Diffusivity and Pressure-transient Analysis - Oil and Gas Well Testing - Petroleum Engineering Previous Year Questions

Q.No. 47 It is desired to determine the radius of investigation (\(r_{inv}\)) of a low-permeability and low-pressure gas reservoir which produces under a constant flow rate. Use the following data:

Absolute permeability (k) = 0.01 mD,

Porosity (φ) = 0.05,

Total isothermal compressibility (\(C_t\)) = 200×10⁻⁶ psia⁻¹, and

Viscosity (μ) = 0.05 cP.

Assuming transient flow conditions are valid, the radius of investigation (\(r_{inv}\)) after 200 hours of gas production (rounded off to one decimal place) is ______ ft.

Flow tests are conducted for oil well in reservoirs P, Q, R and S having different parameters as given in the following table. In all the four cases the wells are tested at 1200 stb/day.

Reservoir	Permeability (mD)	Porosity (%)	Oil Viscosity (cP)	Total Compressibility (× 10-6 psi-1)	Wellbore Radius (ft)	Pay Zone Thickness (ft)
P	100	23	0.8	75	0.5	10
Q	50	21	1.1	70	0.4	12
R	150	25	0.9	80	0.3	15
S	170	28	1.0	90	0.6	20

Identify the reservoir in which the pressure transient reaches earliest at a point 2000 ft away from the wellbore.

Consider the following diffusivity equation for the radial flow of a fluid in an infinite and homogeneous reservoir.
\[ \frac{1}{r} \frac{\partial}{\partial r} \left( r \frac{\partial P}{\partial r} \right) = \frac{1}{\eta} \frac{\partial P}{\partial t} \]
where, \( P \) denotes pressure, \( r \) is the radial distance from the centre of the wellbore, \( t \) denotes time, and, \( \eta \) is the diffusivity constant. The initial pressure of the reservoir is \( P_i \).
The condition(s) used in the derivation of analytical solution of the above equation for pressure transient analysis in an infinite acting reservoir is/are:

Match the flow regimes associated with a vertically fractured well in a reservoir.
(P) Formation Linear Flow
(Q) Fracture Linear Flow
(R) Bilinear Flow
(S) Pseudo-Radial Flow