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.