| Wellbore pressure drop can be important in long horizontal wells in high permeability reservoirs producing large flow rates. If pressure drop in the wellbore is not taken into account in such cases, the productivity of the well and water/gas breakthrough times can be grossly over-estimated. The only way to capture these effects is by considering pressure drop in the wellbore.; Comprehensive, transient, three-dimensional, semi-analytical models are developed in this work to calculate the productivity of a finite-conductivity and an infinite-conductivity horizontal well. The finite-conductivity well model provides a reference solution to calculate the productivity of a horizontal well placed in a box-shaped drainage volume with due consideration to frictional and accelerational pressure drops, fluid inflow effects, and variable skin along the well. We believe that our finite conductivity well model is more general than any published previously. This model can also be used to obtain the desired perforation density along the well so that inflow will be uniform along the entire well length. Using superposition in time, these models can be run under either constant flow rate, constant bottom-hole pressure, or a sequence of these two constraints. A methodology is also developed to calculate the optimum length of a horizontal well under single-phase flow conditions.; Reservoir simulators require a well model to couple the well block pressure to the well pressure. Most of the commercial simulators use the Peaceman well model, which gives significant errors when used on partially penetrating vertical or horizontal wells. A new three-dimensional well model is developed using the infinite and finite conductivity semianalytical models. The new model can be used to calculate the well index necessary to simulate the performance of horizontal wells in conventional reservoir simulators.; When the line source solution of Babu and Odeh (1989) is used to calculate the productivity of a horizontal well in an anisotropic reservoir, the pressure varies along the circumference of the well. Assuming that the uniform pressure inner boundary condition is valid, a new angle is proposed at which the well pressure should be calculated when the line source solution is used in anisotropic reservoirs. |
