More on Deliverability and Quadratic Pressure

Unlike the other formats offered by PetroVR, Deliverability and Quadratic Pressure curves are based on physical properties such as temperature and pressure. Because of this, the construction of the resulting performance involves more sophisticated calculations such as formation volume factors, viscosity, Z-factors, equation of real gasses, the Cullender-Smith algorithm, etc.

The following diagram depicts different components of the calculations using a color code. The objects involved are shown in red boxes. Blue boxes show parameters and intermediate calculations required by the algorithms. Finally, the green box shows the target mapping that determines the natural rate of the well under consideration at a given value of cumulative production.

• Different quantities (mainly Z-factors) are computed from physical properties of the real gas and its contaminants. The values computed depend on dynamic quantities such as temperature and pressure. Contamination factors are also allowed to change dynamically.
• Reservoir Gas In Place can be an input or a calculation. A Recovery Factor can be computed from the Abandonment Pressure, or vice versa.
• Depending on performance type, two different sets of parameters must be provided. Note that in both cases you provide a pressure for the well. In Quadratic Pressure you must provide the Wellhead Pressure. In the case of Deliverability, you can provide either the Bottom Hole Pressure or the Wellhead Pressure. If you enter WHP then Cullender-Smith is used to derive BHP from WHP.
• Iterating from initial to abandonment reservoir pressures, Z-factors are computed at every step. Entering these factors into the real gas equation, gas volumes are derived. As a result a mapping from pressures to cumulative productions is built.
• When the simulation is run, the cumulative production at a given step is used to get the corresponding reservoir pressure.

There are three sub-cases here:

• Quadratic Pressure: Using the pressure computed in (5) and all four curve parameters a, b, c and f, the rate for the current step is calculated.
• Deliverability with BHP: Using the pressure computed in (5), the flow exponent and coefficient curve parameters and the value of BHP, the rate for the current step is calculated.
• Deliverability with WHP: Using the pressure computed in (5) and all the curve parameters, Cullender-Smith is applied to calculate the rate for the current step.