Radial Liquid Pressure Distribution Calculator
Calculate skin-free steady-state radial liquid pressure from wellbore pressure, stock-tank rate, fluid properties and radial position in field units.
Calculate skin-free steady-state radial liquid pressure from wellbore pressure, stock-tank rate, fluid properties and radial position in field units.
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Calculation context and source notes
Calculate pressure outside an ideal well from its skin-free steady-state radial liquid-flow relation. The pressure increases logarithmically with distance from the wellbore for nonnegative production, with constant permeability, thickness and compatible liquid properties.
Enter flowing wellbore pressure and stock-tank oil rate with B_o, viscosity, permeability and thickness on the stated field-unit basis. Choose a radial position at or outside the wellbore. Use the result for a steady-state spatial check, not a transient pressure profile or a skin-corrected well model.
Solves for
p_r (psi)
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Formula, variables, and sourceReproduce the spatial pressure check
At p_wf = 2,500 psi, q_o = 500 STB/day, B_o = 1.2, viscosity 2 cP, permeability 100 mD, thickness 50 ft and wellbore radius 0.328 ft, the logarithmic coefficient is 33.888 psi. At radius 100 ft the result is 2,693.836373 psi. At the wellbore radius it returns exactly 2,500 psi.
Doubling radius from 100 to 200 ft adds the same coefficient times ln(2), or 23.489372 psi, giving 2,717.325745 psi. This equal pressure increment for equal radius ratios is a diagnostic of this steady-state logarithmic relation, not a claim that a transient reservoir has this profile at every time.
| Radius (ft) | Pressure (psi) |
|---|---|
| 0.328 | 2,500 |
| 100 | 2,693.836373 |
| 200 | 2,717.325745 |
Separate boundary pressure, wellbore pressure and skin
The verified source writes the steady-state profile relative to a fixed outer pressure. Evaluating it at the wellbore and subtracting eliminates the outer reference, giving this wellbore-referenced expression. It is an algebraic rearrangement on the same skin-free field-unit basis, not a new correlation. The signed-rate relation is preserved: negative q_o reverses the pressure gradient for injection under the same ideal assumptions, not as an injectivity approval.
For a well with skin, distinguish pressure just outside the near-well region from the measured flowing bottomhole pressure. The source's transient and pseudosteady-state solutions have additional time or boundary terms. Neither replacing a radius nor reusing this logarithm supplies those missing effects, so select the flow regime before applying the profile.
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Worked explanations, controlled studies and printable exercises connected to this calculation.
Related source-backed guides
Formula, variables, and default calculation
Reproducible default result
With the default values shown below, the calculation returns p_r = 2,693.836373 psi. Defaults demonstrate the implementation; they are not recommended field values.
2500
500
2
1.2
100
0.328
100
50
Input definitions
p_wf
psiFlowing Bottom-Hole Pressure
q_o
STB/dayOil Flow Rate
mu_o
cPOil Viscosity
B_o
bbl/STBOil Formation Volume Factor
r
ftRadial Position
r_w
ftWellbore Radius
k
mDPermeability
h
ftNet Pay Thickness
Output definitions
p_r
Pressure at Radial Position
Engineering use, assumptions, and limits
Enter flowing wellbore pressure and stock-tank oil rate with B_o, viscosity, permeability and thickness on the stated field-unit basis. Choose a radial position at or outside the wellbore. Use the result for a steady-state spatial check, not a transient pressure profile or a skin-corrected well model.
Assumptions
- Ideal single-phase, horizontal, steady-state radial flow with constant thickness, permeability and liquid properties.
- Flowing wellbore pressure and radial pressure share a datum; no separate near-well skin pressure drop is added.
Limitations
- No time, transient diffusivity, no-flow boundary, gravity or variable-property pressure solution is included.
- The relation does not account for skin, restricted entry or multiphase effects; a damaged well needs the appropriate additional model.
Common mistakes
- Applying the logarithmic expression inside the wellbore, or mixing surface rate with reservoir volume without B_o.
- Using log10 in place of ln, adding a skin pressure drop twice, or treating this as a pressure-buildup time curve.
Frequently asked questions
What inputs does the Radial Pressure Distribution in Single-Phase Liquid Flow calculator need?
The calculation uses Flowing Bottom-Hole Pressure (p_wf), Oil Flow Rate (q_o), Oil Viscosity (mu_o), Oil Formation Volume Factor (B_o), Radial Position (r), Wellbore Radius (r_w), Permeability (k), Net Pay Thickness (h). Enter values on the units shown beside each field.
What result does this calculator return?
The primary result is pressure at radial position in psi. The formula section shows the declared relationship, variables, and a reproducible default calculation.
What should I check before using the result?
Confirm the unit basis, source applicability, and input quality. No time, transient diffusivity, no-flow boundary, gravity or variable-property pressure solution is included. Applying the logarithmic expression inside the wellbore, or mixing surface rate with reservoir volume without B_o.
Source and record status
Source metadata identifies the relationship implemented by the calculator. Check the cited edition, unit basis, and scope against the engineering case before operational use.
Petroleum Engineering 324: Well Performance Course Work, T. A. Blasingame (2006)
T. A. Blasingame, Texas A&M Petroleum Engineering 324 course work (2006), Problem 3, page 7, equation 3.3. Subtracting the steady-state expression at r_w from the expression at r gives p(r)-p_wf = 141.2 q B mu ln(r/r_w)/(kh). Skin-free ideal radial flow.
Open source reference