the primary-porosity matrix that exists between the cleat. This primary-porosity matrix that exists between the cleat. This system is not accessible to water. Gas flow does occur, however, but is considered restricted to diffusional flow. The major portion of gas stored in coal exists in an adsorbed state, rather than in a free state. When the system is in equilibrium, the free gas saturation is negligible. As water is removed from the macropores, the reservoir pressure is lowered, causing gas to desorb from the pressure is lowered, causing gas to desorb from the micropore surfaces and to diffuse into the macropores. The free gas saturation in the macropore system increases as the desorption process continues until the critical saturation for flow is reached. On reaching this critical value, the gas becomes mobile and is subject to transport in the fractures of the macropore system (Fig. 2). The methane drainage process of coal seams is analogous to the two-porosity system described by Warren and Root. The Warren and Root model applies to fractured hydrocarbon reservoirs that contain both a low-permeability, high-storage, primary-porosity system and a high-permeability, low-storage, secondary-porosity system. Flow can occur only between the primary- and secondary-porosity systems but cannot take place through the primary-porosity elements.

Shales and some tight gas reservoirs have complex, multi-model pore size distributions, including pore sizes in the nanopore range, causing gas to be transported via multiple flow mechanisms through the pore structure. In 1986, Ertekin et al. developed a method to account for dual mechanism (pressure-and concentration-driven) flow for tight formations that incorporated an apparent Klinkenberg gas-slippage factor that is not a constant, which is commonly assumed for tight gas reservoirs. In this work, we extend the dynamic-slippage concept to shale gas reservoirs, for which it is postulated that multi-mechanism flow can occur. Inspired by recent studies that have demonstrated the complex pore structure of shale gas reservoirs, which may include nanoporosity in kerogen, we first develop a numerical model that accounts for multimechanism flow in the inorganic and organic matter framework using the dynamic-slippage concept. In this formulation, unsteady-state desorption of gas from the kerogen is accounted for. We then generate a series of production forecasts using the numerical model to demonstrate the consequences of not rigorously accounting for multi-mechanistic flow in tight formations. Finally, we modify modern rate-transient methods by altering pseudovariables to include dynamic-slippage and desorption effects and demonstrate the utility of this approach with simulated and field cases. The primary contribution of this work is therefore the demonstration of the use of modern rate transient methods for reservoirs exhibiting multimechanistic (non-Darcy) flow. The approach is considered to be useful for analysis of production data from shale gas and tight gas formations as it captures the physics of flow in such formations realistically.

Shales and some tight-gas reservoirs have complex, multimodal pore-size distributions, including pore sizes in the nanopore range, causing gas to be transported by multiple flow mechanisms through the pore structure. Ertekin et al. (1986) developed a method to account for dual-mechanism (pressure-and concentration-driven) flow for tight formations that incorporated an apparent Klinkenberg gas-slippage factor that is not a constant, which is commonly assumed for tight gas reservoirs. In this work, we extend the dynamic-slippage concept to shale-gas reservoirs, for which it is postulated that multimechanism flow can occur. Inspired by recent studies that have demonstrated the complex pore structure of shalegas reservoirs, which may include nanoporosity in kerogen, we first develop a numerical model that accounts for multimechanism flow in the inorganic-and organic-matter framework using the dynamicslippage concept. In this formulation, unsteady-state desorption of gas from the kerogen is accounted for. We then generate a series of production forecasts using the numerical model to demonstrate the consequences of not rigorously accounting for multimechanism flow in tight formations. Finally, we modify modern rate-transient-analysis methods by altering pseudovariables to include dynamic-slippage and desorption effects and demonstrate the utility of this approach with simulated and field cases. The primary contribution of this work is therefore the demonstration of the use of modern rate-transientanalysis methods for reservoirs exhibiting multimechanism (non-Darcy) flow. The approach is considered to be useful for analysis of production data from shale-gas and tight-gas formations because it captures the physics of flow in such formations realistically.

Development and validation of a three-dimensional, twophase, dual porosity, fully implicit, compositional coalbed simulator are presented. Multicomponent sorption equilibria using a thermodynamically consistent ideal adsorbed solution (IAS) theory is implemented to the simulator using a non-equilibrium sorption formulation. The sorption model accounts for the nonideality of the free gas phase, as partial fugacity of the gas component is calculated using the Peng-Robinson equation of state. Model predictions of multicomponent sorption of methane, nitrogen and carbon dioxide mixtures on the coal are found to be in good agreement with experimental measurements. The transport component of the compositional coalbed simulator is verified using an existing two-phase coalbed simulator. Introduction Enhanced coalbed methane recovery by means of injecting other gases into coalbed reservoirs is an attractive recovery technique. Reznik et al.(1) reported their experimental results of carbon dioxide injection in coal seams that can yield close to 100% methane recovery. Similar work performed by Puri and Yee(2) showed that almost all methane adsorbed to coal can be stripped by nitrogen. Modelling of carbon dioxide and nitrogen injection in enhanced coalbed methane recovery processes cannot be accurately achieved using conventional two-phase fluid flow formulations. The complex physico-chemical processes encountered require multicomponent gas sorption formulation to be coupled with compositional fluid flow formulation in coalbed reservoirs. Seidle and Arri(3) proposed a procedure to adapt conventional black oil reservoir models for coalbed methane simulation purposes. In their approach, adsorbed gas is modelled by gas dissolved in immobile oil where adsorption capacity in the physical coalbed is replaced by the solution gas-oil ratio in a black oil model. For a multicomponent gas system, they suggested to use Langmuir sorption constants and molar solution gas-oil ratio to calculate oil-gas equilibrium ratios (K-values). These K-values, together with the free gas concentration, are then used to calculate the adsorbed gas phase mole fraction and the adsorption capacity. Implementing this technique to conventional simulators with a K(p) approach, one can model compositional fluid flow in coalbed methane reservoirs without changing the original computer codes. This technique, however, requires alterations to the porosity, saturations, relative permeabilities and oil phase PVT properties data. Stevenson et al.(4) examined the validity of the thermodynamically consistent IAS and real adsorbed solution (RAS) theories in the prediction of multicomponent sorption at in-seam conditions. Later, Stevenson et al.(5) implemented this multicomponent sorption to their compositional, two-phase coalbed reservoir simulator and performed an economic evaluation and analysis of nitrogen injection for coalseam gas recovery. In these two works, information on the mathematical description of the compositional fluid flow formulation and an explanation on how to implement the sorption modelto the flow equation are not included. The principal objective of this paper is to describe the development of mathematical and numerical models of the simultaneous flow of multicomponent gas and water in coalbed reservoirs. Formulations implement the thermodynamically consistent ideal adsorbed solution (IAS) theory, which can be used as a tool to study the potentials of enhanced coalbed methane recovery in field scale coalbed reservoir simulators.