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Well Flowing Pressure Line-Source Solution by Including Skin Factor Formula

Pwf=Pi+70.6qμBkh[ln(1688ϕμctr2kt)2S]P_{wf}=P_i+\frac{70.6q\mu B}{kh}\left[\ln\left(\frac{1688\phi\mu c_tr^2}{kt}\right)-2S\right]

Well Flowing Pressure Line-Source Solution by Including Skin Factor calculates well flowing pressure for well performance workflows in production engineering.

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How engineers use this formula

Use this formula when the listed inputs (P_i, q, mu, B, k, h, phi, c_t, r, t, S) are known and the assumptions behind the cited well performance 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 3,430.696308 psi.

P_ipsi

3500

qbbl/day

500

mucP

2

Bbbl/STB

1.2

kmD

100

hft

50

phifraction

0.2

c_t1/psi

0.00001

rft

1000

tdays

10

Sdimensionless

3

Inputs

P_i

psi

Initial Reservoir Pressure

q

bbl/day

Flow Rate

mu

cP

Viscosity

B

bbl/STB

Formation Volume Factor

k

mD

Permeability

h

ft

Payzone Thickness

phi

fraction

Porosity

c_t

1/psi

Total Compressibility

r

ft

Reservoir Radius

t

days

Time

S

dimensionless

Skin Factor

Outputs

P_wf

psi

Well Flowing Pressure

S

dimensionless

Skin Factor

P_i

psi

Initial Reservoir Pressure

Source and review

reviewed

Lee, J., Rollins, J.B. and Spivey, J.P. 2003. Pressure Transient Testing, Vol. 9, Society of Petroleum Engineers, Page 13.

Source

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