
One final relationship that is often used in the oil and gas industry is the empirical Rawlins and Schellhardt Backpressure or Deliverability Equation[1]. This equation has the form:
As with all observation-based empirical relationships, to use this equation it must be tuned with appropriate data to determine the values of the tuning parameters, and . To do this, the gas well must be produced at several flowing pressures, , and the resulting stabilized rates measured. Once these tests (Deliverability Tests) are performed, the equation parameters, and , are used to fit the equation to the test results. Table 5.01 a-g summarizes all of the Stabilized Inflow Performance Relationships for gas wells discussed to this point.
In Terms of Pressure including Damage or Stimulation: All pressures greater than 3,000 psi |
||
---|---|---|
Steady-State Flow Regime | Pseudo Steady-State Flow Regime | |
Drawdown | ||
Productivity Index |
||
IPR |
In terms of Pressure including Damage or Stimulation: All pressures greater than 3,000 psi |
||
---|---|---|
Steady-State Flow Regime | Pseudo Steady-State Flow Regime | |
Drawdown | ||
Productivity Index |
||
IPR |
In terms of Pressure-Squared including Damage or Stimulation: All pressures less than 2,000 psi |
||
---|---|---|
Steady-State Flow Regime | Pseudo Steady-State Flow Regime | |
Drawdown | ||
Productivity Index |
||
IPR |
In terms of Pressure-Squared including Damage or Stimulation: All pressures less than 2,000 psi |
||
---|---|---|
Steady-State Flow Regime | Pseudo Steady-State Flow Regime | |
Drawdown | ||
Productivity Index |
||
IPR |
In terms of the Real Gas Pseudo-Pressure including Damage or Stimulation: Valid over the entire pressure range |
||
---|---|---|
Steady-State Flow Regime | Pseudo Steady-State Flow Regime | |
Drawdown | ||
Productivity Index |
||
IPR |
In terms of the Real Gas Pseudo-Pressure including Damage or Stimulation: Valid over the entire pressure range |
||
---|---|---|
Steady-State Flow Regime | Pseudo Steady-State Flow Regime | |
Drawdown | ||
Productivity Index |
||
IPR |
The Rawlins and Schellhardt Backpressure or Deliverability Equation[1] | ||
---|---|---|
Steady-State Flow Regime | Pseudo Steady-State Flow Regime | |
IPR |
The following parameters are used in Table 5.01 or in the development of these equations:
- reservoir pressure at the external boundary of the drainage volume, psi
- flowing well pressure, psi
- average reservoir pressure within the drainage volume, psi
- the real gas pseudo-pressure, psi2/cp
- external radius of the drainage volume, ft
- radius of the well, ft
- pressure at standard conditions (14.7 psi in the U.S.A), psi
- temperature at standard conditions (520°R in the U.S.A), °R
- temperature of the reservoir, °R
- effective permeability to gas in the presence of an immobile water phase, md
- thickness of the reservoir, ft
- gas viscosity, cp
- gas super-compressibility factor, dimensionless
- skin factor, dimensionless
- is the oil production rate during the stabilized production period, SCF/day
- factor in Rawlins and Schellhardt Backpressure or Deliverability Equation[1], SCF/(day-psi(2xn))
- exponent in Rawlins and Schellhardt Backpressure or Deliverability Equation[1], dimensionless
- is the oil phase formation volume factor, bbl/SCF