It is known that there is a discrepancy between field data and the results predicted from the previous equations derived by simplifying three-dimensional（3-D） flow into two-dimensions（2-D）.This paper presents a ne...It is known that there is a discrepancy between field data and the results predicted from the previous equations derived by simplifying three-dimensional（3-D） flow into two-dimensions（2-D）.This paper presents a new steady-state productivity equation for horizontal wells in bottom water drive gas reservoirs.Firstly,the fundamental solution to the 3-D steady-state Laplace equation is derived with the philosophy of source and the Green function for a horizontal well located at the center of the laterally infinite gas reservoir.Then,using the fundamental solution and the Simpson integral formula,the average pseudo-pressure equation and the steady-state productivity equation are achieved for the horizontal section.Two case-studies are given in the paper,the results calculated from the newly-derived formula are very close to the numerical simulation performed with the Canadian software CMG and the real production data,indicating that the new formula can be used to predict the steady-state productivity of such horizontal gas wells.展开更多
The Fox function expression and the analytic expression for the concentration distribution of fractional anomalous diffusion caused by an instantaneous point source in n-dimensional space (n= 1, 2 or 3) are derived by...The Fox function expression and the analytic expression for the concentration distribution of fractional anomalous diffusion caused by an instantaneous point source in n-dimensional space (n= 1, 2 or 3) are derived by means of the condition of mass conservation , the time-space similarity of the solution , Mellin transform and the properties of the Fox function . And the asymptotic behaviors for the solutions are also given .展开更多
基金financial support from the Open Fund(PLN1003) of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation(Southwest Petroleum University)the National Science and Technology Major Project in the l lth Five-Year Plan(Grant No.2008ZX05054)
文摘It is known that there is a discrepancy between field data and the results predicted from the previous equations derived by simplifying three-dimensional（3-D） flow into two-dimensions（2-D）.This paper presents a new steady-state productivity equation for horizontal wells in bottom water drive gas reservoirs.Firstly,the fundamental solution to the 3-D steady-state Laplace equation is derived with the philosophy of source and the Green function for a horizontal well located at the center of the laterally infinite gas reservoir.Then,using the fundamental solution and the Simpson integral formula,the average pseudo-pressure equation and the steady-state productivity equation are achieved for the horizontal section.Two case-studies are given in the paper,the results calculated from the newly-derived formula are very close to the numerical simulation performed with the Canadian software CMG and the real production data,indicating that the new formula can be used to predict the steady-state productivity of such horizontal gas wells.
基金the National Natural Science Foundation of China (10272067) the Doctoral Foundation of Education Ministry of China (1999042211)
文摘The Fox function expression and the analytic expression for the concentration distribution of fractional anomalous diffusion caused by an instantaneous point source in n-dimensional space (n= 1, 2 or 3) are derived by means of the condition of mass conservation , the time-space similarity of the solution , Mellin transform and the properties of the Fox function . And the asymptotic behaviors for the solutions are also given .
