Tracer testing is a powerful tool for reservoir description and evaluation at every stage of the productive life of a reservoir. In this work, we present an analytical and numerical model for the transport of tracer in oil reservoirs containing a high permeability streak. The new analytical model is aimed to aid in the interpretation of tracer tests, provide a better insight into the mechanisms of tracer/EOR fluids transport, understand the role of input parameters, and provide a useful benchmark for numerical simulators. The model is validated by a numerical simulator COMSOL Multiphysics 4.3 which employs finite element technique in its ‘Subsurface Flow" module.
The new analytical model is distinguished with its ability to account for finite longitudinal and transversal tracer dispersions in the high permeability streak and the tracer loss into the bounding low permeability layers. Thus, being possibly the most comprehensive exact analytical unsteady two dimensional tracer transport model, it exhibits the roles of both boundary conditions and fluid mechanics controls simultaneously. Intuitively, one would expect that the coupled one dimensional analytical solutions may be appropriate for the systems with a large aspect ratio defined as the ratio of the length of high permeability zone to its half-width. In this work, however, we demonstrate that the parameter which controls the applicability of one dimensional models is the square root of ratio of the two characteristic times of longitudinal and transverse dispersion. While we have validated the analytical solution with a finite element simulator, the analytical solution in turn provided an advanced benchmark free of numerical dispersion and unphysical oscillations in two-dimensional domains for numerical models.
The nonlinear regression programs coded in MATLAB are employed to interpret the tracer return profiles, and hence, to be able to estimate the models parameters along with related confidence intervals.