Abstract:This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
“…After substituting Equation (3) into Equations ( 9) and (10), gas comprehensive seepage differential equations in the pseudo-pressure form can be expressed as Equations (11) and ( 12): where ψ 1 is the inner zone pseudo-pressure, Pa/s; ψ 2 is the outer zone pseudo-pressure of composite gas reservoir, Pa/s; C g is the gas compressibility coefficient, Pa -1 .…”
Section: Model Description and Solutionmentioning
confidence: 99%
“…It can help to understand the seepage mechanism and the development law of gas reservoirs with high temper-ature and pressure. Compared with the conventional gas reservoir, there is more obvious rock deformation during the development process of the gas reservoir with high temperature and pressure resulting in stronger stress sensitivity effect [10][11][12][13][14][15]. Thus, it is necessary to consider the influence of stress sensitivity effect on well test curves.…”
Some deepwater gas reservoirs with high temperature and pressure have obvious stress sensitivity effect resulting in difficulty in well test interpretations. The influence of stress sensitivity effect on the pressure drawdown well test is discussed in many papers. However, the influence on the pressure buildup well test is barely discussed. For practices in oilfields, the quality of pressure data from the drawdown stage of well test is poor due to the influence of production fluctuation. Thus, the pressure data from the buildup stage is used for well test interpretations in most cases. In order to analyze the influence of stress sensitivity effect on the pressure buildup well test, this paper establishes a composite gas reservoir pressure buildup well test model considering the stress sensitivity effect and the hysteresis effect. Numerical solutions to both pressure drawdown and buildup well test models are obtained by the numerical differentiation method. The numerical solutions are verified by comparing with analytical solutions and the homogeneous gas reservoir well test solution. Then, the differences between pressure drawdown and buildup well test curves considering the stress sensitivity effect are compared. The parameter sensitivity analysis is conducted. Compared with the conventional well test curve, the pressure derivative curve of pressure drawdown well test considering the stress sensitivity effect deviates upward from the 0.5 horizontal line at the inner zone radial flow stage, while it deviates upward from the M/2 (mobility ratio/2) horizontal line at the outer zone radial flow stage. However, for the pressure buildup well test curve considering the stress sensitivity effect, the pressure derivative curve gradually descends to the 0.5 horizontal line at the inner zone radial flow stage, while it descends to the M/2 (mobility ratio/2) horizontal line at the outer zone radial flow stage. The pressure derivative curve of pressure buildup well test considering the hysteresis effect is higher than the curve without considering the hysteresis effect, because the permeability cannot be recovered to its original value in the buildup stage after considering the hysteresis effect. Meanwhile, skin factor and mobility ratio have different effects on pressure drawdown and buildup well test curves. Based on the model, a well test interpretation case from a deepwater gas reservoir with high temperature and pressure is studied. The result indicates that the accuracy of the interpretation is improved after considering the stress sensitivity effect, and the skin factor will be exaggerated without considering the stress sensitivity effect.
“…After substituting Equation (3) into Equations ( 9) and (10), gas comprehensive seepage differential equations in the pseudo-pressure form can be expressed as Equations (11) and ( 12): where ψ 1 is the inner zone pseudo-pressure, Pa/s; ψ 2 is the outer zone pseudo-pressure of composite gas reservoir, Pa/s; C g is the gas compressibility coefficient, Pa -1 .…”
Section: Model Description and Solutionmentioning
confidence: 99%
“…It can help to understand the seepage mechanism and the development law of gas reservoirs with high temper-ature and pressure. Compared with the conventional gas reservoir, there is more obvious rock deformation during the development process of the gas reservoir with high temperature and pressure resulting in stronger stress sensitivity effect [10][11][12][13][14][15]. Thus, it is necessary to consider the influence of stress sensitivity effect on well test curves.…”
Some deepwater gas reservoirs with high temperature and pressure have obvious stress sensitivity effect resulting in difficulty in well test interpretations. The influence of stress sensitivity effect on the pressure drawdown well test is discussed in many papers. However, the influence on the pressure buildup well test is barely discussed. For practices in oilfields, the quality of pressure data from the drawdown stage of well test is poor due to the influence of production fluctuation. Thus, the pressure data from the buildup stage is used for well test interpretations in most cases. In order to analyze the influence of stress sensitivity effect on the pressure buildup well test, this paper establishes a composite gas reservoir pressure buildup well test model considering the stress sensitivity effect and the hysteresis effect. Numerical solutions to both pressure drawdown and buildup well test models are obtained by the numerical differentiation method. The numerical solutions are verified by comparing with analytical solutions and the homogeneous gas reservoir well test solution. Then, the differences between pressure drawdown and buildup well test curves considering the stress sensitivity effect are compared. The parameter sensitivity analysis is conducted. Compared with the conventional well test curve, the pressure derivative curve of pressure drawdown well test considering the stress sensitivity effect deviates upward from the 0.5 horizontal line at the inner zone radial flow stage, while it deviates upward from the M/2 (mobility ratio/2) horizontal line at the outer zone radial flow stage. However, for the pressure buildup well test curve considering the stress sensitivity effect, the pressure derivative curve gradually descends to the 0.5 horizontal line at the inner zone radial flow stage, while it descends to the M/2 (mobility ratio/2) horizontal line at the outer zone radial flow stage. The pressure derivative curve of pressure buildup well test considering the hysteresis effect is higher than the curve without considering the hysteresis effect, because the permeability cannot be recovered to its original value in the buildup stage after considering the hysteresis effect. Meanwhile, skin factor and mobility ratio have different effects on pressure drawdown and buildup well test curves. Based on the model, a well test interpretation case from a deepwater gas reservoir with high temperature and pressure is studied. The result indicates that the accuracy of the interpretation is improved after considering the stress sensitivity effect, and the skin factor will be exaggerated without considering the stress sensitivity effect.
A new model for the determination of the permeability in sandstones under confining pressure is presented. Building on the concepts of digital rock physics a numerical model is derived from a three-dimensional tomographic scan. The pressure-dependent behaviour is mimicked by adding an artificial flow resistance to the pore throats. All permeability simulations are performed using an in-house finite volume code. In a first step, the proposed model is tested based on a given Bentheim sandstone sample and compared with experimental data. In a second step, influencing factors of the model are investigated. Mainly discussed are the influences of the tomographic scan, as well as, the numerical resolution. Overall, the proposed model is observed to be capable of reproducing general trends of the experimental data, whereby the magnitude of the numerically determined permeabilities can strongly depend on the investigated influencing factors.
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