The rock matrix bulk modulus or its inverse, the compressive coefficient, is an important input parameter for fluid substitution by the Biot-Gassmann equation in reservoir prediction. However, it is not easy to accura...The rock matrix bulk modulus or its inverse, the compressive coefficient, is an important input parameter for fluid substitution by the Biot-Gassmann equation in reservoir prediction. However, it is not easy to accurately estimate the bulk modulus by using conventional methods. In this paper, we present a new linear regression equation for calculating the parameter. In order to get this equation, we first derive a simplified Gassmann equation by using a reasonable assumption in which the compressive coefficient of the saturated pore fluid is much greater than the rock matrix, and, second, we use the Eshelby- Walsh relation to replace the equivalent modulus of a dry rock in the Gassmann equation. Results from the rock physics analysis of rock sample from a carbonate area show that rock matrix compressive coefficients calculated with water-saturated and dry rock samples using the linear regression method are very close （their error is less than 1%）. This means the new method is accurate and reliable.展开更多
The KBM method is effective in solving nonlinear problems.Unfortunately,the traditional KBM method strongly depends on a small parameter,which does not exist in most of the practice physical systems.Therefore this met...The KBM method is effective in solving nonlinear problems.Unfortunately,the traditional KBM method strongly depends on a small parameter,which does not exist in most of the practice physical systems.Therefore this method is limited to dealing with the system with strong nonlinearity.In this paper we present a procedure to study the resonance solutions of the system with strong nonlinearities by employing the homotopy analysis technique to extend the KBM method to the strong nonlinear systems,and we also analyze the truncation error of the procedure.Applied to a given example,the procedure shows the efficiencies in studying bifurcation.展开更多
基金supported by the National Nature Science Foundation of China (Grant Noss 40739907 and 40774064)National Science and Technology Major Project (Grant No. 2008ZX05025-003)
文摘The rock matrix bulk modulus or its inverse, the compressive coefficient, is an important input parameter for fluid substitution by the Biot-Gassmann equation in reservoir prediction. However, it is not easy to accurately estimate the bulk modulus by using conventional methods. In this paper, we present a new linear regression equation for calculating the parameter. In order to get this equation, we first derive a simplified Gassmann equation by using a reasonable assumption in which the compressive coefficient of the saturated pore fluid is much greater than the rock matrix, and, second, we use the Eshelby- Walsh relation to replace the equivalent modulus of a dry rock in the Gassmann equation. Results from the rock physics analysis of rock sample from a carbonate area show that rock matrix compressive coefficients calculated with water-saturated and dry rock samples using the linear regression method are very close （their error is less than 1%）. This means the new method is accurate and reliable.
基金supported by the National Natural Science Foundation of China (Grant No.10632040)
文摘The KBM method is effective in solving nonlinear problems.Unfortunately,the traditional KBM method strongly depends on a small parameter,which does not exist in most of the practice physical systems.Therefore this method is limited to dealing with the system with strong nonlinearity.In this paper we present a procedure to study the resonance solutions of the system with strong nonlinearities by employing the homotopy analysis technique to extend the KBM method to the strong nonlinear systems,and we also analyze the truncation error of the procedure.Applied to a given example,the procedure shows the efficiencies in studying bifurcation.
