Practical Analysis of Injection/Falloff Data of Horizontal Wells

Abstract

fax 01-972-952-9435. AbstractWe have constructed new approximate analytical solutions for injection and falloff pressure response which include thermal effects that arise when flooding a reservoir with water having a temperature considerably below of that of the reservoir. We have developed an optimization code based on the Levenberg-Marquardt algorithm and coupled it with our new approximate analytical solutions to obtain a procedure for data analysis where our approximate analytical solutions are used as the forward model in the non-linear regression. We demonstrate that we can generate estimates of absolute permeabilities, the well skin factor, the length of the well and relative premeabilities by matching data to analytical solutions by minimization of a weighted least squares objective function. The relative permeability curves are constructed assuming a power law parametrization. In the horizontal well case, we show that the absolute permeabilities in the three principal directions can be resolved separately provided the duration of the test is sufficiently long.

Pressure Transient Analysis for Injectivity Tests in Multilayer Reservoirs

“…The Thompson and Reynolds' [15] steady-state theory has been used as basis for the development of analytical solutions for injectivity tests in single- [9,11] and multilayer reservoirs [12,16] with vertical wells. In reservoirs with horizontal wells, on the other hand, currently existing analytical solutions can only describe the pressure behavior in single-layer reservoirs [10,11,17].…”

“…Therefore, this work has two main goals: first, a formulation for injection/falloff tests in multilayer reservoirs with multilateral horizontal wells is proposed. This model, which is presented in Chapter 2, is based on the existing single-layer solutions [10,11,17]. Next, in Chapter 3, Green's functions are employed to develop an alternative formulation for injectivity tests in multilayer reservoirs with vertical wells.…”

“…Boughara and Reynolds [17] developed a formulation for injectivity tests that accounts for non-isothermal effects. Their solution considers that the injected water is at a different temperature than the reservoir and the temperature profile may be approximated by a Heaviside function.…”

“…In Eq. (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18), the flood fronts are assumed to remain constant [42,43]. Hence, the integral limits in Eq.…”

“…Therefore, the first and second integral terms of Eq. (2-18) may be numerically equal to zero if the well is shut-in before the water front reaches a vertical boundary; that is, if shut-in time t p is short enough so that the water front propagation is still at the "first radial" regime at the moment of shut-in [17].…”