PSEUDO PRESSURE

Real Gas Pseudo-Pressure

The concept of pseudo-pressure or real gas potential is used commonly in gas well deliverability and transient well tests.

The pseudo-pressure is defined by the following integral equation:

Where:

ψ(p) = pseudo-pressure at pressure p, psi2/cp

pb= an arbitrary base pressure (< p), psia

μ = viscosity of gas, cp

z = gas compressibility factor

(Note that μ and z are both functions of pressure. μ increases with pressure. z takes a value of 1 at zero pressure, then initially drops as pressure increases and eventually rises at higher pressures.)

Numerical integration is performed here using the trapeziodal rule with pb = 0.

PI (PRODUCTIVITY INDEX)

Horizontal Well Productivity Index (Oil)

The steady-state flow equation for a horizontal well is represented by:

Qoh = JhΔp

where Qoh = horizontal well oil flow rate, STB/day

Δ p = pressure drop from drainage boundary to wellbore, psi

Jh = productivity index.

The four commonly-used methods for predicting horizontal well productivity index from fluid properties and reservoir properties are:

-   Borizov’ Method

-  Giger-Reiss-Jourdan Method

-  Joshi’s Method

-  Renard-Dupuy Method

Borizov’s method applies to the isotropic reservoir case where horizontal permeability equals vertical permeabilty. The other three methods apply to the more general anisotropic case.

The equations for each method is given below:

Where:

Jh = productivity index, STB/day/psi

h = thickness, ft

kh= horizontal permeability, md

kv = vertical permeability, md

L = length of horizontal well, ft

reh = drainage radius of horizontal well

rw = wellbore radius, ft

a = half the major axis of the drainage ellipse, ft

Bo = formation volume factor of oil

μ o = oil viscosity

For comparison, the corresponding equation for Vertical Well without skin is given by:

Note that drainage radius (ft) is derivable from drainage area A (acres) as follows:

reh = √[43560A/π]