Estimating absolute and relative permeability using dynamic data: A streamline approach

Incorporation of dynamic data, which are time variant measurements such as production history or transient pressure response, is necessary to obtain reliable reservoir descriptions. This information is particularly useful in identifying properties describing the flow behavior of the reservoir.; This dissertation consists of two major parts. In the first part, oil and water relative permeability functions are estimated based on water-cut response in producing wells. In the second part, spatial distribution of absolute permeability is estimated based on transient pressure response recorded in observing wells during pressure interference tests.; In our inversion approach we use a streamline simulator as a forward model to estimate absolute and relative permeability. Use of streamline simulation in inverse modeling is advantageous in two respects. First, the streamline simulators can serve as an efficient forward model for the inverse problem. Second and more importantly, parameter sensitivities can be formulated as one-dimensional integrals of analytic functions along streamlines. The sensitivities are therefore computed analytically by a single forward simulation.; In our approach to relative permeability estimation, a relative permeability model based on for example core analysis is modified to satisfy measured water-cut history from the field. The breakthroughs or ‘first arrival’ times at producing wells are matched in an iterative procedure. It is shown that the use of a non-parametric representation through B-splines results in more reliable relative permeability estimates than the use of power functions.; For estimation of absolute permeability based on transient pressure response, we generalize streamline modeling to compressible flow by introducing a ‘diffusive’ time-of-flight along streamlines. In particular, we adopt a high frequency asymptotic solution to the diffusivity equation to compute travel times associated with a propagating ‘pressure front’. The arrival times of pressure are matched for observing wells through an iterative procedure. The approach is validated with synthetic cases and a field case from the Conoco Borehole Test Facility (CBTF). The fracture locations inferred are found to be consistent with independent geophysical experiments at CBTF.; An analogy between the ‘diffusive’ time of flight and the radius of drainage is established, and used to obtain the radius of drainage for general heterogeneous media with arbitrary well configuration.