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Reservoir EngineeringThermal Gradients

Horner Formation Temperature from Bottom-Hole Temperature Formula

T=TiClog10(tc+ΔtΔt)T = T_i - C\log_{10}\left(\frac{t_c+\Delta t}{\Delta t}\right)

Horner Formation Temperature from Bottom-Hole Temperature calculates corrected static formation temperature for thermal gradients workflows in reservoir engineering.

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How engineers use this formula

Use this formula when the listed inputs (T_log, C_H, t_c, delta_t) are known and the assumptions behind the cited thermal gradients 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, T_true equals 190.881361 degF.

T_logdegF

180

C_HdegF/log-cycle

-20

t_chr

5

delta_thr

2

Inputs

T_log

degF

Measured Logging Temperature

C_H

degF/log-cycle

Horner Plot Slope for Base-10 Log

t_c

hr

Mud Circulation Time Before Shut-In

delta_t

hr

Time Since Circulation Stopped

Outputs

T_true

degF

Corrected Static Formation Temperature

H_horner

dimensionless

Dimensionless Horner Time Ratio

T_log

degF

Measured Logging Temperature

C_H

degF/log-cycle

Horner Plot Slope for Base-10 Log

t_c

hr

Mud Circulation Time Before Shut-In

delta_t

hr

Time Since Circulation Stopped

Source and review

reviewed

APT International glossary. Borehole temperature model calibration, Horner-type corrections.

Source

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