Turgay Ertekin

Dynamic gas slippage: a unique dual-mechanism approach to the flow of gas in tight formations

A mathematical formulation, applicable to both numerical simulation and transient well analysis that describes the flow of gas in very tight 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 Ficks law of diffusion. Transport through the pressure field is a laminar process and is modeled with Darcys 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 less than or equal to0.01 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.

A parametric study of the effects of coal seam properties on gas drainage efficiency

A mathematical model which simulates the flow of methane and water through a coal seam was developed. Partial differential equations governing the flow of methane and brine were derived from mass balances applied to an elemental volume of the reservoir. A two-dimensional cartesian coordinate system was superimposed on the coal seam and was utilized to transform the continuous flow equations to discrete form by application of finite differences.

The unsteady-state nature of sorption and diffusion phenomena in the micropore structure of coal; Part 2 - Solution

A single-phase 1D mathematical model, is used to study unsteady-state micropore sorption in the composite micropore/fracture coalbed-methane-transport problem. The mathematical model is solved numerically by writing the transport equations in finite-difference form and linearizing the residual form of the difference equations with the generalized Newton-Raphson procedure. The numerical model is used to compare methane production rates predicted by unsteady- and quasisteady-state sorption formulations. Results indicate that the two models give different rates during early degasification periods. The high rates predicted by the unsteady-state model, however, generally approached lower quasisteady-state rates within the first few months of simulation. The numerical model is also used to examine the time-dependent response of concentration gradients in the micropores to changes in fracture pressure, to compare diffusion rates predicted by spherical and cylindrical micropore elements, and to construct dimensionless type-curve solutions to the coalbed-methane flow problem.

State-of-the-Art Modeling for Unconventional Gas Recovery

In this paper a series of mathematical and numerical developments that simulate the unsteady-state behavior of unconventional gas reservoirs is reviewed. Five major modules, considered to be unique to the simulation of gas reservoirs, are identified. The inclusion of these models into gas reservoir simulators is discussed in mathematical detail with accompanying assumptions.

Field development studies by neuro-simulation: an effective coupling of soft and hard computing protocols

Abstract This paper establishes the principles of a novel simulation methodology that effectively brings together the specific advantages of hard and soft computing techniques. Accordingly, the work described in this paper conjoins the accurate and precise nature of the existing hard computing algorithmic approaches with the pragmatic nature of soft computing techniques. The capabilities of the proposed approach are demonstrated by the implementation of the process to various field development studies practised in the petroleum and natural gas industry. In structuring the proposed methodology, full advantages of the deterministic techniques (in terms of the accurate description of the physical phenomena) and the parallel processing power of the artificial neural network technology are taken into account to ensure the solution integrity and solution speed during the overall implementation of the process. By applying the neuro-simulation methodology to field development problems, it is shown that a substantial reduction in cost, energy and time factors of the conventional simulation approach are achieved by the pragmatic character of the artificial neural network technology. Various case studies involving different reservoirs with different flow dynamics in an increasing level of complexity are examined to illustrate the implementation of the neuro-simulation guidelines as well as to highlight the power of the proposed methodology.

An Artificial Neural Network Based Relative Permeability Predictor

Relative permeabilities are complex and important rock-fluid properties of reservoirs in which multi-phase flow conditions prevail. Measuring relative permeabilities in the laboratory using cores obtained from a reservoiris a complicated, time demanding, and labour-intensive task. There has been limited success in mathematical modelling of relative permeabilities based on rocks and fluid properties due to our inability to simulate the non-linear controlling mechanisms in place. Artificial neural networks (ANNs) promise a potential avenue for implicitly incorporating the controlling mechanisms and parameters into a model that can be utilized as an effective tool for relative permeability predictions. The methodology described in this paper exploits the unique topology of ANNs for determining the two-phase (oil-water) relative permeabilities. The ANN is a universal approximator that performs non-linear, multi-dimensional interpolations. In the development stage of the ANN model, a large number of oil-water relative permeability data sets were collected from the literature. These data sets were used to train the model. In composing the architecture of the ANN, only the readily available rock and fluid properties (end-point saturations, porosity, permeability, viscosity, and interfacial tension) have been explicitly incorporated. The predictive ability of the model was tested using experimental data sets that were not used during the training stage. The results are in good agreement with the experimentally reported data. The proposed model exhibits sensitivity to several reservoir properties. The proposed ANN model has a dynamic training base that can be expanded as new data become available.

