Estimating Relative Permeability from Production Data: A Streamline Approach

Abstract

Abstract One of the outstanding challenges in reservoir characterization is to build high-resolution reservoir models that satisfy static as well as dynamic data. Integration of dynamic data so far has mainly focused on estimating spatial distribution of absolute permeability. Among the various properties important for simulating reservoir behavior, the relative permeability curves may be by far the most poorly determined by present methods. Estimation of relative permeability simultaneously with absolute permeability is a strongly nonlinear and ill-posed estimation problem. In this paper we present a streamline-based approach for estimating relative permeabilities from production data. The streamline approach offers two principal advantages. First, we can analytically compute the sensitivity of the production response with respect to relative permeability parameters. The approach is extremely fast and requires a single streamline simulation run. Second, we can exploit the analogy between streamlines and seismic ray tracing to develop a formalism for efficient inversion of production data. Thus, estimation of relative permeabilities is carried out in two steps: (i) matching of breakthrough or first arrival times and (ii) matching of amplitudes of the production response. For relative permeability representations we have used the commonly used power functions and also a more flexible representation through the use of B-splines. The relative advantages of these representations are examined through inversions of water-cut data from a nine-spot pattern. Finally, we address the underlying challenges associated with the simultaneous estimation of absolute and relative permeabilities from production data. We systematically investigate the non-uniqueness associated with the inverse problem and quantitatively evaluate the role of additional data such as pressure response in addition to water-cut history at the wells.