A Streamtube Approach for Modeling Mass and Heat Migration for Thermal Recovery Methods

Abstract

This paper presents a new reservoir simulator for mass and heat migrationbased on the streamtube technique. The current version of the program focuseson characterizing migration of the injected fluid. The method is heavily basedon the distribution of the pore volume along each streamtube calculated byusing the Time-of-Flight method. This information and the 1D solution of massand energy equations are used to determine thermal migration as well astemperature changes at production wells. The streamtubes are derived from anunderlying velocity field, which is obtained from the solution of the pressureequation under the assumption of incompressibility. The compressibility effectsare accounted for in the 1D solutions along periodically changingstreamtubes. Simulations are carried out for a five-spot well pattern in 2D areal domainswith various types of heterogeneity under different injection scenarios. Weconfirmed that the results from the streamtube approach had a reasonablebalance between its ability to provide an insight into the behavior of mass andheat flow and the computational efficiency. Comparisons with a commerciallyavailable simulator both validated the method and illustrated the cases inwhich this method is more useful to reservoir engineers. Introduction Higgins and Leighton1,2 and Higgins et al.3 inthe early 1960's are credited with being the first to apply the streamtubetechnique to model convective displacement in porous media and to set the stagefor a number of papers to follow by other authors. An important step forward inthe attempt to model real field problems is due to Doyle and Wurl4, Bommer and Schechter5, Lake et al.6, Emanuel etal.7, Pozucek and Ramirez8,9. In the 1990'sstreamtube methods continued to be explored. These efforts are described innumerous papers notably by Renard10, Thiele11, Thieleet al.12 and Baek and Hewett13. The application ofthe method for flood front management has been described by numerous otherauthors14–16. The reason behind using the approach has been that itallows a fast evaluation of reservoir performance, and that it has beenextended to accommodate realistic flow physics. These strong points have alsoled to a host of other applications, for example, multiphase upscaling throughthe use of pseudo relative permeability17 and flexible gridgeneration during reservoir simulation18. Previous streamtube methods so far focused on the isothermal flow. Limitedwork has been done to extend the application of streamtube/streamlinesimulation to thermal flood simulation. This is not surprising, as the couplingbetween mass and energy transport in thermal flood simulation adds considerablecomplexity. This then would be coupled with an appropriate thermodynamicformulation to account for condensation/vaporization and changes in propertieswith temperature and pressure. A paper written by Emanuel19 isrelated to the non-isothermal flow application. He developed a fixed streamtubemodel for estimating steam drive performance of single pattern and full fieldscale. Unfortunately this paper does not indicate how the mass and energyconservation is formulated and how to solve the coupled equations along thestreamtubes.