A fluid dynamic model for Single Well Chemical Tracer tests with variable petrophysical and pre-flushing parameters

Abstract

Porosity and permeability are two fundamental reservoir parameters. We study how important large variations in their values are for residual oil saturation estimates from Single Well Chemical Tracer tests. Although porosity and permeability do not enter the classical chromatography formulae, or variations thereof, that does not necessarily imply that they are irrelevant in all real scenarios. This is because porosity and permeability govern how fluids are distributed within the oil-bearing formation, and thus influence dispersion, temperature, rate of hydrolysis of the primary tracer, pH, partitioning etc., all of which may affect the residual oil saturation estimates. We focus on coarsening and fining upwards sedimentary sequences, but we also consider constant porosity scenarios. In addition, we examine how spatial variations in residual oil saturation influence the single value ‘average’ obtained by the tracer test. The impact of pre-flushing on the estimated residual oil saturation estimate is investigated as well. An axially symmetric finite element model was developed that calculates fluid flow in the wellbore as well as in the oil-bearing target formation; reservoir cooling caused by the injection of cold brine; transport of solutes in the brine; and pH driven changes in the rate of hydrolysis of ethyl acetate. A Reynolds Averaged Navier-Stokes equation with an algebraic turbulence model was applied in the wellbore to calculate fluid flow there, whereas the Brinkman equation was used in the porous target formation. The temperature of the brine pumped into the target as a function of time was calculated analytically for a down casing model. pH changes induced by the acetic acid produced by the hydrolysis of ethyl acetate are buffered by solutes in the injected brine as well as by calcite in the oil-bearing formation were accounted for. The transport of solutes calculations account for fluid advection, diffusion, dispersion as well as temperature dependent partitioning of ethyl acetate between the residual oil and the injected brine. We use test data based on published values and a brine composition that is realistic for a sandstone reservoir. The synthetic tracer production curves generated by the model vary only modestly between the various porosity, permeability, residual oil saturation and pre-flushing models. A simple and widely used chromatography formula was applied to estimate the residual oil saturation from the synthetic tracer curves. This yields 18–19% for all porosity-permeability scenarios when the true constant value is 22%. We also studied six cases with variable Sor. In these cases, the chromatographic formula underestimates the average residual oil saturation by 1–3% except in two models where residual oil saturation increases with increasing porosity; then, the estimate is 8% too low. More work is needed to understand why. In summary, we find that variable porosity and permeability do not significantly increase the estimation error relative to constant models, except when the residual oil saturation varies spatially – then, the error may be much larger. Finally, four pre-flushing models all yield 18% residual oil saturation for a true constant value of 22%, i.e., the error is like the tests without pre-flushing.