# Bottomhole flowing pressure during infinite-acting pseudoradial flow

## Input(s)

$$p_{i}$$: Initial Reservoir Pressure (psi)

$$Q_{o}$$: Well Flow Rate (STB/day)

$$B_{o}$$: Oil Formation Volume Factor (bbl/STB)

$$\mu_{o}$$: Oil Viscosity $$(\mathrm{cP})$$

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

$$\mathrm{h}$$: Thickness $$(\mathrm{ft})$$

$$\mathrm{t}$$: Flowing Time (h)

$$\emptyset$$: Porosity (fraction)

$$c_{t}$$: Total Compressibility (1/psi)

$$r_{w}$$: Wellbore Radius (ft)

$$\mathrm{S}$$: Skin (dimensionless)

## Output(s)

$$P_{w f}$$: Wellbore Flowing Pressure (psi)

## Formula(s)

$\begin{gathered} P_{w f}=p_{i}-\left(\frac{162.6 * Q_{o} * \mu_{o} * B_{o}}{k * h}\right) *\left(\log (t)+\log \left(\frac{k}{\emptyset * \mu_{o} * c_{t} * r_{w}^{2}}\right)-3.23+0.87 * S\right) \\ p_{i}-p_{w f}=\Delta p=a+m \log (t) \end{gathered}$

## Reference(s)

Ahmed, T., McKinney, P.D. 2005. Advanced Reservoir Engineering, Gulf Publishing of Elsevier, Chapter: 1, Page: 98.

## Related

### Skin during infinite-acting pseudoradial flow for vertical wells

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