Improvements Of Coal Permeability Model And Threedimensional Numerical Simulation Of Gas Flow In Coal

As a clean energy source, coalbed methane(CBM) has attracted more and more attention from the main coal production countries around the world. CBM recovery induces gas and water flow in coalbed, and this process includes complex physical interactions, such as adsorption/desorption, diffusion and laminar. Thus investigating gas flow in coal contributes to the insights into both the flow process and CBM recovery. A comprehensive literature review on coal permeability experiment, coal permeability model and the numerical simulation of gas flow in coal indicates that the existing coal permeability models still have some deficiencies. Based on these deficiencies, this paper improves the coal permeability model by introducing the coal anisotropy and the internal swelling ratio. The governing equation of single-component gas flow in coal is modified by introducing the improved permeability model. A three-dimensional finite-difference numerical model is proposed based on the modified governing equation. A simulator for investigating the single-component gas flow in coal is developed. By using this simulator, the coal permeability experiments and dry CBM production are simulated.This dissertation proposes a coal permeability that includes the coal anisotropy and the internal swelling ratio. This model is developed based on areal porosity and it can represent the coal permeability evolution with effective stress change and gas sorption. This newly proposed coal permeability model is independent of boundary conditions and it can be extended to the different representations with various boundary conditions. Thus this model is more applicable than the permeability models that were developed for specific boundary conditions. According to the actual boundary conditions in CBM production and coal permeability experiments, the newly proposed coal permeability model is expanded for different boundary conditions, such as uniaxial strain conditions, constant confining stress conditions, constant effective stress conditions and constant pore pressure conditions. As a result, both anisotropic and isotropic model representations are obtained. The isotropic model representations under constant confining stress conditions, constant effective stress conditions and constant pore pressure conditions are validated by using the experimental permeability data reported by other papers. The validation results indicates that the model results agree well with the experimental data by assuming the internal swelling ratio to be constant under constant confining stress conditions. However, the assumption of the internal swelling ratio to be a constant makes the model results deviate from the experimental permeability data under both constant effective stress conditions and constant pore pressure conditions.On the basis of the newly proposed coal permeability model, this dissertation proposes a method for regressing the internal swelling and the internal swelling ratio by using coal permeability data. According to this method, the values of the internal swelling and the internal swelling ratio are obtained under constant confining stress conditions, constant pore pressure conditions and constant effective stress conditions. Under constant confining stress conditions, the internal swelling and the internal swelling ratio increase with ascending pore pressure, and the correlation between the internal swelling and pore pressure still conforms to the Langmuir equation. Under constant pore pressure conditions, the internal swelling and the internal swelling ratio of CH4 and the gaseous CO2 decrease with increasing confining stress. Both the internal swelling and the internal swelling ratio of the supercritical CO2 are almost independent of confining stress. Under constant effective stress conditions, as pore pressure increases, the internal swelling ascends continuously, and the internal swelling ratio decreases at first and then increases. This dissertation and the literature indicate that the internal swelling can be affected by pore pressure, confining stress, gas type, coal structure, and coal microlithotypes. Among these affecting factors, the confining stress should be paid special attention on. The increase in confining stress can reduce the internal swelling and then increase coal permeability. This increase in permeability can offset partial permeability reduction caused by the increase in confining stress. Therefore, the permeability models that did not included the effects of confining stress on the internal swelling normally calculated smaller values than the experimental permeability measurements. In addition, the internal swelling ratio varies in a small range when the stress is greater than five MPa. This indicates this ratio can be assumed to be a constant under in situ conditions of CBM production.The governing equation of the single-component gas flow in coal is modified by introducing the newly proposed coal permeability model, and a new governing equation of gas flow in coal that includes the coal anisotropy is obtained. The finite difference numerical model of this newly proposed governing equation is developed. This numerical model is three-dimensional and adopts non-uniform grid. Subsequently, the consistency, stability and convergence of the finite difference equation are validated. The results show that the finite difference equation is consistent with the original partial differential equation. The conditions of stability and convergence are equivalent and the finite difference equation will be stable and convergent when the bulk porosity is not less than the volumetric internal swelling.Based on the newly proposed finite difference numerical model of single-component gas flow in coal, a numerical simulator called Simulator for Gas Flow in Coal(SGFC) is developed. This simulator can simulate the steady-state and the transient permeability experiment with single-component phase, as well as the dry CBM production. The results simulated by SGFC agree well with the data of real transient