Tracer- and Pressure-Test Analysis for Characterization of Areally Heterogeneous Reservoirs

Abstract

Summary This study compares simulated well-to-well tracer and transient pressuretests in a quadrant of a repeated five-spot with spatial variations inpermeability. Single-layer heterogeneous media with an autocorrelated andlog-normal permeability distribution are generated with a stochasticmoving-average method. Finite difference simulation of pressure behavior inthese systems indicates that the geometric mean of effective permeabilitiesaround injection and production wells is a good approximation for thesteady-state index, defined as the product of permeability variance and adifference, a defined in terms of these quantities, correlates with aheterogeneity index, defined as the product of permeability variance and adimensionless correlation length scale. Tracer flow is simulated with aparticle-tracking procedure. Simi can be matched with solutions of theconvection-dispersion equation index. For larger values of this index, preferential flow paths a they result from flow in a layered system. A methodis proposed to predict the nature of the tracer response qualitatively. Introduction The performance of an EOR process depends primarily on the in situinteraction of the injected fluid with the oil, the heterogeneity of thereservoir rocks, and the coupling between these two effects While fluid mixingand phase behavior can be studied in the laboratory, the nature of variationsin the properties of porous media (e.g., permeability and porosity) can beunraveled only through indirect means. Two kinds of well tests commonly areused for this purpose, well-to-well tracer testing and transient pressuretesting Interwell tracer tests are used to track subsurface fluid movement andto infer formation characteristics. In such tests, a trace slug is driven by achase fluid and the tracer concentration at a adjacent producer is monitored. Quantitative interpretation of tracing test data is based on solutions of theconvection-dispersion equation...............................................(1) Pressure-transient tests are useful for estimating average formationproperties and wellbore conditions and for detecting barrier for fluid flow. Insuch tests, the flow rate at one well is perturbed and the resultant pressureresponse at the same or adjacent well is measured. Analysis of pressure data isbased on solutions of the pressure-diffusion equation:...............................................(2) Most well-test interpretation models compute an effective media urn property(e.g., permeability or dispersivity) that correspond to a fictitioushomogeneous system, whose behavior matches that of the real heterogeneoussystem. If distributed heterogeneities are to be detected qualitatively and/orquantitatively by well tests, how ever, some knowledge of the relationshipbetween these effectively parameters and system heterogeneities is required. Anassociated question of importance is the definition of conditions under whichsuch effective medium approximations can be used to describe what erogenousmedia. In this study, we ask whether well tests can be used to characterizemacroscopic variations in permeability at the interwell scale The system of interest, shown in Fig. i, is one-quarter of a single layer five-spot within arepeated and balanced production/injection pattern in 2D areal geometry. Ourobjective is to simulate both well to-well tracer and transient pressure teststo examine (1) the sensitivity of well-test responses to a heterogeneouspermeability field and (2) the quantification of in-situ permeabilityvariations from the analysis of well-test data. We focus on pressure responsesat injection and production wells and on the apparent mixing (dispersion) atthe interwell scale that results from purely convective tracer flow. Previousstudies of flow and transport through heterogeneous permeable media have beenrestricted to analysis of either the pressure or tracer-test response. Similarwork in the groundwater literature has been summarized. In this paper, and thecompanion work of Mishra and Ramey, our goal is to provide a comparativeassessment of the impact of heterogeneities on pressure- and tracer-testresponses. The approach adopted here is similar to the Monte Carlo simulationprocedure first presented by Warren and Price. First, permeability values areassigned to each node of the grid shown in Fig. 1 such that the assumedstatistics of permeability variation are honored. Then pressure history at theinjection and production wells is simulated until steady state is attained andpressure/time data are analyzed. Finally, convective tracer flow is simulatedand breakthrough tracer-concentration data are analyzed. This procedure is thenrepeated for several arrangements of the permeability field for each set of statistical parameters. Representation of Heterogeneous Media Field evidence indicates that such properties of porous media aspermeability and porosity vary from point to point in a random manner and alsoexhibit spatial correlation. In the petroleum literature, permeabilityvariation has been analyzed statistically; however, measurements of spatialcontinuity with geostatistical techniques have been undertaken only recently. We restrict discussion to heterogeneous media with variations only inpermeability because the effects of porosity variations on subsurface fluidflow and transport have been shown to be small. We assume that permeability isa random function with a known mean, variance, and spatial correlationstructure. We also assume that the flow domain is statistically homogeneous, which implies that the mean is independent of location and the spatialcorrelation between two samples depends only on their separation. Permeabilityis characterized by a log-normal frequency distribution so that variability canbe expressed by the Dykstra-Parsons coefficient...............................................(3) where k50 and k84.1 = 50th and 84.1th percentile values from alog-permeability cumulative distribution function (CDF). variance. Fig. 2 showsa hypothetical log-permeability CDF. Spatial continuity implies correlationbetween permeabilities of gridblocks that fall within a given area in a 2Dsystem. This can be expressed quantitatively through the semivariogram................................................(4) SPEFE P. 45^