Approximate Analytical Solutions for the Pressure Response at a Water Injection Well

Abstract

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.

A new insight for reliable interpretation and design of injection tests

“…Based on the results from Bradvold and Horne, Levitan (2002) developed an analytical solution for calculating pressure by decoupling the saturation and temperature profiles from the pressure response. Peres et al (2004) derived an approximate analytical solution for oilwater bi-phase flow in the case of restricted-entry vertical wells and horizontal wells. However, if the reservoir is gas-bearing, the assumption that saturation and temperature profiles can be decoupled from pressure is no longer acceptable because the reservoir phase properties are strongly pressure and temperature dependent, increasing the nonlinearity of the problem.…”

Approximate solution for pressure behavior during a multiple rate injectivity test

“…Approximate analytical solutions for the injection pressure response at a horizontal water injection well have been presented by Peres et al (2004), using Buckley and Leverett's (1942) solutions to the water saturation profile based on the proposed models for water displacement.…”

Testes De Injetividade Em Reservatório Multicamadas: Solução Aproximada Para Um Esquema De Múltiplas Vazões

“…Soluções analíticas aproximadas para poços verticais foram desenvolvidas por Peres et al (19) em 2004. Para isso, os autores utilizaram a solução de fluxo monofásico adicionado a um termo multifásico que representa a zona bifásica e o comportamento da frente de avanço de água.…”