The productivity index is calculated mathematically as
The productivity index is calculated mathematically as
Factors Affecting the Productivity Index
• Phase Behaviour of Fluids in the Reservoir
• Relative Permeability
• Oil Viscosity
• Oil Formation Volume Factor
• Skin
1.6.2 Phase Behaviour in Petroleum Reservoirs
As reservoir pressure drops below the bubble point, free gas begins to form and thus
the oil relative permeability (kro) is reduced. If a well is produced at a flow rate that
requires the wellbore flowing pressure (Pwf) to be less than the bubble point pressure
(Pb), the oil relative permeability and the productivity index (PI) will be decreased
around the wellbore.
1.6.3 Relative Permeability Behaviour
As free gas form in the pores of a reservoir rock, the ability of the liquid phase to
flow is decreased. Even though the gas saturation may not be great enough to allow
gas to flow, the space occupied by the gas reduces the effective flow area of the
liquid. Conversely, in gas reservoir, the relative permeability to gas will be decreased
if liquid saturation develops either as a result of retrograde condensation or water
formation in the pores.
1.6.4 Oil Viscosity Behaviour
The viscosity of oil saturated with gas at constant temperature will decrease as
pressure is decreased from an initial pressure to bubble point pressure (Pb). Below
Pb, the viscosity will increase as gas comes out of solution leaving the heavier
components of the hydrocarbon.
Oil Formation Volume Factor
As pressure is decreased in the reservoir, the hydrocarbon will expand and when the
bubble point pressure is reached for an oil reservoir, gas starts coming out of solution
which causes the oil to shrink thereby reducing the volume of the oil.
1.6.6 Skin
A well that is damaged results in low fluids flow potential. Thus, formation damage
is an impairment of reservoir permeability around the wellbore, leading to low or no
well production or injection. Or simply refers to the decrease in permeability that
occurs in the near wellbore region of a reservoir. Formation damage is often
quantified by “Skin” factor. Skin is strictly a measure of an excess pressure in the
producing formation as fluids flow into a well. Skin alters the flow of fluid; that is an
impairment to flow.
The excess pressure drop can occur from one or several of a wide variety of
causes such as drilling mud, cement, completion fluid filtrate invasion, solids
invasion, perforating damage, fines migration, formation compaction, swelling
clays, asphaltene/paraffin deposition, scale precipitation, emulsions, reservoir compaction, relative permeability effects, effects of stimulation treatments, etc.
Application of Dimensionless Parameters in Calculating
Flow Rate and Bottom Flowing Pressure
Now, let us write the pressure drop in dimensionless pressure
Shape Factors for Various Closed Single – Well Drainage Areas
Check for the flow regime at the given shape of the reservoir
Note, at any given time, the reservoir will behave like an infinite acting system,
that is, the reservoir is still undergoing transient flow condition if
tDA calculated ð Þ < tDA tabulated ð Þ
Thus, PD is calculated based on area as: