Estimation of reservoir properties using transient pressure data: An asymptotic approach

Abstract

Abstract. An asymptotic formulation of the inverse problem for flow reveals that the inversion may be partitioned into two complementary subproblems. In the first problem the arrival time associated with the peak slope of the transient curve is directly related to reservoir properties. The second inverse problem is similar to current methods for interpreting flow data; the transient head amplitudes are related to reservoir storage and conductivity. The first subproblem, the arrival time inversion, involves much less computation than does amplitude matching. Furthermore, it appears to be more robust with respect to the starting model. Therefore the solution to the arrival time inversion provides a starting model for amplitude matching. The methodology is particularly suited to the analysis of observations from well tests. We apply the approach to observations from two interference tests conducted at the Borehole Test Facility in Oklahoma. Using the transient pressure measurements, we image a shallow conductive fracture. The existence and location of the fracture has been verified by both geophysical and borehole data. In particular, core from a slant well contains an open, vertical fracture which coincides with our conductive feature.

An Integrated Approach to Characterizing Bypassed Oil in Heterogeneous and Fractured Reservoirs Using Partitioning Tracers

“…However, in field situations, we typically have a step change in rate or pressure. As shown in Vasco et al (2000), a similar expression as in Eq. (7) occurs for a step change in pressure or flow rate if one considers the time derivative of pressure.…”

“…Our approach differs from earlier work in that we compute the peak amplitude sensitivities directly using a semi-analytic expression. This proves to be much more efficient than the previous approach based on Born approximation as proposed by Vasco et al (2000).…”

“…The travel time is then determined as the arrival time of the peak, and the maximum magnitude of the derivative is defined as the peak amplitude. For time varying injection one must de-convolve the input, as discussed in Vasco et al (2000). Note that field data usually contain fluctuations and direct differentiation of the data may be problematic.…”

“…In the context of tracer test analysis, several authors have shown the effectiveness of a travel time inversion of the tracer concentration or peak concentration data (Harvey and Grelick, 1995;Vasco and Datta-Gupta, 1999;Bellin and Rubin, 2004). However, the role of travel time inversion for the pressure data has only been realized relatively recently (Vasco et al, 2000;Kulkarni et al, 2001;Brauchler et al, 2003). Our goal here is to obtain a high resolution estimation of permeability distribution based on travel time inversion of transient pressure data.…”

“…Our proposed approach is particularly well-suited for interference tests and hydraulic tomography where a large number of pressure measurements may be available for a detailed description of the subsurface property distribution (Gottelib and Dietrich, 1995;Yeh and Liu, 2000;Vesselinov et al, 2001;Liu et al, 2002;Brauchleret al, 2003). Vasco et al, (2000) and Kulkarni et al, (2001) utilized a travel time inversion akin to seismic tomography to integrate interference pressure data into reservoir models. The travel time of pressure is derived by differentiating the transient pressure data with respect to time and corresponds to the arrival time of the peak of transient pressure time derivative.…”