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

Transient Pressure Behavior of CBM Wells during the Injection Fall-Off Test Considering the Quadratic Pressure Gradient

Conventional coalbed methane (CBM) reservoir models for injection fall-off testing often disregard the quadratic pressure gradient's impact. This omission leads to discrepancies in simulating the transient behavior of formation fluids and extracting critical reservoir properties. Accurate determination of permeability, storability, and other properties is crucial for effective reservoir characterization and production forecasting. Inaccurate estimations can lead to suboptimal well placement, ineffective production strategies, and ultimately, missed economic opportunities. To address this shortcoming, we present a novel analytical model that explicitly incorporates the complexities of the quadratic pressure gradient and dual-permeability flow mechanisms, prevalent in many CBM formations where nanopores are rich, presenting a kind of natural nanomaterial. This model offers significant advantages over traditional approaches. By leveraging variable substitution, it facilitates the derivation of analytical solutions in the Laplace domain, subsequently converted to real-space solutions for practical application. These solutions empower reservoir engineers to generate novel type curves, a valuable tool for analyzing wellbore pressure responses during injection fall-off tests. By identifying distinct flow regimes within the reservoir based on these type curves, engineers gain valuable insights into the dynamic behavior of formation fluids. This model goes beyond traditional approaches by investigating the influence of the quadratic pressure gradient coefficient, inter-porosity flow coefficient, and storability ratio on the pressure response. A quantitative comparison with traditional models further elucidates the key discrepancies caused by neglecting the quadratic pressure gradient. The results demonstrate the proposed model's ability to accurately depict the non-linear flow behavior observed in CBM wells. This translates to more reliable pressure and pressure derivative curves that account for the impact of the quadratic pressure gradient.

Development of Empirical and Artificial Neural Network Model for the Prediction of Sorption Time to Assess the Potential of CO2 Sequestration in Coal

Geological sequestration of CO2 in a coal seam is considered an attractive option to reduce the carbon footprint. It has an additional advantage of enhancing the recovery of coalbed methane, which has less sorption affinity toward coal in comparison to CO2. Desorption of gases from coal is controlled by various parameters, including reservoir depth and coal rank. A representative factor for desorption and diffusion in coal is the sorption time. It is an indicator which helps in estimation and evaluation of gas movement in the coal seam. Coals exhibiting high sorption time allow greater quantities of CO2 injection and hold potential for CO2 sequestration. Therefore, reliable and cost-effective estimation of sorption time is very important prior to investment in projects related to CO2 sequestration. Generally, proximate and gas content analyses are part of the preliminary analysis of coal for the assessment of its potential as a coal-bed methane reservoir. In this study, data generated using these analyses were found very useful for estimating the sorption time and CO2 sequestration potential of coal. The coal samples were collected from different depths of the Mand Raigarh coalfield for testing, and an empirical equation and artificial neural network (ANN)-based model have been developed to predict the sorption time of coal. The developed empirical equation predicts the sorption time with a coefficient of determination value of 0.88 and a root mean squared error value of ±1.07 days. Furthermore, the developed ANN model has been found to be very efficient in prediction with a correlation coefficient value of 0.97.

Transient Pressure Analysis of a Multiple Fractured Well in a Stress-Sensitive Coal Seam Gas Reservoir

This paper investigates the bottom-hole pressure (BHP) performance of a fractured well with multiple radial fracture wings in a coalbed methane (CBM) reservoir with consideration of stress sensitivity. The fluid flow in the matrix simultaneously considers adsorption–desorption and diffusion, whereas fluid flow in the natural fracture system and the induced fracture network obeys Darcy’s law. The continuous line-source function in the CBM reservoir associated with the discretization method is employed in the Laplace domain. With the aid of Stehfest numerical inversion technology and Gauss elimination, the transient BHP responses are determined and analyzed. It is found that the main flow regimes for the proposed model in the CBM reservoir are as follows: linear flow between adjacent radial fracture wings, pseudo-radial flow in the inner region or Stimulated Reservoir Volume (SRV), and radial flow in outer region (un-stimulated region). The effects of permeability modulus, radius of SRV, ratio of permeability in SRV to that in un-stimulated region, properties of radial fracture wings, storativity ratio of the un-stimulated region, inter-porosity flow parameter, and adsorption–desorption constant on the transient BHP responses are discussed. The results obtained in this study will be of great significance for the quantitative analyzing of the transient performances of the wells with multiple radial fractures in CBM reservoirs.

