Proper design and analysis of an oil wellrequires knowledge of reservoir flow rates into the wellbore at current as wellas future conditions. Minimally, the pressure at the bottom of the well and thecorresponding liquid production rate is needed for design and analysis. Therelationship between the liquid influx into the wellbore and the driving force– caused by the difference between the average reservoir pressure and thebottom hole flowing pressure – is called the Inflow Performance Relationship orIPR.The simplest IPR representation is astraight line wherein the flow rate is directly proportional to the drivingforce or the pressure differential between the average reservoir pressure PRand the bottom hole flowing pressure PWFAproper production well-test would provide values for the bottom hole flowingpressure and the corresponding flow rate. The average reservoir pressure can beeither inferred from shut-in pressures or reservoir simulation techniques. This IPRrelationship can also be derived from the Darcy equation on flow in porousmedia under simplified assumptions of radial, single-phase (liquid) flow in ahomogeneous 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 inbbl/STB, re is well drainage radius in ft, and rw is wellbore radiusin ft.
Forthe cases where this relationship holds, mainly where the PWF is abovethe bubble point pressure, PB, the Productivity Index will be theinverse of the slope of the IPR line.Theconstant PI is simple and easy to apply. It fits wells producing at bottom holepressures above the bubble point on an active water drive mechanism, when thegas phase is present in the reservoir, i.
e. the bottom hole pressure is belowthe bubble point, the straight-line inflow performance relationship does notapply because gas released from the solution interferes with liquid flow in thereservoir. In such a situation, PI decreases with increasing pressure differentialbecause more gas comes out of the solution as flowing bottom hole pressuredrops 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 gascap reservoirs.
Undersuch circumstances, Vogel’s dimensionless correlation provides a reasonableRelationshipbetween production flow rate and pressure-entities:Where,q is production rate at bottom hole pressure PWF in STB/day andpsi respectively. PR is the average reservoir pressure in psi. q max –also called AOFP for Absolute Open Flow Potential – is the maximum production ratein STB/day corresponding to zero flowing bottom hole pressure.Inorder to use Vogel’s method, reservoir pressure and a single stabilized flowrate with corresponding flowing bottom hole pressure is required.Alternatively, multiple flow rate tests taken at a constant reservoir pressuremay be used to solve for AOFP and/or PR. It should be noted that whendeveloping an IPR using Vogel’s method, large errors can occur if a stabilizedproduction rate is obtained for a relatively low-pressure differential.Whena reservoir is under saturated, i.e.
the reservoir pressure is above the bubblepoint pressure, a combination of linear IPR and non-linear Vogel IPR may beused as shown in figure 5 below. One of the following equations is useddepending on the flowing bottom hole pressure value:Verticallift performance means the relationship between the flow rate and thecorresponding bottom hole pressure that is required to deliver the fluids tothe surface against a specified back pressure dictated by the separationrequirements. It is also called outflow performance in the Nodal Analysis wherea node is considered at the middle of the perforations depth. Asfluids travel from the bottom hole to the surface, pressure losses occurthroughout the system, primarily because of the gravitational losses due tochange in elevation and the frictional resistance offered by various flowsystem components like tubing, safety device(s), surface chokes, flow line,etc. The total pressure differential between the bottom hole and the surface isthe summation of the pressure drops occurring in all of the system components.
Thepressure drop through any component varies with production rate as well as theaverage pressure which exists in the component because of changes in the fluidproperties. The selection and sizing of the individual components is veryimportant, but because of the interaction amongst the components, a change inthe pressure drop in one may change the pressure drop behavior in all theothers. Outflow performance attempts to capture this complex interaction.