INFLOW PERFORMANCE RELATIONSHIP (IPR)

IPR For Vertical Solution Gas-Drive Wells

 

The relationship between well flow rate and the pressure drawdown (or flowing bottomhole pressure FBHP) is defined as the Inflow performance relationship (IPR). If the FBHP is below the bubblepoint pressure or if inertial effects become significant at high rates, IPR becomes curvilinear rather than linear.

A number of empirical methods have been proposed to generate IPRs, beginning with the seminal work of Vogel on the subject. These methods usually require a least one stabilized flow test (so-called single-point test) in which flow rate, FBHP and average reservoir pressure are measured. These 3 attributes uniquely define the IPRs coresponding to that reservoir pressure.

In Vogel’s method, the IPR curve for a well producing saturated oil from a solution gas drive reservoirs can be approximated by the dimensionless quadratic equation:

The standard Vogel’s method was modified by Klins et al to explicitly account for the effects of bubblepoint presure and skin, as follows:

where

qo = oil flow rate, bbl/day

(qo)max = oil flow rate at FBHP = 0, bbl/day

(qo)maxs=0 = oil flow rate at FBHP = 0 & skin = 0, bbl/day

pwf = FBHP = flowing bottom hole pressure, psia

pr = reservoir pressure, psia

pb = bubblepoint pressure, psia

s = skin factor, dimensionless, psia

M = skin-dependent multiplier

n = bubblepoint-dependent exponent

IPR For Slanted Solution Gas-Drive Wells

The relationship between well flow rate and the pressure drawdown (or flowing bottomhole pressure FBHP) is defined as the Inflow performance relationship (IPR). If the FBHP is below the bubblepoint pressure or if inertial effects become significant at high rates, IPR becomes curvilinear rather than linear.

A number of empirical methods have been proposed to generate IPRs along the lines of the seminal work of Vogel on the subject. These methods usually require a least one stabilized flow test (so-called single-point test) in which flow rate, FBHP and average reservoir pressure are measured. These 3 attributes uniquely define the IPRs coresponding to that reservoir pressure.

Cheng’s Model applies to the cases where the well penetrates the producing interval at an angle. The angle ranges from zero (vertical well) to 90 degrees (horizontal well). The model is a semi-analytical one, wherein the coefficients of the polynomial equations vary with the inclination angle. For example, the correlations for the 30 and 75 degrees scenarios are respectively:

[qo/qomax]30° = 0.9959 – 0.1254[pwf/pr] – 0.8682[pwf/pr]2

[qo/qomax]75° = 0.9915 + 0.1002[pwf/pr] – 1.0829[pwf/pr]2

where :

qo = oil flow rate, bbl/day

qomax = oil flow rate at FBHP = 0, bbl/day

pwf = FBHP = flowing bottom hole pressure, psi

pr = reservoir pressure, psi

θ = slant or deviation angle, degrees

IPR For Horizontal Solution Gas-Drive Wells

The relationship between well flow rate and the pressure drawdown (or flowing bottomhole pressure FBHP) is defined as the Inflow performance relationship (IPR). If the FBHP is below the bubblepoint pressure or if inertial effects become significant at high rates, IPR becomes curvilinear rather than linear.

Only a few empirical methods have been proposed to generate IPRs for horizontal wells along the lines of the seminal work of Vogel , notably by Cheng, Kabir and more recently by Retnanto & Economides. The latter appears to be a more coherent method and will be implemented here. Their IPR method is based on estimates of reservoir/well architecture and fluid properties, rather than stabilized flow tests. The shapes of the horizontal well IPRs are similar to Vogel’s; the central task is to evaluate the maximum oil flow rate (absolute open flow potential).

Retnanto-Economides’s model for the case where the well is in the vertical middle of the reservoir, can be represented by the following series of equations:

where :

qo = oil flow rate, bbl/day

qomax = oil flow rate at FBHP = 0, bbl/day

pwf = FBHP = flowing bottom hole pressure, psi

pr = reservoir pressure, psi

pb = reservoir pressure, psi

J = productivity index, STB/day/psi

h = thickness, ft

n = exponent in IPR equation

kh= horizontal permeability, md

kv = vertical permeability, md

s = skin factor, md

L = length of horizontal well (aligned to x-direction), ft

Xe = extent of drainage area in x-direction, ft

Ye = extent of drainage area in y-direction, ft

CH = Shape factor, semi-analytic function of L,Xe,Ye

re = drainage radius of horizontal well

rw = wellbore radius, ft

Bo = formation volume factor of oil

μ o = oil viscosity