Mathematical model of methane driven by hydraulic fracturing in gassy coal seams

During hydraulic fracturing in gassy coal, methane is driven by hydraulic fracturing. However, its mathematical model has not been established yet. Based on the theory of ‘dual-porosity and dual-permeability’ fluid seepage, a mathematical model is established, with the cleat structure, main hydraulic fracture and methane driven by hydraulic fracturing considered simultaneously. With the help of the COMSOL Multiphysics software, the numerical solution of the mathematical model is obtained. In addition, the space–time rules of water and methane saturation, pore pressure and its gradient are obtained. It is concluded that (1) along the direction of the methane driven by hydraulic fracturing, the pore pressure at the cleat demonstrates a trend of first decreasing and later increasing. The pore pressure gradient exhibits certain regional characteristics along the direction of the methane driven by hydraulic fracturing. (2) Along the direction of the methane driven by hydraulic fracturing, the water saturation exhibits a decreasing trend; however, near the cleat or hydraulic fracture, the water saturation first increases and later decreases. The water saturation in the central region of the coal matrix block is smaller than that of its surrounding region, while the saturation of water in the entire matrix block is greater than that in the cleat or hydraulic fracture surrounding the matrix block. The water saturation at the same space point increases gradually with the time progression. The space–time distribution rules of methane saturation are contrary to those of the water saturation. (3) The free methane driven by hydraulic fracturing includes the original free methane and the free methane desorbed from the adsorption methane. The reduction rate of the adsorption methane is larger than that of free methane.

Gas Diffusion in Coal Powders is a Multi-rate Process

Gas migration in coal is strongly controlled by surface diffusion of adsorbed gas within the coal matrix. Surface diffusion coefficients are obtained by inverse modelling of transient gas desorption data from powdered coals. The diffusion coefficient is frequently considered to be dependent on time and initial pressure. In this article, it is shown that the pressure dependence can be eliminated by performing a joint inversion of both the diffusion coefficient and adsorption isotherm. A study of the log–log slope of desorbed gas production rate against time reveals that diffusion within the individual coal particles is a multi-rate process. The application of a power-law probability density function of diffusion rates enables the determination of a single gas diffusion coefficient that is constant in both time and initial pressure.

CO2 Adsorption–Desorption Kinetics from the Plane Sheet of Hard Coal and Associated Shrinkage of the Material

The paper presents the results of studies on sorption and CO2 desorptions from coals from two Polish mines that differed in petrographic and structural properties. The tests were carried out on spherical and plane sheet samples. On the basis of the sorption tests, the effective diffusion coefficient was calculated on the plane sheet samples based on a proper model. Similar tests were performed on the spherical samples. Mathematical model results for plane sheet samples were compared with the most frequently chosen model for spherical samples. The kinetics of CO2 desorption from plane sheet samples were compared with the kinetics of sample shrinkage. In both samples, the shrinkage was about 0.35%. The size change kinetics and CO2 desorption kinetics significantly differed between the samples. In both samples, the determined shrinkage kinetics was clearly faster than CO2 kinetics.

