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 and Pressure Derivative Analysis for Injection Tests With Variable Temperature Without Type-Curve Matching

“…As we see permeability results agree with the value reported by Boughrara and Reynolds (2007). Simulation runs were also performed for other four temperatures.…”

“…Where Equations 2, 3 and 4: Using the assumption that both the water front and the temperature front fall inside a "steady state region" so that total rate is equal to injection rate, Q inj , and following a procedure similar to the one presented by Boughrara and Reynolds (2007), a modifi ed analytical solution for cold water injection in a hot oil reservoir drained by a vertical well is presented here as Equation 8:…”

“…It is required to estimate permeability and skin factor from a fi eld example provided by Boughrara and Reynolds (2007). Figure 3 presents the pressure and pressure derivative data for an injection test in a hot reservoir at a temperature of 180°F when μ o (T oi ) = 1,553 cp.…”

“…That solution was initially introduced for the calculation of the injection pressure in an isothermic system. It was later modified by Boughrara and Reynolds (2007) to consider a system with variable temperature in vertical wells. In this work, the pressure response was obtained by numerical solution of the anisothermical model using the Gauss Quadrature method to solve the integrals, and assuming that both injection and reservoir temperatures were kept constant during the injection process and the water saturation is uniform throughout the reservoir.…”