Darcian-Non-Darcian Seepage And Solute Transport In Pore-Fracture Double-Porosity Aquifer

Well testing in double-porosity fractured aquifers or oil and gas reservoirs is one of the long-lasting research problems in hydrogeology and petroleum engineering.The double-porosity medium can be approximated as a two interrelated continuum（fracture network and rock matrix）with two distinctively different porosities.Most of those studies in double-porosity fractured aquifers only concern Darcian flow in the fractured continuum,while the flow in fractured media is likely to be non-Darcy flow actually.In this study,we will expand such studies from Darcian flow regime to non-Darcian flow regime,established the double-porosity Darcian-non-Darcian flow confined well flow model,and according to occurring of unconfined flow condition in fracture continuum with the pumping continuing,expanded non-Darcian confined well flow model to confined-unconfined well flow model.Under the condition of radial steady-state flow formed by pumping,the double-permeability solute transport model of radial convergence flow was established,and solved numerically by finite difference method.Under the assumption that the non-Darcian flow follows the power law,a linearization approximation is utilized to develop the hydraulic head Laplace-domain solutions,which are subsequently inverted to give spatiotemporal distributions of fracture media in real-time domain.The results of dimensionless parameter analysis show that,a larger dimensionless quasi conductivity coefficient K_{q D} leads to a larger drawdown in the early stage,and a smaller drawdown in the late stage.The dimensionless parameters C_D and influence the drawdown in transitional state,and when the values get larger,the drawdown in in transitional state becomes smaller.A pumping test conducted in Huangtun,Anhui province of China has been applied to test the non-Darcian flow effect in a double-porosity aquifer,in which a particle swarm optimization（PSO）algorithm has been applied to seek the optimal hydraulic parameters among different inversion models.The results show that the non-Darcian flow model can well better describe the double-porosity aquifer pumping process,and better predict water level drawdown among the water recovery phase.If the non-Darcian flow effect is not taken into consideration,the hydrogeological parameters of the double-porosity aquifer will be overestimated.The Boulton delayed yield from storage above the water table is introduced to establish the non-Darcian confined-unconfined well flow model in the double porosity fracture medium with the process of confined-unconfined transition.The analytical solution of hydraulic head drawdown in the fracture in Laplace space is obtained through an approximative linearization and Laplace transform,and subsequently inverted to give spatiotemporal distributions of fracture media in real-time domain.The influence of non-Darcian power law index,reciprocal of delay index and gravity feed water degree of fractures on water level drop in fractures is analyzed.The results show that with the increase of the non-Darcian power index,the non-Darcian effect in the fracture becomes stronger,the water flow in the fracture is not only affected by the viscous force,but also by the inertia force,and the energy loss（head loss）generated by the fracture flow is larger;the larger the gravity storage coefficient S_df of the fracture is,the larger the gravity water release of the fracture is when unconfined condition occurs,the smaller the hydraulic head drawdown of the fracture is.The larger reciprocal of delay index a of the fracture is,the smaller the delay of the gravity water release from the fracture is in the process of unconfined condition,the smaller the hydraulic head drawdown of the fracture is.Compared with the confined well flow model,the closer the pumping well is,the earlier the unconfined zone occurs,the more sufficient the gravity water release from the fracture,and the applicability of confined-unconfined well flow model to inverse the hydraulic head drawdown in Huangtun Jurassic aquifer system is better than confined well flow model.The farther from the pumping well,the greater the delay of gravity water release,and the smaller gravity water content release from fracture.There is no significant difference between the results of inversion water level drawdown process between confined-unconfined well flow model and confined well flow model.Therefore,When the observation well is far enough away from the pumping well,although there is a confined-unconfined zone near the pumping well,the double-porosity confined well flow model can still be used to invert the hydrogeological parameters of the double-porosity confined aquifer.Under the condition of steady-state radial convergent flow field formed by pumping in double porosity medium,a mathematical model of radial convergent double-permeability solute transport was established and numerically solved by finite difference method.Through the parameter analysis,we have discussed the fracture and the actual velocity in porous media,the effective porosity ratio and longitudinal dispersion coefficient,and the mass exchange coefficient between the fracture and pore parameters on the influence of solute concentration curve.The results show that the larger the velocity difference between the fracture and the pore matrix,the longer the time interval between the occurrence of the peak concentration,the greater the difference of peak concentration.The larger the effective porosity ratio between the pore matrix and fracture,the higher the proportion of solutes into the porous media,and thus the higher the second peak concentration caused by the pore matrix,otherwise,the peak concentration is lower.The longitudinal dispersion between different media affects the peak concentration and the concentration penetration curve in the medium,and thus affects the concentration penetration curve in the aquifer.The mass transfer coefficient between pore matrix and fracture influences the concentrations in both media.When the mass transfer coefficient is larger,the concentration exchange capacity from rock matrix to fracture is larger,and the concentration penetration curve in the fracture gradually shows the characteristics of tailing,or exhibits an irregular hump shape.When the mass transfer coefficient reaches a certain value,the closer the arrival time of the peak concentration in the fracture and porous media is,the smaller the difference between the peak concentration in the fracture and porous media is.At this time,the concentration penetration curve in the aquifer is no longer bimodal.The double-permeability solute transport model can well reveal the double-peak characteristics of fluorescein sodium concentration breakthrough curve in Jurassic aquifer,but does not necessarily yield good results for monitoring the trailing characteristics of concentration decay curve in the later monitoring period.