This paper presents a new analytical solution to investigate the mechanism of transient confinedunconfined flow in a confined aquifer induced by pumping with a large rate during mine drainage.The study focuses on unde...This paper presents a new analytical solution to investigate the mechanism of transient confinedunconfined flow in a confined aquifer induced by pumping with a large rate during mine drainage.The study focuses on understanding the impact of non-Darcian effect on flow towards a fully penetrated pumping well.The nonlinear relationship between specific discharge and the hydraulic gradient is described using Izbash's equation.A novel approximate method is developed to linearize the mathematical model,and the solution is derived using the Boltzmann transform.The proposed solution is validated by comparing it with previous works.The findings indicate that increased non-Darcian index,quasi-hydraulic conductivity,and specific storage have negatively affect the development of the unconfined region and aquifer drawdown,as greater turbulence flow accelerates recharge to the pumping well.Drawdown is found to be sensitive to the non-Darcian index,quasi-hydraulic conductivity,while it is unaffected by specific yield and specific storage.The conclusions provide valuable insights for mine drainage and the application of geological and hydrological conditions.展开更多
The salient significance of the solution of radial diffusivity equation to well testing analysis done in oil and gas industry cannot be over-emphasized. Varieties of solutions have been proposed to the radial diffusiv...The salient significance of the solution of radial diffusivity equation to well testing analysis done in oil and gas industry cannot be over-emphasized. Varieties of solutions have been proposed to the radial diffusivity equation, of which the Van Everdingen-Hurst constant terminal rate solution is the most widely accepted and the others are approximate solution having their respective limitations. The main objective of this project, being its first application to oil and gas industry, is to use a new mathematical technique, the homotopy analysis method (HAM) to solve the radial diffusivity equation for slightly compressible fluid. In Using HAM, the Boltzmann transformation method was used to transform the radial PDE to ODE, then a homotopy series was then constructed for the new equation with the linear boundary condition from the original radial diffusivity equation of slightly compressible fluid and the final equation then solved using computation software Maple. The result gotten reveals that the homotopy analysis method gives good results compared to the Van Everdingen and Hurst Solution (Exact solution) and thus proves to be very effective, simple, and accurate when compared to other form of solutions. Hence from the results gotten, Homotopy Analysis Method can therefore be applied in solving other non-linear equations in the petroleum engineering field since it is simple and accurate.展开更多
In this paper,we present a Cole-Hopf transformation based lattice Boltzmann(LB) model for solving one-dimensional Burgers' equation,and compared to available LB models,the effect of nonlinear convection term can b...In this paper,we present a Cole-Hopf transformation based lattice Boltzmann(LB) model for solving one-dimensional Burgers' equation,and compared to available LB models,the effect of nonlinear convection term can be eliminated.Through Chapman-Enskog analysis,it can be found that the converted diffusion equation based on the Cole-Hopf transformation can be recovered correctly from present LB model.Some numerical tests are also performed to validate the present LB model,and the numerical results show that,similar to previous LB models,the present model also has a second-order convergence rate in space,but it is more accurate than the previous ones.展开更多
基金Supported by the Natural Science Foundation of Anhui Province(1508085MA10)the Natural Science Foundation of Anhui Provincial Education Department(KJ2012Z394)the Students Innovation Training Project of China(201410379021)
基金supported by the national natural science foundation of China(Grant Numbers 41807197,2017YFC0405900,and 51469002)the natural science foundation of Guangxi(Grant Numbers 2017GXNSFBA198087,2018GXNSFAA 138042,and GuiKeAB17195073)Hebei high level talent funding project(B2018003016).
文摘This paper presents a new analytical solution to investigate the mechanism of transient confinedunconfined flow in a confined aquifer induced by pumping with a large rate during mine drainage.The study focuses on understanding the impact of non-Darcian effect on flow towards a fully penetrated pumping well.The nonlinear relationship between specific discharge and the hydraulic gradient is described using Izbash's equation.A novel approximate method is developed to linearize the mathematical model,and the solution is derived using the Boltzmann transform.The proposed solution is validated by comparing it with previous works.The findings indicate that increased non-Darcian index,quasi-hydraulic conductivity,and specific storage have negatively affect the development of the unconfined region and aquifer drawdown,as greater turbulence flow accelerates recharge to the pumping well.Drawdown is found to be sensitive to the non-Darcian index,quasi-hydraulic conductivity,while it is unaffected by specific yield and specific storage.The conclusions provide valuable insights for mine drainage and the application of geological and hydrological conditions.
文摘The salient significance of the solution of radial diffusivity equation to well testing analysis done in oil and gas industry cannot be over-emphasized. Varieties of solutions have been proposed to the radial diffusivity equation, of which the Van Everdingen-Hurst constant terminal rate solution is the most widely accepted and the others are approximate solution having their respective limitations. The main objective of this project, being its first application to oil and gas industry, is to use a new mathematical technique, the homotopy analysis method (HAM) to solve the radial diffusivity equation for slightly compressible fluid. In Using HAM, the Boltzmann transformation method was used to transform the radial PDE to ODE, then a homotopy series was then constructed for the new equation with the linear boundary condition from the original radial diffusivity equation of slightly compressible fluid and the final equation then solved using computation software Maple. The result gotten reveals that the homotopy analysis method gives good results compared to the Van Everdingen and Hurst Solution (Exact solution) and thus proves to be very effective, simple, and accurate when compared to other form of solutions. Hence from the results gotten, Homotopy Analysis Method can therefore be applied in solving other non-linear equations in the petroleum engineering field since it is simple and accurate.
基金Supported by the National Natural Science Foundation of China under Grant No.51576079
文摘In this paper,we present a Cole-Hopf transformation based lattice Boltzmann(LB) model for solving one-dimensional Burgers' equation,and compared to available LB models,the effect of nonlinear convection term can be eliminated.Through Chapman-Enskog analysis,it can be found that the converted diffusion equation based on the Cole-Hopf transformation can be recovered correctly from present LB model.Some numerical tests are also performed to validate the present LB model,and the numerical results show that,similar to previous LB models,the present model also has a second-order convergence rate in space,but it is more accurate than the previous ones.
