Page 241 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

410 Reservoir Engineering

Productivlty Index
The productivity index, J, is a measure of the ability of a well to produce
hydrocarbon liquids:

9.
J, =- (5-128)
P. - Pllf
where is the flow rate of oil in stock-tank barrels of oil per day, p, is the
external pressure in psi, Pw, is the flowing bottomhole pressure in psi, and the
quantity (p, - p,) is referred to as the pressure drawdown. Because the flow
rate in this case is in STB/D, the oil productivity index u,) has units of STB/
D/psi. Since only q and pwr can be measured directly, p, is commonly replaced
with which can be determined from pressure transient testing.
After the well has been shut in for a period of time (usually at least 24 to 72
hours or longer depending on reservoir characteristics), the well is put on
production at a low rate with a small choke. The rate of production is recorded
as a function of flow time. When the production rate has stabilized, the flow
rate is increased by increasing the choke, and flaw rate is monitored with time.
This process is repeated until a series of measurements has been recorded [19].
In order to attain a stabilized productivity index, a minimum time is required
after each individual flow-rate change. This time can be approximated by two
equations [66,197]:

(5-129)

(5-1 30)

where t, is the stabilization time in hours, k is the permeability in md, I$ is the
porosity as a fraction, p is viscosity in cp, c, is total compressibility in psi-’, A
is area in ft*, and re. is the external radius in feet which should be based on
the distance to the farthest drainage boundary for the well. For large systems
or reservoirs with low permeability, very long stabilization times may be required.
Equation 5-128 assumes that productivity index does not change with flow
rate or time, and in some wells the flow rate will remain proportional to the
pressure drawdown over a wide range of flow rates. However, in many wells,
the direct relationship is not linear at high flow rates as shown in Figure 5-129.
The causes for the deviation in the straight-line behavior can include insufficient
producing times at each rate, an increase in gas saturation near the wellbore
caused by the pressure drop in that region, a decrease in permeability of oil
due to the presence of gas, a reduction in permeability due to changes in
formation compressibility, an increase in oil viscosity with pressure drop below
the bubble point, and possible turbulence at high rates of flow.
A plot of oil production rate versus bottomhole pressure, termed the inflow
performance relationship (IPR), was proposed as a method of analysis of flowing
and gas-lift wells [223]. Vogel [224] calculated dimensionless IPR curves for
solution gas reservoirs that covered a wide range of oil PVT and relative
permeability characteristics. From computer simulations, Vogel [224] showed that