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Water Injection Bottom-Hole Pressure from Radial Flow Formula

Piwf=Pe+qwμwBw[ln(re/rw)+s]0.00708krwkhP_{iwf}=P_e+\frac{q_w\mu_wB_w[\ln(r_e/r_w)+s]}{0.00708k_{rw}kh}

Water Injection Bottom-Hole Pressure from Radial Flow calculates flowing bottom-hole injection pressure for injection wells workflows in production engineering.

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How engineers use this formula

Use this formula when the listed inputs (P_e, q_w, mu_w, B_w, r_e, r_w, s, k_rw, k, h) are known and the assumptions behind the cited injection wells 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_iwf equals 3,151.649313 psi.

P_epsi

3000

q_wSTB/day

500

mu_wcP

0.7

B_wrb/STB

1.02

r_eft

1000

r_wft

0.328

sdimensionless

1

k_rwfraction

0.6

kmD

100

hft

50

Inputs

P_e

psi

External Boundary or Reservoir Pressure

q_w

STB/day

Water Injection Rate

mu_w

cP

Water Viscosity

B_w

rb/STB

Water Formation Volume Factor

r_e

ft

Drainage Radius

r_w

ft

Wellbore Radius

s

dimensionless

Skin Factor

k_rw

fraction

Relative Permeability to Water

k

mD

Absolute Permeability

h

ft

Net Pay Thickness

Outputs

P_iwf

psi

Flowing Bottom-Hole Injection Pressure

Source and review

reviewed

Baker, R.O., Yarranton, H.W. and Jensen, J.L. 2015. Practical Reservoir Engineering and Characterization, radial Darcy field-unit water equation.

Source

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