Diffusional Effects in the Recovery of Methane From Coalbeds

Impact of unrecovered shale gas reserve on methane emissions from abandoned shale gas wells

Shale gas, with its abundance and lower carbon footprint compared to other fossil fuels, is an important bridge fuel in the ongoing energy transition. However, a notable concern in shale gas exploration is fugitive methane emissions during the extraction, development, and transport of natural gas. While most existing works evaluate methane emissions released by well fracking, completion and operation, the greenhouse footprint of unproductive shale gas wells (often abandoned or orphaned) has received little scrutiny. A large fraction of these emissions from abandoned shale gas wells are due to the diffusive transport of methane trapped in nanoporous shale matrix, which is poorly understood. Here, we develop a theoretical kinetic approach to predict methane diffusive flux from heterogeneous shale matrix. Our theoretical model is based on a layer sequence formulation and accurately considers multiple flow mechanisms, including viscous flow, gas slippage, and Knudsen diffusion and their mutual interactions. The model is validated against the observed methane diffusion data obtained from high-pressure and high-temperature experimental measurements on Marcellus shale. We find that methane diffusive flux increases as reservoir pressure decreases. We estimate methane emission due to diffusive transport up to 20 × 103 m3 per well per day, which is comparable to emissions from flowback fluid. For the first time, unrecovered natural gas in the shale matrix is demonstrated to be the main source of methane emissions from abandoned shale gas wells. Given the long-lasting nature of diffusive transport to shale gas seepage, it is suggested that regulatory requirements should be implemented to provide long-term monitoring of methane emissions from abandoned shale gas wells.

Effective Approach with Extra Desorption Time to Estimate the Gas Content of Deep-Buried Coalbed Methane Reservoirs: A Case Study from the Panji Deep Area in Huainan Coalfield, China

In this study, 11 core coal samples were collected from deep-buried coalbed methane (CBM) reservoirs with burial depth intervals of 900-1500 m for gas estimation content by a direct method. In desorption experiments, the cumulative gas desorption data were recorded within 2 h in the field on the basis of the China National Standard method. For accuracy, two improved methods were proposed. The results show that the gas contents of deep-buried coal samples based on the China National Standard and mud methods are 3.58-9.89 m³/t (average of 6.03 m³/t) and 3.74-10.05 m³/t (average of 6.20 m³/t), respectively. The proposed Langmuir equation and logarithmic equation methods exhibited nonlinear relationships between the cumulative desorption volume and desorption time, which yield values of 6.33-13.34 m³/t (average of 9.36 m³/t) and 6.15-13.86 m³/t (average of 10.37 m³/t), respectively. In addition, the two proposed methods combine the raw data within 2 h by the China National Standard method and additional desorption points during extra time, which are helpful for the ability of the hypothetical methods to calculate the gas content. The Langmuir equation method is a relatively more accurate method to estimate the gas content in comparison with the proposed logarithmic method, which is based on the relative error and comparison plots of actual data and simulated results. From the perspective of numerical value, the Langmuir equation method gives values 1.06-3.39 times (average of 1.86 times) those of the China National Standard method. These analyses show that the proposed Langmuir equation method with extra desorption points is an effective method to determine the gas content of deep-buried CBM reservoirs.

The Impact of Equilibrium Gas Pressure and Coal Particle Size on Gas Dynamic Diffusion in Coal

The diffusion coefficient of gases in coal varies with time. This study aims to develop an unsteady dynamic diffusion (UDD) model based on the decay of diffusion coefficient with time and the change of integral. This study conducted a series of gas desorption and diffusion experiments with three different combinations of particle sizes and gas pressures and compared the diffusion coefficients of the three models. The UDD model exhibited good fitting results, and both the UDD and bidisperse models fitted the experimental data better than the unipore model. In addition, the dynamic diffusion coefficient (DDe) decreased rapidly in the initial stage but gradually decreased to a stable level in the later stage. All the effective diffusion coefficients of the three models negatively correlated with the particle size. In the unipore model, the diffusion coefficient of coal samples with three particle sizes increased with gas pressure. In the bidisperse and UDD models, the diffusion coefficients (Dae, Die, and DDe) of 0.25–0.5 mm and 0.5–1.0 mm coal samples increased with gas pressure. However, DDe and Dae of 1.0–1.25 mm coal samples increased first and then decreased. Furthermore, Die decreased first and then increased, with no sign of significant pressure dependence. Finally, the correlation and significance between the constant and diffusion coefficient in the UDD model was investigated.