permeability experiment. This indicates SGFC can simulate the single-component gas flow in real small-scale coal sample. The results simulated by SGFC also agree well with those simulated by the commercial CBM simulators. This indirectly indicates that SGFC can simulate the singlecomponent gas flow in real large-scale coal seam. Therefore, the simulation results of SGFC are reliable.The steady-state and the transient permeability experiment under constant confining stress conditions are respectively simulated by using SGFC. The results show that the permeability of the model center can be treated as the “true” permeability of the coal sample. The permeability values calculated by the permeability model is totally coincide with the permeability data of the model center for both simulations. At lower pore pressures, the “experimental” permeability data deviate from the permeability data of the model center for both simulations. With increasing pore pressure, the deviations moderate. At high pore pressures, the “experimental” permeability of the steady-state method are almost equal to the permeability of the model center. However, the “experimental” permeability of the transient method still deviates apparently from the permeability of the model center. At the same pore pressure, the “experimental” permeability of the steadystate method is more close to the permeability of the model center compared to the transient method. This result indicates that the simulation results of the steady-state method are more accurate than the transient method under the conditions of this dissertation.The sensitivities of the steady-state method and the transient method to the experimental conditions under constant confining stress conditions are simulated and analyzed by using SGFC. The results show that whether the sorption inside the coal sample equilibrates decides the success of both methods. The key of the sorption equilibration is the experiment time. Therefore, sufficient experiment time is crucial for both methods. The flux difference between the inlet and outlet indicates the accuracy of the steady-state method. As the flux difference reduces, the accuracy of the experiment results increases. The ratio of the gas pressure difference between the upstream and downstream indicates the accuracy of the transient method. As the ratio approximates to zero, the accuracy of the experiment results increases.The simulation results of the permeability experiment and the sensitivity analysis indicate that some principles should be paid attention to when conducting the coal permeability experiments. Among these principles, some are common for both method: sufficient experiment time should be guaranteed; with constant experiment time, increasing the pore pressure, decreasing the gas pressure step and shortening the core length will improve the accuracy of the experiment results. For the steady-state method, the following principles should also be noticed: with constant experiment time, increasing the gas pressure difference between the inlet and outlet will increase the accuracy of the experiment; with sufficient experiment time, the sorption equilibration should be achieved inside the coal sample, and Eq.(1.1) should be used to calculate permeability. For the transient method, the following principle should be noticed: with constant experiment time, decreasing the upstream volume or increasing the downstream will increase the accuracy of the results.The dry CBM production with vertical wells is simulated by using SGFC. The results show that the pore pressure, CH4 content and gas rate decrease while the permeability increases with gas production. The decreasing speeds of pore pressure and CH4 content are inconsistent, and the former is greater than the later. As initial production stage, the gas rate decreases rapidly. The time for the gas rate decreasing to its initial value is only 259 days, and the gas rate decreases to less than 500 m3/d at the production time of 1000 days. As this time, about 45% CH4 of nearly 80% production region still deposits in the coalbed.Since the newly proposed coal permeability model introduces the permeability anisotropy and the internal swelling ratio, the sensitivities of the dry CBM production with vertical wells to these two properties are simulated and analyzed by using SGFC. The results show that both the permeability anisotropy and the internal swelling ratio greatly affects dry CBM production. The affecting degree varies significantly and complexly with gas production as well. The effects of permeability anisotropy on pore pressure, permeability and CH4 content have a “peak”, while its effects on gas rate have a “valley”. The effects of the internal swelling ratio on pore pressure, permeability and CH4 content increases continuously, while its effects on gas rate varies non-monotonically. This dissertation simulates the effects of permeability anisotropy on CBM production with vertical well, its effects of horizontal production are not investigated. Since the permeability of the vertical direction to bedding plane is greatly small, the permeability anisotropy between the directions parallel and perpendicular to the bedding plane may be more significant. Thus the effects of permeability anisotropy on CBM production with horizontal well may be also more great. Besides, increasing the internal swelling ratio has positive effects on CBM production, and decreasing coal stress and hydraulic-fracturing can increase the internal swelling ratio.Although some useful insights and conclusions are obtained, this dissertation have deficiencies. These deficiencies include none coal permeability experiment is conducted, SGFC cannot simulate the mixed gas and water flow processes in coal during the actual CBM production, the results of the decoupled simulation and the coupled simulation are not thoroughly compared or analyzed, and the CBM production with horizontal wells is not simulated. Nevertheless, these deficiencies are the challenges that the author wants to address in the future. If the conditions permit, the author hopes to continue to investigate these topics.