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>

where

where

* <math>\bar{p}</math> = initial or current average reservoir pressure (psia)

* <math>\bar{p}</math> = initial or current average reservoir pressure (psia)

* ''p''_wf = flowing bottomhole pressure (psia)

* ''p''_wf = flowing bottomhole pressure (psia)

* ''μ'' = viscosity (cp)

* ''μ'' = [[viscosity]] (cp)

* ''B'' = formation volume factor (rcf/MSCF)

* ''B'' = formation volume factor (rcf/MSCF)

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>

The surface shut-in and flowing pressure measurements are converted to bottomhole conditions and a log-log plot of <math>\bar{p}^{2} - p_{\rm wf}^{2}</math> versus flow rate, ''q'', is generated ([[:file:production-testing_fig2.png|Figure 2]]). The four points define a straight line with a slope that is generally between 0.5 and 1.0. This straight line is extrapolated to determine gas flow rate at a point where the flowing bottomhole pressure is zero; this rate is referred to as the absolute open flow (AOF) potential of the well.

The surface shut-in and flowing pressure measurements are converted to bottomhole conditions and a log-log plot of <math>\bar{p}^{2} - p_{\rm wf}^{2}</math> versus flow rate, ''q'', is generated ([[:file:production-testing_fig2.png|Figure 2]]). The four points define a straight line with a slope that is generally between 0.5 and 1.0. This straight line is extrapolated to determine gas flow rate at a point where the flowing bottomhole pressure is zero; this rate is referred to as the absolute open flow (AOF) potential of the well.

Multi-point test data can also be used to estimate permeability using a variable rate flow test analysis.<ref name=pt09r20>Odeh, A. S., Jones, L. G., 1965, Pressure drawdown analysis, variable-rate case, in Pressure Analysis Methods: Dallas, TX, American Institute of Mining, Metallurgical and Petroleum Engineers, Society of Petroleum Engineers Reprint Series No. 9, 256 p.</ref> For gas wells, the data are plotted as

Multi-point test data can also be used to estimate permeability using a variable rate flow test analysis.<ref name=pt09r20>Odeh, A. S., and L. G. Jones, 1965, Pressure drawdown analysis, variable-rate case, in Pressure Analysis Methods: Dallas, TX, American Institute of Mining, Metallurgical and Petroleum Engineers, Society of Petroleum Engineers Reprint Series No. 9, 256 p.</ref> For gas wells, the data are plotted as

:<math>\frac{\bar{p}^{2} - p_{\rm wfn}^{2}}{q_{n}} \mbox{ versus } \frac{1}{q_{n}} \sum\limits_{j=0}^{n-1} \Delta q_{j} \log (t_{n} - t_{j})</math>

:<math>\frac{\bar{p}^{2} - p_{\rm wfn}^{2}}{q_{n}} \mbox{ versus } \frac{1}{q_{n}} \sum\limits_{j=0}^{n-1} \Delta q_{j} \log (t_{n} - t_{j})</math>

[[Category:Production engineering methods]]

[[Category:Production engineering methods]]