Reservoir Simulation in CBM

5.2.1 Numerical Models in CMG-GEM

Coal is heterogeneous, comprising of micropores (matrix) and macropores (cleats).

Cleats is a distinct network of natural fractures and can be subdivided into face and butt cleats. Typically, cleats are saturated with water in the virgin coalbeds of the US, and no methane is adsorbed to the surface of cleats (Pillalamarry et al., 2011). It is not possible to explicitly model individual fractures since the specific geometry and other characteristics of the fracture network are generally not available. To circumvent this challenge, a

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porosity model (Warren and Root, 1963) was proposed to describe the physical coal structure for gas transport simplification. This model does not require the knowledge of the actual geometric and hydrological properties of cleat systems. Instead, it requires average properties, such as effective cleat spacing (Zimmerman et al., 1993). Based on this model, gas transport can be categorized into three stages as desorption from coal surface, diffusion through the matrix and from the matrix to cleat network, and Darcy's flow through cleat system and stimulated fractures towards wellbore (King, 1985; King et al., 1986). The rate of viscous Darcian flow depends on the pressure gradient and permeability of coal. In contrast, gas diffusion is concentration-driven, and the diffusion coefficient quantitatively governs its rate. However, the application of Warren and Root model (cubic geometric model) to CBM reservoirs depicts matrix as a high-storage, low-permeability, and primary-porosity system and cleats as a low-storage, high permeability and secondary-primary-porosity system (Thararoop et al., 2012). Based on this concept, matrix flow within the primary-porosity system is ignored, and gas flow can only occur between matrix and cleats and through cleats (Remner et al., 1986). In fact, the assumption that the desorbed gas from the coal matrix can directly flow into the cleat system has been shown to frequently engender erroneous prediction of CBM performance, where gas breakthrough time was underestimated, and gas production was overestimated (Reeves and Pekot, 2001).

Especially for those mature CBM fields at low reservoir pressure, gas diffusion through coal matrix cannot be ignored, and it can be the determining parameter for the overall gas output from the wellbore. For mature wells, gas deliverability of cleats can be orders of magnitude higher than it of the matrix due to sorption-induced matrix shrinkage (Clarkson

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et al., 2010; Liu and Harpalani, 2013b). Thus, coal permeability may not be as the limiting parameter for gas flow and production, and the ability of gas to desorb and transport into cleat/fracture system takes the determining role to define the late stage production decline behavior of CBM wells. A better representation of CBM reservoirs as a porosity, dual-permeability systems has been implemented in the latest modeling works (Reeves and Pekot, 2001; Thararoop et al., 2012) with the implication that matrix provides alternate channels for gas flow on top of fluid displacement through cleats. Their study showed a promising agreement between simulated results and the field productions with consideration of diffusive flux from the matrix to the cleat/fracture system.

5.2.2 Effect of Dynamic Diffusion Coefficient on CBM Production

Gas in coal primarily resides in the adsorbed phase on the surface of micropores, where sorption kinetics and diffusion process control gas transport from matrices towards cleats. Diffusion rate is typically characterized by sorption time. By definition, sorption time is a function of the diffusion coefficient and cleat spacing (Sawyer et al., 1987) is commonly used to quantify gas matrix flow in commercial CBM simulators. The past simulation results proved that CBM reservoirs with a shorter sorption time (faster desorption/diffusion process) would have a higher peak gas production rate as well as higher cumulative gas production at the early production stage (Remner et al., 1986;

Ziarani et al., 2011). The underlying mechanism of this phenomenon is that desorbed gas would accumulate in the low-pressure region around the wellbore until critical gas saturation was reached. The formulation of the gas bank would inhibit the relative

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permeability of water. At the same time, increase the mobility of gas such that a higher diffusion rate or smaller sorption time with a stronger gas bank is expected to have a higher gas production rate at the de-watering stage. These results demonstrated that the diffusional flow of gas in the coal matrix has a significant influence on gas production behavior within the CBM well throughout its life cycle. Diffusion coefficient (𝐷), as discussed, describes the significance of the diffusion process and varies with pore structure and pressure of matrix. Albeit the sorption time or diffusion coefficient can be a dominant factor controlling the gas production of a CBM well, most reservoir models are comparable to Warren and Root (1963) model. These models always assume that total flux is transported through cleats, and the high-storage matrix only acts as a source feeding gas to cleats with a constant sorption time. It is apparent that this traditional modeling approach violates the nature of gas diffusion in the coal matrix, where the diffusion coefficient is a pressure-dependent variable rather than a constant during gas depletion as discussed in Chapter 2 and Chapter 4. As expected, the traditional modeling approach may not significantly mispredict the early and medium stage of production behavior since the permeability is still the dominant controlling parameter. However, the prediction error will be substantially elevated for mature CBM wells which the diffusion mass flux will take the dominant role of the overall flowability. This prediction error will result in an underestimation of gas production in late stage for mature wells.

This study intends to investigate the impact of the dynamic diffusion coefficient on CBM production throughout the life span of fairway wells. The numerical method was adopted to simulate the gas extraction process as the complexity of sorption and diffusion

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processes make it is impossible to solve the analytical solutions explicitly (Cullicott, 2002).

Currently, cleat permeability is still the single most important input parameter in commercial CBM simulators, including the CMG-GEM, and IHS-CBM simulator to control the gas transport in coal seam (CMG‐GEM, 2015; Mora et al., 2007). Numerous studies (Clarkson et al., 2010; Liu and Harpalani, 2013a, 2013b; Shi and Durucan, 2003a;

Shi and Durucan, 2005) reported the cleat permeability growth during depletion in San Juan Basin that has been elaborately implemented in current CBM simulators. Regarding the mass transfer through the coal matrices, we want to point out that these simulators always assume a constant diffusion coefficient/sorption throughout the simulation time span. This assumption contradicts both the experimental observations in literatures (Mavor et al., 1990a; Wang and Liu, 2016) and this work in Chapter 4, and theoretical studies in Chapter 2 on gas diffusion in the nanopore system of coal, where the diffusion coefficient was found to be highly pressure- and time-dependent. There are minimal studies on the dynamic diffusion coefficient of coal and how it affects CBM production at different stages of depletion. This current study provides a novel approach to couple the dynamic diffusion coefficient into current CBM simulators. The objective is to implicitly involve the progressive diffusion in the flow modeling to enable the direct use of lab measurements on the pressure-dependent diffusion coefficient in the numerical modeling of CBM and improve the well performance forecasting. For this purpose, numerically simulated cases are critically examined to match the field data of multiple CBM wells in the San Juan fairway region. The integration of pressure-dependent diffusion coefficient into coal reservoir simulation would unlock the recovery of a larger fraction of gas in place in the

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fairway region, which also improves the evaluation of the applicability of enhanced recovery in San Juan Basin.