Productivity and injectivity of horizontal wells. Quarterly report, January 1, 1996--March 31, 1996

A reservoir simulator solves the flow equations numerically on grids defining a reservoir region. However, when a well is located in a grid-block, the block pressure is not equal to the well pressure. In order to join the well to the grid blocks in which the well is located, it is usual to use a single phase model to obtain the appropriate Well Index. The Well Index is based on the concept of an effective well radius at which the pressure of the block applies. This approach requires the flow in the area around the well to be radial. Peaceman has proposed more general expressions for the effective radius, but all based on 2D flow. As reservoirs are generally thin, a horizontal well cannot be far from the top or bottom boundary. In the case of multilateral wells, the situation is even worse, since the flow is perturbed not only by the boundaries but also by the other wells. Moreover, horizontal wells can be efficient in low permeability reservoirs, where the steady-state (or pseudo-steady-state) regime does not establish rapidly. This means that a single constant value for the well index cannot be used for all times. The objective of this study is then to evaluate well indices for different configurations of horizontal wells. The well index will be computed for a homogeneous anisotropic single-phase flow and will then be reintroduced in the simulator for the full three-phase study. The well index relates the pressure in the block to the pressure in the well for a given flow rate. If these two pressures are known, the well index can be deduced easily. The block pressure can be evaluated by a simulator. The well pressure for a three-dimensional single-phase flow is not known analytically in general, but can be computed by the semi-analytical method described briefly below.