One of the outstanding challenges in reservoir characterization is to build high-resolution reservoir models that satisfy static as well as dynamic data. However, integration of dynamic data typically requires the solution of an inverse problem that can be computationally intensive and becomes practically infeasible for fine-scale reservoir models. A critical issue here is computation of sensitivity coefficients, the derivatives of dynamic production history with respect to model parameters such as permeability and porosity.
We propose a new analytic technique that has several advantages over existing approaches. First, the method utilizes an extremely efficient three-dimensional multiphase streamline simulator as a forward model. Second, the parameter sensitivities are formulated in terms of one-dimensional integrals of analytic functions along the streamlines. Thus, the computation of sensitivities for all model parameters requires only a single simulation run to construct the velocity field and generate the streamlines. The integration of dynamic data is then performed using a two-step iterative inversion that involves (i) "lining up" the breakthrough times at the producing wells and then (ii) matching the production history. Our approach follows from an analogy between streamlines and ray tracing in seismology. The inverse method is analogous to seismic waveform inversion and thus, allows us to utilize efficient methods from geophysical imaging.
We have applied the proposed approach to a highly heterogeneous carbonate reservoir in west Texas. The reservoir model consists of 50,000 cells and includes multiple patterns with 42 wells. Water-cut histories from 27 producing wells are utilized to characterize porosity and permeability distribution in the reservoir, a total of 100,000 parameters.