Changes

==Single-point tests==

==Single-point tests==

Single-point tests are usually simple productivity tests that typically involve a measurement (or estimate) of initial or average reservoir pressure and a measurement of flow rate and flowing bottomhole pressure (which can be estimated from flowing surface pressure) at stabilized producing conditions.<ref name=pt09r1>Allen, T. O., Roberts, A. P., 1978, Production Operations, Volume 1 : Tulsa, OK, Oil and Gas Consultants International, 225 p.</ref> From these data, the productivity index, PI, can be calculated as follows:

Single-point tests are usually simple productivity tests that typically involve a measurement (or estimate) of initial or average reservoir pressure and a measurement of flow rate and flowing bottomhole pressure (which can be estimated from flowing surface pressure) at stabilized producing conditions.<ref name=pt09r1>Allen, T. O., and A. P. Roberts, 1978, Production Operations, Volume 1: Tulsa, OK, Oil and Gas Consultants International, 225 p.</ref> From these data, the productivity index, PI, can be calculated as follows:

:<math>\mbox{PI} = \frac{q}{\bar{p} - p_{\rm wf}} \mbox{ (for oil)} = \frac{q\mu B}{\bar{p}^{2} - p_{\rm wf}^{2}} \mbox{ (for gas)}</math>

:<math>\mbox{PI} = \frac{q}{\bar{p} - p_{\rm wf}} \mbox{ (for oil)} = \frac{q\mu B}{\bar{p}^{2} - p_{\rm wf}^{2}} \mbox{ (for gas)}</math>

The productivity index can be a useful indicator of well productivity and wellbore condition during the life of a well. PI will generally decrease over time due to declining reservoir pressure, changes in producing conditions, and/or [[production problems]].

The productivity index can be a useful indicator of well productivity and wellbore condition during the life of a well. PI will generally decrease over time due to declining reservoir pressure, changes in producing conditions, and/or [[production problems]].

Single-point tests can also be used to estimate formation permeability<ref name=pt09r15>Lee, W. J., Kuo, T. B., Holditch, S. A., McVay, D. A., 1984, Estimating formation permeability from single-point flow data: Proceedings of the 1984 SPE/DOE/GRI Unconventional Gas Recovery Symposium, Pittsburgh, PA, p. 175–186.</ref> with an iterative solution of the transient radius of drainage equation (Equation 2) and the pseudosteady-state flow equation (Equation 3), as follows:

Single-point tests can also be used to estimate formation permeability<ref name=pt09r15>Lee, W. J., T. B. Kuo, S. A. Holditch, and D. A. McVay, 1984, Estimating formation permeability from single-point flow data: Proceedings of the 1984 SPE/DOE/GRI Unconventional Gas Recovery Symposium, Pittsburgh, PA, p. 175–186.</ref> with an iterative solution of the transient radius of drainage equation (Equation 2) and the pseudosteady-state flow equation (Equation 3), as follows:

:<math>r_{\rm d} = \left(\frac{kt}{376\phi \mu c_{\rm t}}\right)^{1/2}</math>

:<math>r_{\rm d} = \left(\frac{kt}{376\phi \mu c_{\rm t}}\right)^{1/2}</math>