Question

%20Eng%20l%20Sept%20201 6%20(1 ).pdf PCB 2023/ PDB 2023 1. a Given isothermal congressibility, e- 2L show that the CHshow that the compressibiny factor for compressible ftuld is P 8 marks) b. With the aid of suitable equations, explain the behaviour of specific volume with increasing pressure for Lincompressible fluids 3 marks) compressible fluids, and 3 marks] il slightly compressible fluids. 3 marks) Explain how fluid flow in hydraulic fractured reservoir can be represented by linear floyw (4 marks! d List down FOUR (4) assumptions employed by Darcy s law 4 marksj PCB 2023/ PDB 2023 1. Given isothermal compressibility,c show that the נ1-( compressibility factor for compressible fluid is ,c, , 18 marks] With the aid of suitable equations, explain the behaviour of specific volume with increasing pressure for i incompressible fluids, b. 3 marks ii compressible fluids, and 3 marks] slightly compressible fluids. 3 marks C. Explain how fluid flow in hydraulic fractured reservoir can be represented by linear flow. 4 marks] d. List down FOUR (4) assumptions employed by Darcy's law. 4 marks]

Answer 1

a. Solving only the initial part

The isothermal compressibility is defined by

C= 이.

The real gas law is given by:

Zn.R

ZnRI

Now taking derivative w.r.t P at constant T

Zn RT op p-

V OZ op

Dividing by V on both sides:

$\frac{1}{V}\frac{\partial V}{\partial p}|_{T}=\frac{1}{Z}\frac{\partial Z}{\partial p}|_{T}-\frac{1}{p}$

Now substituting in the compressibiliity equation:

$C=-\frac{1}{V}\frac{\partial V}{\partial p}|_{T}=\frac{1}{p}-\frac{1}{Z}\frac{\partial Z}{\partial p}|_{T}$

Hence proved

d. Darcy's law presents the equation of a fluid flowing through a porous medium:

1. Kinetic energy can be ignored

2. Homogeneous porous medium

3. fluid properties are constant.

4. Single-phase flow