Numerical simulation was used to verify that properly conducted deliverability tests in gas wells would yield reliable values for permeability, skin factor, non-Darcy parameter, and stabilized well performance coefficient. Furthermore, the correctness of pseudostabilization time, used in obtaining the stabilized performance coefficient, was verified. Pseudostabilization flow time should not be mistaken for the stabilization time, which is defined as the time corresponding to the onset of pseudosteady-state flow behavior. Stabilization time is 2.52 times greater than pseudostabilization time for radial flow.
The boundary condition at the wellbore included the use of chokes to control flow rates. Wellbore storage and non-Darcy flow effects were also included in the numerical simulation. Both Rawlins and Schellhardt empirical equation as well as the theory-based pressure drawdown equation were successfully used in deliverability calculations using the numerical simulation results.
Gas well deliverability tests are multirate tests consisting of three or more flows with rates and pressures recorded as a function of time. These tests are required by state regulatory agencies for proration purposes. Furthermore, these tests can provide information useful for reservoir forecasting, skin damage evaluation, and establishing a base performance curve for future comparisons.
The basic work towards development of a practical test was carried out by Pierce and Rawlins. Rawlins and Schellhardt introduced the concept of backpressure testing using the flow-after-flow test. Cullender presented the isochronical test as an empirical method and Katz et al. presented the modified isochronal test consisting of equal flow and shut-in periods.
Rawlins and Schellhardt historical backpressure (or gas deliverability) equation is:
(1)
From integration of quadratic form of Forchheimer equation (known as non-Darcy flow equation) one can obtain the following steady-state solution:
(2)
Where:
(3)
(4)
(5)
(6)
It is well known that during transient flow the following analog of slightly compressible flow generally applies to gas wells (especially for p < 2000 psia):
Where:
(7)
(8)
Eq. 7 can be written in a form similar to Eq. 2 as follows:
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