Representation of pressure field and fluid flows in the proximity of a horizontal well based on the instant point sources

The boundary value problem of transient pressure field development around a horizontal well in a laterally infinite, inhomogeneous, anisotropic reservoir is formulated under assumption of slow spatial variation of the matrix permeability along the well axis. The well is represented as a linear fluid source/sink. The pressure distribution is expressed in the integral form on the basis of the instant point source perturbation function found explicitly. The inverse problem for fluid in/outflow density rates simulation is reduced to solution of the integral equation at a given pressure inside the well. A computational procedure is developed and implemented to predict the in/outflow rates along the well and estimate the impact of the permeability variations on the well performance. Series of calculations for constant, linear, and variable permeability cases are analyzed and compared. The difference of the obtained solution from the so-called “locally-constant” permeability approximation is demonstrated, accuracy and applicability of the latter approach are discussed.