Proper design and analysis of an oil well

requires knowledge of reservoir flow rates into the wellbore at current as well

as future conditions. Minimally, the pressure at the bottom of the well and the

corresponding liquid production rate is needed for design and analysis. The

relationship between the liquid influx into the wellbore and the driving force

– caused by the difference between the average reservoir pressure and the

bottom hole flowing pressure – is called the Inflow Performance Relationship or

IPR.The simplest IPR representation is a

straight line wherein the flow rate is directly proportional to the driving

force or the pressure differential between the average reservoir pressure PR

and the bottom hole flowing pressure PWFA

proper production well-test would provide values for the bottom hole flowing

pressure and the corresponding flow rate. The average reservoir pressure can be

either inferred from shut-in pressures or reservoir simulation techniques.

This IPR

relationship can also be derived from the Darcy equation on flow in porous

media under simplified assumptions of radial, single-phase (liquid) flow in a

homogeneous reservoir, whereby:Where,

k is effective permeability in mD, h is pay thickness in ft, ?

is liquid viscosity in cP, B is liquid formation volume factor in

bbl/STB, re is well drainage radius in ft, and rw is wellbore radius

in ft.

For

the cases where this relationship holds, mainly where the PWF is above

the bubble point pressure, PB, the Productivity Index will be the

inverse of the slope of the IPR line.The

constant PI is simple and easy to apply. It fits wells producing at bottom hole

pressures above the bubble point on an active water drive mechanism, when the

gas phase is present in the reservoir, i.e. the bottom hole pressure is below

the bubble point, the straight-line inflow performance relationship does not

apply because gas released from the solution interferes with liquid flow in the

reservoir. In such a situation, PI decreases with increasing pressure differential

because more gas comes out of the solution as flowing bottom hole pressure

drops below the bubble point pressure. Even under a constant drawdown scenario

– when the difference between PR and PWF is maintained constant –

the decrease in PI occurs with increasing recovery for solution drive or gas

cap reservoirs.

Under

such circumstances, Vogel’s dimensionless correlation provides a reasonable

Relationship

between production flow rate and pressure-entities:Where,

q is production rate at bottom hole pressure PWF in STB/day and

psi respectively. PR is the average reservoir pressure in psi. q max –

also called AOFP for Absolute Open Flow Potential – is the maximum production rate

in STB/day corresponding to zero flowing bottom hole pressure.In

order to use Vogel’s method, reservoir pressure and a single stabilized flow

rate with corresponding flowing bottom hole pressure is required.

Alternatively, multiple flow rate tests taken at a constant reservoir pressure

may be used to solve for AOFP and/or PR. It should be noted that when

developing an IPR using Vogel’s method, large errors can occur if a stabilized

production rate is obtained for a relatively low-pressure differential.When

a reservoir is under saturated, i.e. the reservoir pressure is above the bubble

point pressure, a combination of linear IPR and non-linear Vogel IPR may be

used as shown in figure 5 below. One of the following equations is used

depending on the flowing bottom hole pressure value:Vertical

lift performance means the relationship between the flow rate and the

corresponding bottom hole pressure that is required to deliver the fluids to

the surface against a specified back pressure dictated by the separation

requirements. It is also called outflow performance in the Nodal Analysis where

a node is considered at the middle of the perforations depth.

As

fluids travel from the bottom hole to the surface, pressure losses occur

throughout the system, primarily because of the gravitational losses due to

change in elevation and the frictional resistance offered by various flow

system components like tubing, safety device(s), surface chokes, flow line,

etc. The total pressure differential between the bottom hole and the surface is

the summation of the pressure drops occurring in all of the system components.The

pressure drop through any component varies with production rate as well as the

average pressure which exists in the component because of changes in the fluid

properties. The selection and sizing of the individual components is very

important, but because of the interaction amongst the components, a change in

the pressure drop in one may change the pressure drop behavior in all the

others. Outflow performance attempts to capture this complex interaction.