Vogel vs Straight-Line IPR: Choosing the Model

An inflow performance relationship, or IPR, connects reservoir inflow rate to flowing bottom-hole pressure for a stated reservoir condition. A straight-line model uses a constant productivity index. The simple Vogel model has a curved pressure-rate relationship associated with saturated solution-gas-drive oil conditions. Choose between them by checking the phase behavior and calibration basis before comparing numerical outputs.

This lesson overlays two synthetic curves with the same reservoir pressure of 3,000 psia and the same extrapolated zero-flowing-pressure rate of 1,000 STB/day. That normalization isolates their shapes. It does not represent two calibrated models of one measured well. Move the pressure-ratio slider to compare points, then use the individual calculators with inputs appropriate to your own stated case.

Drawdown is reservoir pressure Pr minus flowing bottom-hole pressure Pwf. The two pressures need a common datum and compatible reference. This lesson uses absolute pressures in psia for the Vogel ratio; their difference is drawdown in psi. A single-phase productivity index J is oil rate divided by drawdown, expressed here as STB/day/psi. If J is treated as constant for the conditions of interest, rearranging the definition gives q = J(Pr − Pwf), a straight line on a pressure-rate plot.

A test-derived J also belongs to its reservoir condition, completion and flow regime. Changes in mobility, skin or pressure support can change that relationship. Record which reservoir pressure estimate and stabilized flow measurement are paired, rather than combining values from unrelated times. A mathematically straight line alone does not verify that the underlying assumptions describe the well.

A constant-J oil model is a useful idealization when the relevant inflow region remains single phase and the chosen flow-regime assumptions are suitable. Reservoir pressure above bubble point is not enough by itself: flowing pressure can fall below bubble point near the well. Identify both pressures relative to bubble point before extending a straight line across a large drawdown range.

Vogel's 1968 work developed a dimensionless curved relationship from calculated solution-gas-drive cases. The simple form used here is intended for saturated oil conditions. When reservoir pressure is above bubble point and the inflow path crosses below it, a piecewise or composite treatment may be needed. Neither single-form calculator here implements that composite construction, so an arbitrary switch between the two curves does not complete the model.

Let r = Pwf/Pr and let qmax be the extrapolated rate at Pwf = 0. Vogel gives q/qmax = 1 − 0.2r − 0.8r². To make a straight line share the same intercept, choose J = qmax/Pr; its normalized equation becomes q/qmax = 1 − r. Both curves then give zero rate at r = 1 and the selected maximum at r = 0.

For Pr = 3,000 psia and qmax = 1,000 STB/day, the line uses J = 1/3 STB/day/psi. This is a declared normalization, not a J inferred from the 1,500-psi Vogel point. A comparison that calibrates both models to one measured test point would generally have different zero-pressure intercepts. Keep those two comparison designs separate when interpreting which curve gives the higher rate.

The comparison chart places normalized oil rate on the horizontal axis and pressure ratio on the vertical axis. Each slider position selects a horizontal pressure level. At r = 0.5, the Vogel curve intersects it at normalized rate 0.7, while the line intersects at 0.5. Multiplying by the shared 1,000-STB/day intercept gives 700 and 500 STB/day respectively.

Check both endpoints as well as that interior point. At zero drawdown, r = 1, both rates are zero; the lesson evaluates the line as J times drawdown to avoid dividing by zero in the PI definition. At r = 0, both return qmax by construction. That zero-pressure point is an extrapolated intercept for normalization, not a proposed operating condition.

Suppose an applicable test gives 700 STB/day at Pwf = 1,500 psia with Pr = 3,000 psia. Fitting the simple Vogel expression to that point gives qmax = 700/0.7 = 1,000 STB/day. Fitting a straight line to the same point instead gives J = 700/1,500 = 0.4666667 STB/day/psi and an extrapolated intercept of 1,400 STB/day.

Both fitted models reproduce that one test by construction, yet they disagree elsewhere. A single matching point therefore cannot establish which model predicts a well over a pressure range. Use suitable phase information, representative tests and model assumptions to assess the application. The interactive comparison retains the common-intercept basis throughout so its changing rate difference is easy to interpret.

An IPR supplies reservoir inflow at a selected bottom-hole pressure. A producing system must also lift and transport the fluid through tubing and surface equipment. Determining an operating point requires compatible outflow information and a system solution. The highest rate displayed by an inflow equation does not establish a lift capacity, tubing limit or stable production rate.

Use the Vogel calculator for the supported curved inflow point, and use the productivity-index calculator to evaluate J from rate and drawdown for a suitable linear case. These tools expose the scalar relationships. They do not perform a complete nodal analysis or choose a model from a well test automatically. Carry the stated calibration and pressure regime into any later system analysis.