Modeling Tracer Flow in Oil Reservoirs Containing High Permeability Streaks

Abstract

Tracer testing is finding extensive applications in petroleum engineering including determining inter well flow characteristics and has the potential tobe used as a tool for reservoir characterization. However, many tracer tests have still been designed poorly and used in a rather qualitative manner. Despite the fact that a number of previously published analytical models for a quantitative evaluation are instructive, there is still a great need for more sophisticated analytical models to study the collective role of transport parameters. Owing to these facts, in this work we present an analytical model for the transport of tracer in oil reservoirs containing a high permeability streak that may provide a better insight into the mechanisms of tracer/EORfluids transport in oil reservoirs. The new model has several distinguishing aspects. First, both finite longitudinal and transversal tracer dispersions have been accounted in the high permeability streak as well as the tracer loss into the bounding low permeability layers. Thus, being the first analytical unsteady two dimensional tracer transport model, it allows one to observe the roles of both boundary conditions and fluid mechanics controls simultaneously. This is superior feature of the model over the previous analytical models that assume either boundary conditions or fluid mechanics controls dominate. In addition, since the solution is free of numerical dispersion and unphysical oscillations especially in two-dimensional domains, it serves as a higher step-stone for validation of numerical models. Being a general solution of the convection dispersion equation, the new solution will find application in all modern fluid injection processes particularly heat transients during cold water injection, miscible and chemical displacement processes and thermal recovery methods as well. Introduction Reservoir description and evaluation is a continuous process over the productive life of a reservoir. Consider for example development of a reservoir block during a primary or secondary production period. The development of each block generally needs at least several wells and hence determining the degree of connectivity and possible well interference is of vital importance. Bingyu et al.1 states that there are three phases of block development for a specific system such as water drive or steam soak and so on. At the beginning of reservoir development the direction of fractures, the degree of heterogeneity and the effect of injected water are of interest. At later stages of the development determination of the utilization efficiency of injected water, displacement status among wells and the source of produced water becomes important. At the final phase, existence of high permeability streaks, the distribution of oil saturation needs to be determined and the evaluation of the development should be carried out. The tracer test technology has emerged as a powerful tool for studying the interwel flow and transport characteristics2,3. Since any attempt to identify each of previously mentioned features could benefit greatly from interwell tracer tests, the results of tracer tests could contribute greatly to reservoir evaluation and subsequent operational adjustments in each phase of reservoir development. Consider also the enhanced oil recovery period, where an enhanced oil recovery technique involves injection of a small slug of an expensive fluid followed by a less expensive driving fluid. For instance, during a chemical or miscible flood reservoir heterogeneities may lead to channeling due to preferential flow paths and hence to inefficient use of the oil displacing fluid3. Caused by dispersion or loss into confining layers, slugde gradation leading to loss of microscopic displacement efficiency is also a major concern. Tracer tests providing information about the existence and scale of preferential flow paths leading to volumetric and dispersion characteristics leading to microscopic displacement inefficiencies, provide valuable in sightinto how a reservoir would perform in a chemical/miscible displacement process.

Simulation study on waterflood front: Block Hade of Tarim Oilfield in Northwest China

“…Dispersion in porous media refers to the spreading of contaminants over a greater region than would be predicted solely from the average water velocity vectors [13][14][15] . Dispersion is caused by mechanical dispersion, a result of deviations of actual velocity on a microscale from the average water velocity, and by molecular diffusion driven by concentration gradients.…”

Application of iterated Laplace transformation to tracer transients in heterogeneous porous media

“…Then, the dimensionless governing equations consist of two coupled linear differential equations representing the transport in fracture and matrix [9,10] …”

“…(22) has been derived in many transport studies [9,10] and mostly been computed using numerical Laplace transform inversion techniques such as either Stehfest [7], Dubner Abate or Crump algorithms [8].…”