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Reservoir EngineeringPressure Transient Analysis

Pseudosteady-State Dimensionless Pressure Drop for Fractured Vertical Well Formula

PD=2πtDA+0.5ln(xexf)2+0.5ln(2.2458Cf)+1.385P_D=2\pi t_{DA}+0.5\ln\left(\frac{x_e}{x_f}\right)^2+0.5\ln\left(\frac{2.2458}{C_f}\right)+1.385

Pseudosteady-State Dimensionless Pressure Drop for Fractured Vertical Well calculates wellbore dimensionless pressure drop for pressure transient analysis workflows in reservoir engineering.

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How engineers use this formula

Use this formula when the listed inputs (t_DA, C_f, x_e, x_f) 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_D equals 1.921224 dimensionless.

t_DAdimensionless

0.1

C_fdimensionless

30

x_eft

1000

x_fft

300

Inputs

t_DA

dimensionless

Dimensionless Time Based on Drainage Area

C_f

dimensionless

Fractured Vertical Well Shape Factor

x_e

ft

Half Side Length of Square Drainage Area

x_f

ft

Fracture Half-Length

Outputs

P_D

dimensionless

Wellbore Dimensionless Pressure Drop

t_DA

dimensionless

Dimensionless Time Based on Drainage Area

C_f

dimensionless

Fractured Vertical Well Shape Factor

Source and review

reviewed

Joshi, S. D. Horizontal Well Technology, PennWell Publishing Company, Chapter 7, Page 211.

Source

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