Stochastic heterogeneity, dispersion and field tracer response

This research seeks to contribute towards improved performance prediction of hydrocarbon reservoirs through a quantitative description of heterogeneities and formulation of improved numerical algorithms for fluid flow modeling.;We examine the applicability of high resolution monotonic schemes for modeling tracer motion in permeable media. For convection-dominated flows, we achieve sharp resolution of discontinuities by introducing a new flux limiter that is third-order accurate in space and time in the smooth regions and results in oscillation-free numerical solution by imposing the total variation diminishing (TVD) criteria. The proposed third-order scheme has been shown to significantly minimize numerical dispersion and grid orientation effects by application to the linear convection-diffusion equation at large Peclet numbers and also, to multidimensional tracer flow problem in a quadrant of a five-spot.;For studying flow through heterogeneous permeable media we assume permeability to be a stochastic random variable defined by a probability distribution and a spatial covariance structure. We then quantify channeling (convective) and dispersive behavior in heterogeneous media exhibiting different degrees of spatial correlations using a new dispersion-free semianalytic transit time approach. The variance of arrival times at the producer is related to the flow characteristics of the medium through a spectral decomposition. We use a simple one-dimensional stochastic model to characterize the transition from channeling to dispersion and anomalous diffusion in fractal fields. A heuristic model of channeling is shown to effectively represent the tracer response from permeability fields exhibiting long range correlations.;We propose a type-curve approach to analyzing two-well tracer data to estimate geostatistical heterogeneity parameters. Theoretical frequency response functions are obtained by mixing contributions from individual streamlines at a producer for different degrees of reservoir heterogeneities and spatial correlations. The results are used to build theoretical transfer function and phase spectrum. A type curve approach is then adopted to analyze field tracer history by comparing the theoretical and field observed transfer function and phase relations, leading to an estimate of the heterogeneity parameter. The technique is illustrated with a field example.;Finally, we propose an approach to generate an integrated reservoir description by combining data of widely varying scales. We discuss and compare three different algorithms based on combinatorial optimization schemes for generating stochastic permeability fields. The algorithms are not restricted to Gaussian random fields and have the potential to accomplish geologic realism by combining data from many different sources. We introduce a 'heat bath' algorithm for simulated annealing as an alternative to the commonly used 'Metropolis' algorithm and a new stochastic modeling technique based on the 'genetic' algorithm. We apply these algorithms to a set of outcrop and tracer flow data and examine associated uncertainties in predictions.