By Zhangxin Chen
This e-book covers and expands upon fabric awarded by way of the writer at a CBMS-NSF nearby convention in the course of a ten-lecture sequence on multiphase flows in porous media and their simulation. It starts with an outline of classical reservoir engineering and simple reservoir simulation tools after which progresses via a dialogue of varieties of flows single-phase, two-phase, black oil (three-phase), unmarried section with multicomponents, compositional, and thermal. the writer presents an intensive word list of petroleum engineering phrases and their devices, besides simple circulation and shipping equations and their strange gains, and corresponding rock and fluid houses. the sensible points of reservoir simulation, resembling information accumulating and research, number of a simulation version, background matching, and reservoir functionality prediction, are summarized. viewers This publication can be utilized as a textual content for complicated undergraduate and first-year graduate scholars in geology, petroleum engineering, and utilized arithmetic; as a reference publication for geologists, petroleum engineers, and utilized mathematicians; or as a guide for practitioners within the oil undefined. must haves are calculus, easy physics, and a few wisdom of partial differential equations and matrix algebra. Contents record of Figures; checklist of Tables; checklist of Notation; Preface; creation; bankruptcy 1: A word list of Petroleum phrases; bankruptcy 2: Single-Phase circulation and Numerical answer; bankruptcy three: good Modeling; bankruptcy four: Two-Phase stream and Numerical answer; bankruptcy five: The Black Oil version and Numerical resolution; bankruptcy 6: delivery of Multicomponents in a Fluid and Numerical answer; bankruptcy 7: Compositional move and Numerical answer; bankruptcy eight: Nonisothermal movement and Numerical answer; bankruptcy nine: useful issues in Reservoir Simulation; Bibliography; Index.
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Extra resources for Reservoir Simulation: Mathematical Techniques in Oil Recovery (CBMS-NSF Regional Conference Series in Applied Mathematics, 77)
1 − Swc − Sor Sno = So ≥ Sor , Sw ≥ Swc , Note that Sno + Snw + Sng = 1. The relative permeability of oil is defined by kro = Sno βw βg . , the three-phase system reduces to a water and oil system. 32), gives βw = krow (Sw ) . 33) Similarly, to determine βg , we choose Sw = Swc so that βw = 1 and kro = krog . 32) yields krog (Sg ) βg = . 32) gives the expression of kro for Stone’s model I. This model reduces exactly to two-phase data only if the following condition is satisfied: krow (Swc ) = krog (Sg = 0) = 1.
23) while the oil phase relative permeability is kro = (1 − 2Snw )3/2 2 − (1 − 2Snw )1/2 . 5. 2 Three-Phase Relative Permeability In contrast, the determination of relative permeabilities for three-phase flow is rather difficult. From experiments, a ternary diagram for the relationship between the relative permeabilities and saturations can be shown as in Fig. 6. This diagram is based on the level curve of the relative permeability being equal to 1% for each phase. From it we can figure out where single-, two-, or three-phase flow occurs under different combinations of saturations.
Using the J-function, typical curves for pc can be obtained from experiments. This function is also the basis for some theoretical methods of measuring permeability k (Ashford, 1969). For three-phase flow, two capillary pressures are needed: pcow = po − pw , pcgo = pg − po . 19) Note that the third capillary pressure, pcgw , can be found using pcow and pcgo : pcgw = pg − pw = pcow + pcgo . 20) pcow = pcow (Sw ), pcgo = pcgo (Sg ), where Sw and Sg are the phase saturations of water and gas, respectively.
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