fax 01-972-952-9435. AbstractThe first and fifth authors have previously used the Thompson-Reynolds steady-state theory to derive solutions for the pressure response at a water injection well. In the vertical well case, their solutions assumed a completepenetration well; in the horizontal well case, they assumed that the well is equidistant from the top and bottom of the formation. Here, we construct approximate analytical pressure solutions for the restricted-entry vertical well case and for a horizontal well for the case where the well's axis is not equidistant from the top and bottom boundaries. The solutions are based on adding to the single-phase solution, a multiphase term which represents the existence of the two-phase zone and the movement of the water front. We present models for the movement of water based on a combination of Buckley-Leverett equations that allow us to accurately compute the multiphase flow component of the analytical solution. By comparison with a finite-difference simulator using grid refinement and a hybrid grid, it is shown that our multiphase flow solutions are accurate.The analytical solutions provide insight into the behavior of injectivity tests at horizontal an vertical wells. For example, for a restricted-entry case, it is shown that the pressure derivative may be negative throughout an injection test even when the duration of the test exceeds ten or more days. We also show that for a well near a fault, the ratio of slopes reflected by derivative data will not in general be equal to two but is given by a formula that involves the mobility ratio. In the restricted-entry vertical well case, we provide the equations for three flow regimes.

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