Changes

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., 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:

:<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}) \label{978-1-62981-110-9_458_eq1(1)}</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

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., 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:

:<math>r_{\rm d} = \left(\frac{kt}{376\phi \mu c_{\rm t}}\right)^{1/2} \label{978-1-62981-110-9_458_eq2(2)}</math>

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

:<math>k = \frac{141.2q\mu B}{h(\bar{p} - p_{\rm wf})} \left[\ln \left(\frac{r_{\rm d}}{r_{\rm w}}\right) - \frac{3}{4} + s'\right] \label{978-1-62981-110-9_458_eq3(3)}</math>

:<math>k = \frac{141.2q\mu B}{h(\bar{p} - p_{\rm wf})} \left[\ln \left(\frac{r_{\rm d}}{r_{\rm w}}\right) - \frac{3}{4} + s'\right]</math>

where

where

The plot is made on Cartesian coordinate paper. A straight line with slope, ''m''′, should result; this slope is used in Equation 4 to calculate permeability:

The plot is made on Cartesian coordinate paper. A straight line with slope, ''m''′, should result; this slope is used in Equation 4 to calculate permeability:

:<math>k = \frac{1637T\mu z}{m'h} \label{978-1-62981-110-9_458_eq4(4)}</math>

:<math>k = \frac{1637T\mu z}{m'h}</math>

where

where

The apparent skin factor can also be determined from this plot. If the intercept of the plot (the value of Δ''p''²/''q'' where the time plotting function is zero) is denoted by ''b'', then

The apparent skin factor can also be determined from this plot. If the intercept of the plot (the value of Δ''p''²/''q'' where the time plotting function is zero) is denoted by ''b'', then

:<math>s' = 1.151 \left[\frac{b}{m'} - \log \left(\frac{k}{\phi\mu c_{\rm t}r_{\rm w}^{2}}\right) + 3.23\right] \label{978-1-62981-110-9_458_eq5(5)}</math>

:<math>s' = 1.151 \left[\frac{b}{m'} - \log \left(\frac{k}{\phi\mu c_{\rm t}r_{\rm w}^{2}}\right) + 3.23\right]</math>

Since multi-point test data are available for virtually all gas wells, this method of analysis often proves to be a useful way of estimating permeability and skin factor, especially when drawdown or buildup tests are not available.

Since multi-point test data are available for virtually all gas wells, this method of analysis often proves to be a useful way of estimating permeability and skin factor, especially when drawdown or buildup tests are not available.