An analytical solution for heterogeneous and anisotropic anticline reservoirs under well injection

Recent advances in modeling of well hydraulics

“…Several studies provided analytical solutions for groundwater flow problems in aquifers whose plan views are rectangular [7][8][9], wedge-shaped [10][11][12][13][14][15] and triangular [16], and in aquifers whose cross sectional views are step-like [17,18].…”

“…The model has two flow equations along with two Moench's free surface equations to describe the flows in the skin zone and formation zone, separately. In a study on the dynamic response of tidal fluctuations in unconfined aquifers, Yeh and Kuo[18] examined the effect of neglecting the second-order terms in Eq. (18) on the accuracy of their analytical solution which is developed using the simplified free surface equation as the top boundary condition.…”

A general analytical solution for steady flow in heterogeneous porous media

“…Notable examples include the solutions of Obdam and Veling [1987], Janković and Barnes [1999a], and Barnes and Janković [1999]. A number of special closed-form solutions, including flow through circular and elliptical inclusions, are documented in Strack [1989] and there are a number of one-dimensional solutions available for both steady state and transient flow in piecewise-homogeneous domains [e.g., Yeh and Kuo, 2010;Liang and Zhang, 2013;Hu and Jiao, 2014]. Simulation of flow through highly heterogeneous conductivity fields using analytical approaches is possible via the superposition of solutions for piecewise constant heterogeneity [e.g., Janković et al, 2003]; this approach is very successful, enabling the solution to problems with tens of thousands of inclusions.…”