Inflow Performance Relationship (IPR) For Solution Gas-Drive Reservoirs—Analytical Considerations

Abstract This work provides the analytical development of "Vogel"-type Inflow Performance Relation (or IPR) correlations for solution gas-drive reservoir systems using characteristic flow behavior. Specifically, we provide the following results: An analytical form of the quadratic (Vogel) IPR correlation: q o q o , max = 1 − v [ p w f p ¯ ] − ( 1 − v ) [ p w f p ¯ ] 2 Where the v-parameter is defined for the solution gas-drive reservoir case using the oil mobility function (i.e., [(ko/(μoBo)]) — this definition is given by: v = 2 [ k o / ( μ o B o ) ] p ¯ = 0 [ k o / ( μ o B o ) ] p ¯ + [ k o / ( μ o B o ) ] p ¯ = 0 The analytical form for a cubic IPR correlation: q o q o , max = 1 − α [ p w f p ¯ ] − β [ p w f p ¯ ] 2 − γ [ p w f p ¯ ] 3 The analytical form for a quartic IPR correlation: q 0 q 0 , max = 1 − ε [ p w f p ¯ ] − σ [ p w f p ¯ ] 2 − η [ p w f p ¯ ] 3 − θ [ p w f p ¯ ] 4 The practical value of this work is that we have proven that an IPR can be written for a given solution gas-drive reservoir system directly from rock-fluid properties and fluid properties. The "theoretical" value of this work is that we provide a "characteristic" formulation of the oil mobility profile [ko/(μoBo)], which is given as: [ 1 − [ k o / ( μ o B o ) ] p [ k o / ( μ o B o ) ] p i ] = 1 − ζ [ p ¯ p i ] + ( 1 − ζ ) [ p ¯ p i ] 2 − 2 ( 1 − ζ ) [ p ¯ p i ] 3 ( ζ ≤ 1 ) This proposed "characteristic" mobility model is validated against numerical simulation results from the literature and from work performed as part of this study. Note that the characteristic mobility is only a function of the characteristic parameter (ζ), the initial and average reservoir pressures (pi and p¯), and the oil-phase mobility evaluated at the initial reservoir pressure [ko/(μoBo)]pi.