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Fluid flow fundamentals (view source)
Revision as of 17:11, 20 January 2014
, 17:11, 20 January 2014→Empirical IPR equations
===Productivity index equation for undersaturated oil===
===Productivity index equation for undersaturated oil===
The production rate in undersaturated oil wells is linearly proportional to the drawdown, and the IPR is a straight line (Figure 2a). The equation is
The production rate in undersaturated oil wells is linearly proportional to the drawdown, and the IPR is a straight line ([[:file:fundamentals-of-fluid-flow_fig2.png|Figure 2a]]). The equation is
:<math>q_{\rm o} = J(p_{\rm R} - p_{\rm wf})</math>
:<math>q_{\rm o} = J(p_{\rm R} - p_{\rm wf})</math>
:<math>q_{\rm o} = c(p_{\rm R}{}^{2} - p_{\rm wf}{}^{2})^{n}</math>
:<math>q_{\rm o} = c(p_{\rm R}{}^{2} - p_{\rm wf}{}^{2})^{n}</math>
It has two characteristic constants: the back pressure constant, c, and the back pressure exponent, ''n''. The exponent ''n'' is a dimensionless number between 0.5 and 1.0. It approaches 1.0 for low rate wells and 0.5 for very high rate wells. Values of ''n'' and ''c'' can be determined graphically from a log-log plot of multiple rate test data in the form of (''p''<sub>R</sub><sup>2</sup> – ''p''<sub>wf</sub><sup>2</sup>) versus ''q'' (Figure 2b). The data point can be fitted to a straight line whose slope is 1/n.
It has two characteristic constants: the back pressure constant, c, and the back pressure exponent, ''n''. The exponent ''n'' is a dimensionless number between 0.5 and 1.0. It approaches 1.0 for low rate wells and 0.5 for very high rate wells. Values of ''n'' and ''c'' can be determined graphically from a log-log plot of multiple rate test data in the form of (''p''<sub>R</sub><sup>2</sup> – ''p''<sub>wf</sub><sup>2</sup>) versus ''q'' ([[:file:fundamentals-of-fluid-flow_fig2.png|Figure 2b]]). The data point can be fitted to a straight line whose slope is 1/n.
===Quadratic equation for saturated oil and gas wells===
===Quadratic equation for saturated oil and gas wells===
:<math>(p_{\rm R}{}^{2} - p_{\rm wf}{}^{2}) = Aq + Bq^{2}</math>
:<math>(p_{\rm R}{}^{2} - p_{\rm wf}{}^{2}) = Aq + Bq^{2}</math>
The characteristic constants ''A'' and ''B'' are the corresponding slope and the intercept of the straight line obtained from a Cartesian plot of the multiple rate test data (Figure 2c) in the following form:
The characteristic constants ''A'' and ''B'' are the corresponding slope and the intercept of the straight line obtained from a Cartesian plot of the multiple rate test data ([[:file:fundamentals-of-fluid-flow_fig2.png|Figure 2c]]) in the following form:
:<math>(p_{\rm R}{}^{2} - p_{\rm wf}{}^{2})/q\quad \mbox{versus}\quad (A + Bq)</math>
:<math>(p_{\rm R}{}^{2} - p_{\rm wf}{}^{2})/q\quad \mbox{versus}\quad (A + Bq)</math>
For wells producing below bubblepoint pressure, ''p''<sub>b</sub> while the reservoir pressure is above the bubblepoint (''p''<sub>wf</sub>''<sub>b</sub>p''
For wells producing below bubblepoint pressure, ''p''<sub>b</sub> while the reservoir pressure is above the bubblepoint (''p''<sub>wf</sub>''<sub>b</sub>p''
<sub>R</sub>), the IPR assumes the shape shown in Figure 2(d). It can be represented by the following equations:
<sub>R</sub>), the IPR assumes the shape shown in [[:file:fundamentals-of-fluid-flow_fig2.png|Figure 2d]]. It can be represented by the following equations:
:<math>\mbox{for } p_{\rm wf} > p_{\rm b},\quad q_{\rm o} = J(p_{\rm R} - p_{\rm wf})</math>
:<math>\mbox{for } p_{\rm wf} > p_{\rm b},\quad q_{\rm o} = J(p_{\rm R} - p_{\rm wf})</math>