Development of a coal shrinkage?swelling model accounting for water content in the micropores

Changes in cleat permeability of coal seams are influenced by internal stress, and release or adsorption of gas in the coal matrix during production/injection processes. Coal shrinkage?swelling models have been proposed to quantify such changes; however none of the existing models incorporates the effect of the presence of water in the micropores on the gas sorption of coalbeds. This paper proposes a model of coal shrinkage and swelling, incorporating the effect of water in the micropores. The proposed model was validated using field permeability data from San Juan basin coalbeds and compared with coal shrinkage and swelling models existing in the literature.

Effects of Matrix Shrinkage and Swelling on the Economics of Enhanced-Coalbed-Methane Production and CO2 Sequestration in Coal

In this work, the Palmer-Mansoori model for coal shrinkage and permeability increases during primary methane production was rewritten to also account for coal swelling caused by CO{sub 2} sorption. The generalized model was added to a compositional, dual porosity coalbed-methane reservoir simulator for primary (CBM) and ECBM production. A standard five-spot of vertical wells and representative coal properties for Appalachian coals was used. Simulations and sensitivity analyses were performed with the modified simulator for nine different parameters, including coal seam and operational parameters and economic criteria. The coal properties and operating parameters that were varied included Youngs modulus, Poissons ratio, cleat porosity, and injection pressure. The economic variables included CH{sub 4}, price, Col Cost, CO{sub 2} credit, water disposal cost, and interest rate. Net-present value (NPV) analyses of the simulation results included profits resulting from CH{sub 4}, production and potential incentives for sequestered CO{sub 2}, This work shows that for some coal seams, the combination of compressibility, cleat porosity, and shrinkage/swelling of the coal may have a significant impact on project economics.

Development and Testing of a Static/Dynamic Local Grid-Refinement Technique

This paper reports that simple, efficient, and stable static and dynamic local grid-refinement procedures for multi-dimensional, multi-base petroleum reservoir problems are developed and tested by isothermal reservoir simulation.

Simulating Carbon Dioxide Sequestration/ECBM Production in Coal Seams: Effects of Coal Properties and Operational Parameters

Carbon dioxide sequestration is a promising technology for reducing anthropogenic greenhouse gas emissions while fossil fuels are still being used. The costs associated with CO2 sequestration are often high; however, in certain circumstances (e.g., enhanced oil recovery) these costs can be more than offset by the benefits of additional incremental hydrocarbon production. Primary production of coalbed methane is a well-developed technology, but secondary production, through the injection of CO2 or N2 has undergone relatively little study. Recent research suggests that carbon dioxide preferentially sorbs to coal, displacing methane, making CO2-enhanced coalbed methane production an ideal candidate for CO2 sequestration. We use PSU-COALCOMP, a dual-porosity coalbed methane simulator, to model primary and secondary production of methane from coal, for a variety of coal properties and operational parameters. Our base well pattern consists of four horizontal production wells that form a square, with four smaller horizontal producers/injectors at the square’s center. Primary production of methane and water is simulated until a specified reservoir pressure is reached, after which CO2 is injected in the center wells to displace methane, extending the reservoir’s production of methane. Production continues until the CO2 concentration in the produced gas is too high. By modifying coal properties, such as permeability, porosity, degree of anisotropy, and sorption rates, we have approximated different types of coals. By varying operational parameters, such as injector length, injection well pressure, time to injection, and production well pressure, we can evaluate different production schemes to determine an optimum for each coal type. Any optimization requires considering a tradeoff between total methane produced (or CO2 sequestered) and the rate of methane production. Values of aggregate methane production and methane production rate are presented for multiple coal types and different operational designs.