The effect of a tectonic stress field on coal and gas outbursts

Coal and gas outbursts have always been a serious threat to the safe and efficient mining of coal resources. Ground stress (especially the tectonic stress) has a notable effect on the occurrence and distribution of outbursts in the field practice. A numerical model considering the effect of coal gas was established to analyze the outburst danger from the perspective of stress conditions. To evaluate the outburst tendency, the potential energy of yielded coal mass accumulated during an outburst initiation was studied. The results showed that the gas pressure and the strength reduction from the adsorbed gas aggravated the coal mass failure and the ground stress altered by tectonics would affect the plastic zone distribution. To demonstrate the outburst tendency, the ratio of potential energy for the outburst initiation and the energy consumption was used. Increase of coal gas and tectonic stress could enhance the potential energy accumulation ratio, meaning larger outburst tendency. The component of potential energy for outburst initiation indicated that the proportion of elastic energy was increased due to tectonic stress. The elastic energy increase is deduced as the cause for a greater outburst danger in a tectonic area from the perspective of stress conditions.

Material-Balance Techniques for Coal-Seam and Devonian Shale Gas Reservoirs With Limited Water Influx

Summary

This paper presents the development of two material balance methods for unconventional gas reservoirs. One method is appropriate for estimating gas-in-place while the second is appropriate for making future reservoir predictions. These techniques differ from the material balance methods for conventional gas reservoirs, in that, the effects of adsorbed gas are included. Both methods are developed using the assumptions traditionally associated with the material balance approach. For estimating original gas-in-place, the additional assumption of equilibrium between the free and adsorbed gas phases is required (ie., gas desorption is assumed to be strictly pressure dependent). Simplified forms of this generalized equation corresponding to special cases (volumetric reservoirs, etc.) are also presented. No additional simplifying assumptions are required for making future reservoir predictions.

The results of both methods are compared to those of a rigorous finite-difference simulator developed specifically for unconventional gas reservoirs. These comparisons are made to determine the effects of all assumptions and the magnitude of these effects.

Due to the assumption of equilibrium, the first approach is appropriate for shut-in wells or flowing wells in reservoir undergoing rapid desorption. The assumption of rapid desorption corresponds to reservoirs with a high natural fracture density (small primary-porosity matrix blocks) or with a high diffusion coefficient.

It is believed that the techniques presented in this paper provide basic tools currently unavailable to engineers working with unconventional gas reservoirs.

Introduction

The material balance equation is one of the fundamental tools used to determine the original gas-in-place and production performance of conventional gas reservoirs. For conventional gas reservoirs, the material balance equation has the form:

Equation (1)

or, in terms of p/Z:

Equation (2)

These equations are derived with the following assumptions:

. The gas and reservoir rock are non-reactive.

. The reservoir acts as a constant-volume tank (ie., changes in porosity with pressure decline are negligible).

The Unsteady-State Nature of Sorption and Diffusion Phenomena in the Micropore Structure of Coal: Part 1 - Theory and Mathematical Formulation

Summary

A single-phase, 1D mathematical formulation is developed in radial/cylindrical coordinates to examine unsteady-state micropore sorption in a composite micropore/fracture, coalbed-methane transport problem. In the formulation, the micropore transport equation accounts for unsteady-state sorption and diffusion in the primary porosity. Gas entering the fracture network is considered a source term in the fracture-transport equation. The micropore and fracture systems are coupled by equating the gas pressure at the surface of the micropore elements to the pressure in the fracture network.

Introduction

Coalbed-methane reservoirs are characterized by a dual-porosity nature. Gas molecules stored in the micropore structure by adsorption are subject to desorption from the coal grain surfaces and to diffusional transport to a well-defined, natural fracture network. Laminar flow dominates in the fracture network where methane gas flows simultaneously with formation water.

Gas transport in the micropores is generally modeled with quasisteady- or unsteady-state sorption formulations. In the first case, the matrix-to-fracture gas transfer rate is calculated from the average concentration gradient in the matrix elements over a discrete timestep. In contrast, unsteady-state formulations use a nonuniform micropore concentration gradient to determine the matrix transfer rate. Quasisteady-state models offer the advantage of simplified mathematics, which can reduce computer simulation costs.

Reservoir Characteristics of Coal Seams. Coal seams are characterized by a natural fracture network commonly referred to as cleat. The cleat system consists of two perpendicular fissures, the more predominant of which is the face cleat. The butt cleat is less continuous and often ends when it intersects the face cleat. Fig. 1 is a highly idealized representation of the physical relationship between the matrix and fracture system.

Numerical Simulation of the Transient Behavior of Coal-Seam Degasification Wells

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.

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Dynamic Gas Slippage: A Unique Dual-Mechanism Approach to the Flow of Gas in Tight Formations

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.