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

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:

  $qoqo,max=1−v[pwfp¯]−(1−v)[pwfp¯]2$

  Where the v-parameter is defined for the solution gas-drive reservoir case using the oil mobility function (i.e., [(k_o/(μ_oB_o)]) — this definition is given by:

  $v=2[ko/(μoBo)]p¯=0[ko/(μoBo)]p¯+[ko/(μoBo)]p¯=0$

• The analytical form for a cubic IPR correlation:

  $qoqo,max=1−α[pwfp¯]−β[pwfp¯]2−γ[pwfp¯]3$

• The analytical form for a quartic IPR correlation:

  $q0q0,max=1−ε[pwfp¯]−σ[pwfp¯]2−η[pwfp¯]3−θ[pwfp¯]4$

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 [k_o/(μ_oB_o)], which is given as:

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 (p_i and $p¯$⁠), and the oil-phase mobility evaluated at the initial reservoir pressure [k_o/(μ_oB_o)]_pi.