By V. M. Starzhinskii

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**Extra info for Applied methods in the theory of nonlinear oscillations**

**Sample text**

What is the pore volume of the barrier island? Express your answer in barrels and cubic meters. 8 Use Eq. 12) to derive Eq. 20). DAT. ROF. How much oil and water were originally in place? 826. Estimate cumulative gas production at abandonment from a graph of P/Z versus Gp (Figure 2-2). TSS. How does this result compare to the value of cumulative gas production found in Part B? 6) Bg Bgc Bg ' Bo Bt Btw cf G Gi Gpc Gps m N Np Rso Rsi Rsw Rswi Sg So Sw Swi Swig Swio We Wi Wp ∆P Pi P gas formation volume factor (FVF) (RB/SCF) gas cap FVF (RB/SCF) injected gas FVF (RB/SCF) oil FVF (RB/STB) Bo + (Rsi - Rso)Bg = composite oil FVF (RB/STB) Bw + (Rswi - Rsw)Bg = composite water FVF (RB/STB) formation (rock) compressibility (1/psia) initial gas in place (SCF) cumulative gas injected (SCF) cumulative gas cap gas produced (SCF) cumulative solution gas produced as evolved gas (SCF) ratio of gas reservoir volume to oil reservoir volume initial oil in place (STB) cumulative oil produced (STB) solution gas-oil ratio (SCF/STB) initial solution gas-oil ratio (SCF/STB) solution gas-water ratio (SCF/STB) initial solution gas-water ratio (SCF/STB) gas saturation (fraction) oil saturation (fraction) water saturation (fraction) initial water saturation (fraction) initial water saturation in gas cap (fraction) initial water saturation in oil zone (fraction) cumulative water influx (STB) cumulative water injected (STB) cumulative water produced (STB) Pi - P = reservoir pressure change (psia) initial reservoir pressure (psia) reservoir pressure corresponding to cumulative fluid times (psia) Chapter 3 Multiphase Flow Concepts Several basic concepts are needed to understand multiphase flow.

They are defined here and then applied in later sections. 1 Interfacial Tension On all interfaces between solids and fluids, and between immiscible fluids, there is a surface free energy resulting from electrical forces. These forces cause the surface of a liquid to occupy the smallest possible area and act like a membrane. Interfacial tension (IFT) refers to the tension between liquids at a liquid-liquid interface. Surface tension refers to the tension between fluids at a gas-liquid interface.

5 Fractional Flow Equation with Gravity Gravity can be included in the fractional flow equation as follows. First, let us consider the two-phase flow of oil and water in a tilted linear system. 23) Combining Eqs. 24) w o ∂x Akk w Akk ro where we have used qt = qo + qw. 27) Multiphase Flow Concepts 43 Pcow oil-water capillary pressure (psi) = Po - Pw x direction of linear flow (ft) α dip angle of formation (degrees) γo oil specific gravity (pure water = 1) γw water specific gravity (pure water = 1) The general expression for fw includes all three terms governing immiscible displacement, namely the viscous term (kro/krw)(µ w/µ o), the capillary ( ) pressure term ∂Pcow ∂x and the gravity term γ w − γ o sin α .

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