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Reservoir EngineeringPressure Transient Analysis

Infinite-Acting Pseudoradial Bottomhole Flowing Pressure Formula

Pwf=pi162.6QoμoBokh[log10t+log10(kϕμoctrw2)3.23+0.87S]P_{wf}=p_i-\frac{162.6Q_o\mu_oB_o}{kh}\left[\log_{10}t+\log_{10}\left(\frac{k}{\phi\mu_oc_tr_w^2}\right)-3.23+0.87S\right]

Infinite-Acting Pseudoradial Bottomhole Flowing Pressure calculates bottomhole flowing pressure for pressure transient analysis workflows in reservoir engineering.

Calculate

How engineers use this formula

Use this formula when the listed inputs (p_i, Q_o, B_o, mu_o, k, h, t, phi, c_t, r_w, S) are known and the assumptions behind the cited pressure transient analysis relationship match the engineering case being checked.

Assumptions

  • Input values are representative for the well, reservoir, fluid, or equipment case being evaluated.
  • The declared units match the field-unit constants used in the formula.
  • The cited formula applies to the selected petroleum engineering workflow.

Limitations

  • The calculation does not replace a full engineering model or operating procedure.
  • Accuracy depends on the source correlation, assumptions, input quality, and unit consistency.

Common mistakes

  • Mixing unit systems without converting the inputs.
  • Using default example values as field recommendations.
  • Applying the formula outside the source assumptions.

Default example

Using the default inputs, P_wf equals 3,835.843788 psi.

p_ipsi

4000

Q_oSTB/day

500

B_obbl/STB

1.2

mu_ocP

1

kmD

100

hft

50

th

10

phifraction

0.2

c_t1/psi

0.00001

r_wft

0.25

Sdimensionless

2

Inputs

p_i

psi

Initial Reservoir Pressure

Q_o

STB/day

Oil Flow Rate

B_o

bbl/STB

Oil Formation Volume Factor

mu_o

cP

Oil Viscosity

k

mD

Permeability

h

ft

Formation Thickness

t

h

Flowing Time

phi

fraction

Porosity

c_t

1/psi

Total Compressibility

r_w

ft

Wellbore Radius

S

dimensionless

Skin Factor

Outputs

P_wf

psi

Bottomhole Flowing Pressure

p_i

psi

Initial Reservoir Pressure

Q_o

STB/day

Oil Flow Rate

B_o

bbl/STB

Oil Formation Volume Factor

h

ft

Formation Thickness

S

dimensionless

Skin Factor

Source and review

reviewed

Advanced Reservoir Engineering, Ahmed, T., McKinney, P. D. (2005)

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

Source

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