# Proper liquid viscosity in cP, B is liquid formation

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.

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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.