Quadratic Pressure

This option calculates the well deliverability based on the following 2 equations:

P2BHP = bP2WHP + cQ2Vertical flow equation, where:
  • Q is the production rate
  • PBHP is the flowing Bottom Hole Pressure.
  • PWHP is the flowing Wellhead Pressure.
  • b and c are flow coefficients.
b, c and Wellhead Pressure are required inputs. 		P2RES = P2BHP+aQ+fQ2 Linearized non-linear Darcy equation (Al-Hussainy and Ramey 1966Closed Al-Hussainy, R. and Ramey, H.J. Jr., “Application of Real Gas Flow Theory to Well Testing and Deliverabilty Forecasting”, SPE 1243-PA, Journal of Petroleum Technology, Vol. 18, No. 5, pp. 637-642, May 1966.) for radial flow, where f is the slope and a is the intercept in a plot of (P(pseudo)reservoir - P(pseudo)bottom hole) / Q vs. Q in a Semi-Steady-State multi-rate test.
  • Q is the production rate.
  • PRES is the reservoir pressure.
  • PBHP is the flowing Bottom Hole Pressure.
  • a is the Inflow Constant.
  • f is the non-Darcy Flow Coefficient.
a and f are required inputs.

The rest of the inputs allow you to characterize the declines for the secondary fluids - water and gas in the case of oil producers, water and oil for gas producers. (See Primary- and secondary-fluid curves.)

  • Water Yield Factor: Use this option to enable input of Water Cut as a factor of rate.
  • Oil Yield Factor: Use this option to enable input of dimensionless GOR, a factor which will be multiplied by the Initial GOR defined in the Fluids Tab.
Unlike other performance types, Deliverability and Quadratic Pressure do not allow you to define either Water Yield Factor or Oil Yield Factor by means of a Table table, but only as none, as a constant or using a function.

For further details, see More on Deliverability and Quadratic Pressure.