Experimental and Simulation Studies on Adsorption and Diffusion Characteristics of Coalbed Methane

Coalbed methane (CBM) content is generally estimated using the isotherm theory between pressure and adsorbed amounts of methane. It usually determines the maximum content of adsorbed methane or storage capacity. However, CBM content obtained via laboratory experiment is not consistent with that in the in-situ state because samples are usually ground, which changes the specific surface area. In this study, the effect of the specific surface area relative to CBM content was investigated, and diffusion coefficients were estimated using equilibrium time analysis. The differences in adsorbed content with sample particle size allowed the determination of a specific surface area where gases can adsorb. Also, there was an equilibrium time difference between fine and lump coal, because more time is needed for the gas to diffuse through the coal matrix and adsorb onto the surface in lump coal. Based on this, we constructed a laboratory-scale simulation model, which matched with experimental results. Consequently, the diffusion coefficient, which is usually calculated through canister testing, can be easily obtained. These results stress that lump coal experiments and associated simulations are necessary for more reliable CBM production analysis.

Stochastic reservoir simulation for the modeling of uncertainty in coal seam degasification

Coal seam degasification improves coal mine safety by reducing the gas content of coal seams and also by generating added value as an energy source. Coal seam reservoir simulation is one of the most effective ways to help with these two main objectives. As in all modeling and simulation studies, how the reservoir is defined and whether observed productions can be predicted are important considerations. Using geostatistical realizations as spatial maps of different coal reservoir properties is a more realistic approach than assuming uniform properties across the field. In fact, this approach can help with simultaneous history matching of multiple wellbores to enhance the confidence in spatial models of different coal properties that are pertinent to degasification. The problem that still remains is the uncertainty in geostatistical simulations originating from the partial sampling of the seam that does not properly reflect the stochastic nature of coal property realizations. Stochastic simulations and using individual realizations, rather than E-type, make evaluation of uncertainty possible. This work is an advancement over Karacan et al. (2014) in the sense of assessing uncertainty that stems from geostatistical maps. In this work, we batched 100 individual realizations of 10 coal properties that were randomly generated to create 100 bundles and used them in 100 separate coal seam reservoir simulations for simultaneous history matching. We then evaluated the history matching errors for each bundle and defined the single set of realizations that would minimize the error for all wells. We further compared the errors with those of E-type and the average realization of the best matches. Unlike in Karacan et al. (2014), which used E-type maps and average of quantile maps, using these 100 bundles created 100 different history match results from separate simulations, and distributions of results for in-place gas quantity, for example, from which uncertainty in coal property realizations could be evaluated. The study helped to determine the realization bundle that consisted of the spatial maps of coal properties, which resulted in minimum error. In addition, it was shown that both E-type and the average of realizations that gave the best match for invidual approximated the same properties resonably. Moreover, the determined realization bundle showed that the study field initially had 151.5 million m³ (cubic meter) of gas and 1.04 million m³ water in the coal, corresponding to Q90 of the entire range of probability for gas and close to Q75 for water. In 2013, in-place fluid amounts decreased to 138.9 million m³ and 0.997 million m³ for gas and water, respectively.

Sequential Gaussian co-simulation of rate decline parameters of longwall gob gas ventholes

Gob gas ventholes (GGVs) are used to control methane inflows into a longwall mining operation by capturing the gas within the overlying fractured strata before it enters the work environment. Using geostatistical co-simulation techniques, this paper maps the parameters of their rate decline behaviors across the study area, a longwall mine in the Northern Appalachian basin. Geostatistical gas-in-place (GIP) simulations were performed, using data from 64 exploration boreholes, and GIP data were mapped within the fractured zone of the study area. In addition, methane flowrates monitored from 10 GGVs were analyzed using decline curve analyses (DCA) techniques to determine parameters of decline rates. Surface elevation showed the most influence on methane production from GGVs and thus was used to investigate its relation with DCA parameters using correlation techniques on normal-scored data. Geostatistical analysis was pursued using sequential Gaussian co-simulation with surface elevation as the secondary variable and with DCA parameters as the primary variables. The primary DCA variables were effective percentage decline rate, rate at production start, rate at the beginning of forecast period, and production end duration. Co-simulation results were presented to visualize decline parameters at an area-wide scale. Wells located at lower elevations, i.e., at the bottom of valleys, tend to perform better in terms of their rate declines compared to those at higher elevations. These results were used to calculate drainage radii of GGVs using GIP realizations. The calculated drainage radii are close to ones predicted by pressure transient tests.

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.