Effect of Vertical Fractures on Reservoir Behavior-Incompressible Fluid Case

Abstract

The pressure and production behavior of a homogeneous cylindricalreservoir producing a single fluid through a centrally located verticalfracture of limited lateral extent was determined by using mathematicalmethods to solve the appropriate differential equation. It is assumedthat there is no pressure drop within the fracture - that is, thatthe fracture capacity is infinite. It was found that the production-ratedecline of such a reservoir is constant (except for very early times)when the flowing bottom-hole pressure remains constant. The production-ratedecline increases as the fracture length increases. Thus, the lateralextent of fractures can be determined from the production-rate declinesbefore and after fracturing or from the decline rate after fracturingwhen the properties of the formation and fluids are known. The productionbehavior over most of the productive life of such a fractured reservoircan be represented by an equivalent radial-flow reservoir of equalvolume. The effective well radius of this equivalent reservoir isequal to one-fourth the total fracture length (within 7 per cent);the outer radius of this equivalent reservoir is very nearly equal(within 3.5 per cent) to that of the drainage radius of the fracturedwell. The effective well radius of a reservoir producing at semisteadystate is also very nearly equal to one-fourth the total fracturelength. It thus appears that the behavior of vertically fracturedreservoirs can be interpreted in terms of simple radial-flow reservoirsof large wellbore.