Page 111 - Introduction to Petroleum Engineering

96 MULTIPHASE FLOW

q
Tubing
Casing

p fwb p res
Reservoir
FIgURE 5.12 Productivity index terms.

Example 5.4 Well PI
A 20 psia pressure drawdown is required to produce 500 STBO/day. Use well
PI to estimate the oil production rate at 10 psia pressure drawdown.
Answer
q 500 STBO/day
PI = o = = 25 STBO/day/pisa
∆ p 20 psia
Therefore
q = PI ×∆ p = (25 STBO/day/psia)×10 psia = 250 STBO/day
o

The radial form of Darcy’s law can be used to write the productivity index (PI) for
radial flow into a vertical well as
.
q 0 00708 kh
PI =  = r r ) + ) (5.18)
enet
∆ p µ  B (ln ( e / w S

where the variables and associated units are tabulated as follows:
PI = productivity index (STB/D/psi)
q = volumetric flow rate of phase ℓ (STB/D)

∆p = p − p fwb
res
p = reservoir pressure (psi)
res
p = flowing wellbore pressure (psi)
fwb
k = effective permeability (md) = kk abs
r
e
k = relative permeability of phase ℓ
r
k abs = absolute permeability (md)
h = net thickness (ft)
net
μ = viscosity of phase ℓ (cp)
ℓ
B = FVF of phase ℓ (RB/STB)
