In

the single well system, oil and associated fluids move from the reservoir to

the tank. Energy losses must be overcome in order for fluids to flow through

various interconnected components from the reservoir to the stock tank.

Figure 12 below shows the locations of

commonly used nodes.The Systems Analysis or NODAL analysis concept:

inflow involves the components (inside the reservoir) = outflow all of the

components (from intake point (6) and up word to point (1)). In

the gas lifted well, generally the solution node is selected at the mid

perforations depth.

At

this location, IPR (inflow performance relation) = VLP (vertical lift

performance).as shows in the figure -13 below.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 PWFThe

proportionality constant is referred to as the Productivity Index or PI or

J. The flow rate is given by the following expression:

In

the English units, q is flow rate in STB/day, and the pressures – PR and

PWF – are in psig, resulting in the units of PI to be

STB/day/psi.

A

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.