Application of coherence theory to a reservoir enhanced oil recovery simulator

The theory of coherence, as originally developed by Helfferich, was restricted to a number of stringent premises for the sake of simplicity and clarity, but the more general utility of the concept is apparent. The purpose of the present work is to apply both the principle and the theory of coherence, in a more general way, to the development of a simulator for an enhanced oil recovery (EOR) process, surfactant-assisted waterflooding. The coherence-based simulator incorporates first-order effects, with scope for the first time to accommodate two or three dimensions, two fluid phases (aqueous, oleic) and one adsorbent phase, and four components (oil, water, surfactants 1 and 2). Due to low concentrations and short chain lengths, surfactants partition solely between the adsorbent and aqueous phases, and fractional flow is a function of saturation only. The equations necessary for the simulator are presented, followed by the mathematics required for the extension of coherence theory to the multidimensional, multiphase, multicomponent flow. The material transport equations are decoupled from the momentum transport equations; the complex, time changing flow-field requires a numerical solution, which then allows a direct calculation of the movement of the coherent wave fronts through time and space. The concept of a partial coherent solution, in which a group of dependent variables moves with a common wave velocity, is applied; each group possesses its own characteristic wave velocity and eigenvalue. Under the model premises, such a 'partially' coherent solution exists, because the coherent waves representing fluid-phase saturations and those representing the surfactant aqueous-phase compositions can exist independently. The existence of a partial coherent solution makes the prediction of reservoir response much more straightforward. This simpler solution does not generally exist if surfactants partition into the oleic phase and/or fractional flow is a function of surfactant composition; should either occur, a globally coherent solution still exists, but its calculation is more complex and difficult to handle. An efficient and versatile simulator algorithm is possible, and its operation is described. The simulator is used to predict the system response; comparison with calculations based on traditional, numerical integration methods verifies the prediction of coherence theory as applied in the simulator. The attainment of both partially and totally coherent wave behaviour is verified in the context of the simulator. The nature of the simulator allows for physical insights into, and predictions of, reservoir response during process application. An efficient simulator, utilising large time steps, is also possible. This approach has a strong potential for use in the screening and testing of ideas in enhanced oil recovery, and wider application seems possible. (C) 2003 Elsevier B.V. All rights reserved.