By Myron B. III. Allen
This research is an outgrowth of my doctoral dissertation at Princeton college. i'm really thankful to Professors George F. Pinder and William G. grey of Princeton for his or her suggestion in the course of either my study and my writing. i feel that finite-element collocation holds promise as a numer ical scheme for modeling complex flows in porous media. even if, there appears a "conventional knowledge" protecting that collocation is hopelessly beset through oscillations and is, ultimately, essentially beside the point for multiphase flows. i am hoping to dispel those objections, knowing that others will stay for additional paintings. The U. S. nationwide technology beginning funded a lot of this examine via provide quantity NSF-CEE-8111240. desk OF CONTENTS summary ;; FOREWORD ;; ; bankruptcy ONE. THE actual procedure. 1.1 creation. 1 1.2 The reservoir and its contents. five 1.3 Reservoir mechanics. nine 1.4 Supplementary constraints. 18 1.5 Governing equations. 26 bankruptcy . REPRESENTING FLUID-PHASE habit. 39 2.1 Thermodynamics of the fluid procedure. forty 2.2 regular equation-of-state tools. forty five 2.3 Maxwell-set interpolation.
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Additional resources for Collocation Techniques for Modeling Compositional Flows in Oil Reservoirs
8,9, ... 7J I --- I '" (I) . 925 .. MOLE FRACTION CO 2 Figure 2-4. 93K using the Peng-Robinson equation of state. 313 COJIIIuted pressure (MFa) WITH DATA MEASURED BY OLDS ET AL. U949).. 88 (Ie) Teap. TABLE 2-1. 8609 (K) (MPa, mole fraction) Final value k Initial guess Talii'. D2 < 10- 2 Pa ) FOR TIlE RUNS LISTED IN TABLE 2-1. Mole fraction CO 2 TABLE 2-2.
This description of equilibria admits a geometric interpretation that has some heuristic value in the remainder of the chapter. 1-1) define the set of single-phase thermodynamic states that lie at the limit of thermostatic equilibrium. set ~ of the thermodynamic system. This set is called the Maxwell If a single-phase system confined to thermostatic equilibrium crosses the Maxwell set, it bifurcates, becoming a system of coexisting phases each of which lies on the Maxwell set. Therefore in miscible gas floods the Maxwell set provides informa- tion, not only about when the fluids change from a single-phase regime to a two-phase regime and vice versa, but also about the values of the thermodynamic variables associated with each coexisting phase.
One way to resolve this apparent paradox, as Welge (1952) shows, is to replace fV by its convex hull, drawn as the dashed line in Figure 1-1. Welge's construction yields the single-valued but discontinuous saturation profile drawn in Figure 1-2. 3-16). 5-15) The Buckley-Leverett-Welge solution is a weak solution but not a classical solution, since it is discontinuous. Nonetheless, it is the physically correct solution to the Buckley-Leverett problem. Helfferich' 5 theory. Recently, Helfferich (1981, 1982) has presented a unified generalization of the Buckley-Leverett theory to multicomponent flows in porous media with interphase mass transfer, and this work sheds some light on the equations governing miscible gas flopds.
Collocation Techniques for Modeling Compositional Flows in Oil Reservoirs by Myron B. III. Allen