Coefficient of compressibility, isothermal

Here, Cv is the heat capacity of solvent at constant volume a (deg-1) is its coefficient of thermal expansion dr (cm2 dyne-1) is the coefficient of isothermal compressibility. From Eq. (49) it is seen that the molecular weight of solute is simply ... 

Here, (instead of the more cumbersome notation 0T1) is used for the coefficient of isothermal compressibility of liquid 1. The presence of the second liquid gives rise... 

Evaluations of Rd and Y necessitate a knowledge of certain physical properties of the two liquids and the mixtures. The variation of refractive index with concentration is measured readily by refractometry, if I nT, — n21 is large. The coefficient of isothermal compressibility of a mixture t2 requires specialised equipment. Alternatively, it can be determined from the heat capacity and the coefficient of isentropic compressibility87, 88, the latter being yielded from velocity of sound data88. However, provided and 02 for the pure compounds are known, j312 is evaluated most conveniently on the basis of additivity, thus ... 

The coefficient of isothermal compressibility is defined as the fractional change of volume as pressure is changed at constant temperature. The defining equations are... 

Fig. 6-2. Typical shape of the coefficient of isothermal compressibility of a gas as a function of pressure at constant reservoir temperature.

This coefficient normally is referred to simply as compressibility or gas compressibility. You must understand that the term compressibility is used to designate the coefficient of isothermal compressibility whereas, the term compressibility factor refers to z-factor, the coefficient in the compressibility equation of state. Although both are related to the effect of pressure on the volume of a gas, the two are distinctly not equivalent. 

EXAMPLE 6-4 The following table gives volumetric data at 150°F for a natural gas. Determine the coefficient of isothermal compressibility for this gas at 150°F and 1000 psia. 

We recognize that the equation of state for an ideal gas does not describe adequately tire behavior of gases at temperatures and pressures normally encountered in petroleum reservoirs. However, Equation 6-6 does illustrate that we can expect the coefficient of isothermal compressibility of a gas to be inversely proportional to pressure. Equation 6-6 can be used to determine the expected order of magnitude of gas compressibility. 

The compressibility equation is the most commonly used equation of state in the petroleum industry. We will combine this equation with the equation which defines the coefficient of isothermal compressibility. Since z-factor changes as pressure changes, it must be considered to be a variable. 

EXAMPLE 6-7 Calculate the coefficient of isothermal compressibility of the dry gas given in Example 6-3 at 220°F and 2100 psig. 

We now turn to black oils. We consider those physical properties which are required for the reservoir engineering calculations known as material balance calculations. These properties are formation volume factor of oil, solution gas-oil ratio, total formation volume factor, coefficient of isothermal compressibility, and oil viscosity. Also, interfa-cial tension is discussed. 

At pressures above the bubble point, the coefficient of isothermal compressibility of oil is defined exactly as the coefficient of isothermal compressibility of a gas. At pressures below the bubble point an additional term must be added to the definition to account for the volume of gas which evolves. 

As with gases, the coefficient of isothermal compressibility of oil usually is called compressibility or, in this case, oil compressibility. 

The definition of the coefficient of isothermal compressibility at pressures above the bubble point is... 

The coefficient of isothermal compressibility is important in the study of volatile oil reservoirs. Values of compressibility are higher for volatile oils than for black oils. Values from 20 X 10 6psi I to 60 x 10—6 psi—1 are common at pressures above the bubble point. The relationship of compressibility to pressure for volatile oils is the same as given in Figure 8-7. The discontinuity at the bubble point is greater for volatile oils than for black oils. 

Tabulate values of coefficient of isothermal compressibility for use in the pressure ranges indicated in the table. Does the trend in the results agree with the shape of. Figure 8-5 ... 

Calculate and plot the coefficient of isothermal compressibility against pressure. Does your graph look like Figure 8—5 ... 

Determine the value of the coefficient of isothermal compressibility of the black oil of Exercise 8-10 for use between 3500 and 4000 psig. 

EXAMPLE 10-8 Calculate coefficients of isothermal compressibility at pressures above bubble point for Good Oil Co. No. 4,... 

Next, procedures for estimating values of the coefficient of isothermal compressibility and oil viscosity are discussed. The chapter ends with methods of estimating hydrocarbon liquid-gas interfacial tension. 

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