# 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)

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

## Reference(s)

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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### Analysis of a well from a PI test

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