Analysis of a flow test with smoothly varying rates


\(t_{1}\): Time at \(P_{w f 1}\) from Given Values or Trendline (h)

\(t_{2}\): Time at \(P_{w f 2}\) from Given Values or Trendline (h)

\(\mathrm{q}_{1}\): Flow Rate at \(\mathrm{P}_{\mathrm{wf} 1}(\mathrm{STB} /\) day \()\)

\(\mathrm{q}_{2}\): Flow Rate at \(\mathrm{P}_{\mathrm{wf} 2}(\mathrm{STB} /\) day \()\)

\(\mathrm{p}_{\mathrm{i}}\): Initial Pressure (psi)

\(\mathrm{p}_{\mathrm{wf} 2}\): Wellflow Pressure at Point 2 from Given Values or Trendline (psi)

\(\mathrm{p}_{\mathrm{wf} 1}\): Wellflow Pressure at Point 1 from Given Values or Trendline (psi)

\(\mathrm{p}_{\mathrm{wf}}\): Pressure Value at \(t=1 \mathrm{~h}(\mathrm{psi})\)

q: Flow Rate (STB/day)

B: Volume Factor (RB/STB)

\(\mathrm{h}\): Thickness of Reservoir (ft)

\(\mu\): Viscosity of Oil (cP)

\(\varnothing\): Porosity (fraction)

\(c_{t}\): Compressibility (1/psi)

\(\mathrm{r}_{\mathrm{w}}\): Wellbore Radius (ft)


\(\mathrm{m}\): Slope of Line (dimensionless)

\(\mathrm{k}\): Permeability \((\mathrm{mD})\)

s: Skin Factor (dimensionless)


\[ \begin{gathered} \mathrm{m}=\frac{\left(\frac{\mathrm{p}_{\mathrm{i}}-\mathrm{p}_{\mathrm{wf} 2}}{\mathrm{q}_{2}}\right)-\left(\frac{\mathrm{p}_{\mathrm{i}}-\mathrm{p}_{\mathrm{wf} 1}}{\mathrm{q}_{1}}\right)}{\log \left(\mathrm{t}_{2}\right)-\log \left(\mathrm{t}_{1}\right)} \\ \mathrm{k}=162.6 * \mathrm{~B} * \frac{\mu}{\mathrm{m} * \mathrm{~h}} \\ \mathrm{~s}=1.151 *\left(\frac{1}{\mathrm{~m}\left(\frac{\mathrm{p}_{\mathrm{i}}-\mathrm{p}_{\mathrm{wf}}}{\mathrm{q}}\right)}-\log \left(\frac{\mathrm{k}}{\emptyset * \mu * \mathrm{c}_{\mathrm{t}} * \mathrm{r}_{\mathrm{w}}^{2}}\right)+3.23\right) \end{gathered} \]


Lee, J., Rollins, J. B., & Spivey, J. P. (2003). Pressure Transient Testing (Vol. 9). Richardson, Texas: Society of Petroleum Engineers, Page: 31.


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