Analytical and Numerical Solution of Nonisothermal Buckley-Leverett Flow Including Tracers

Abstract

Abstract Mass balances for two immiscible fluids and tracer and convective heat balance form a system of three equations (non-isothermal Buckley-Leverett Problem - ref. 1 -with Tracers). Tracer component is considered to investigate the propagation of a tracer in order to track the flood (or to track a miscible inert contaminant introduced during drilling). We have solved the resulting non-isothermal two-phase convective flow equation in porous media analytically, including a tracer component (i.e., cold or hot waterflooding with and without tracer). Method Of Characteristics (MOC) is used as a solution technique after transforming the balance equations in a form that can easily be solved with two Welge tangents (refs. 2-7). Our solution technique is valid for both radial and linear flow models. In practice, these solutions can be used:To investigate the convective flow behavior around the wells (i.e., sudden fluid losses, convective near-well tracer propagation, analyzing pressure transients).To interpret formation testing tool responses by detecting the location of the thermal front or to estimate the temperature buildup time that is needed for Horner type of analysis (for the identification of the formation temperature).To calculate the location of the cold or hot water front (thermal water) while injecting cold or hot water. This will yield the limit of the maximum temperature disturbance around the well.To test/scale relative thermal effects of various systems against each other.To test the accuracy of simulators and provide benchmark solutions.To interpret relevant laboratory experiments quickly. Such solutions helped us to understand the depth of influence of the temperature variations and its influence on the transport properties, in both radial and linear systems. Solutions analytically proved that the thermal front propagates much slower than the flood front. This explains why isothermal black oil simulators still work although the injected water temperature is not always equal to the reservoir temperature. Furthermore, we have checked/verified our results against a commercial thermal simulator (ref. 8) and investigated the impact of numerical diffusion on the thermal front as well as conductivity. This part of the work revealed that the temperature front is more prone to numerical diffusion.