Modeling Conformance as Dispersion

Abstract

Summary For decades the effect of physical dispersion (in-situ mixing) in porous media has been of interest in reservoir engineering and groundwater hydrology. Dispersion can affect the development of multicontact miscibility and bank breakdown in enriched-gas drives and miscible solvent floods of any mobility ratio. The magnitude or extent of dispersion is quantified by the rock property physical dispersivity, α, which is on the order of 0.01 ft for consolidated rocks and several times smaller for sandpacks, as found in many laboratory measurements. Numerical studies of the effect of dispersion on enriched-gas drives and field tracer tests often use input values of a scale-dependent dispersivity 100 to 1,000 or more times larger than ≈0.01 ft. These large scale-dependent dispersivity values stem from large apparent dispersivities (αa) determined by matching the 1D convection/diffusion (C/D) equation to production-well-effluent tracer-concentration profiles observed in field tracer tests. A scale-dependent dispersivity can be used only as a fitting factor to match or explain the effluent profile of a single producer at a fixed distance from an injector. It cannot represent physical dispersion to justify the conclusions reached by its use in simulations of enriched-gas-drive, field-tracer-test, or other reservoir displacement processes. It has no predictive value in any numerical simulation. The scale-dependent apparent dispersivities reflect conformance or other behavior not governed by the 1D C/D equation and should not be used to justify large dispersivities as input to numerical studies. This paper shows that large apparent dispersivities observed in field tests can result with physical dispersivity no larger than the ≈0.01-ft laboratory-measured value. Heterogeneity alone (no physical dispersivity or molecular diffusion) causes no in-situ mixing and cannot explain observed large apparent echo-test dispersivities. Large apparent dispersivities for two reported echo (single-well inject/produce) tracer tests are shown to result from a model with drift alone and no dispersion. The widely reported scale dependence of apparent dispersivity is a simple and necessary consequence of mis-applying the 1D C/D equation, with its single parameter of Peclet number, L/α, to conformance it does not describe. The conformance portion, aac, of apparent dispersivity, αa, is scale-dependent, but physical dispersivity is a rock property independent of scale and time. The value of αa approximately obeys an additive dispersivity principle, αa≈α + αac, where αac is dispersivity representing conformance and αaG>>α in field displacements.