Analysis of a flow test with smoothly varying rates

Input(s)

\(t_{1}\): 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)

Output(s)

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

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

s: Skin Factor (dimensionless)

Formula(s)

Reference(s)

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