Introduction reservoir engineering 6 Productivity Index (PI or j) The productivity index

 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 com￾paction, 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: