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Reservoir EngineeringPressure Transient Analysis

Dimensionless Vertical Well Critical Rate Correlations – Hoyland, Papatzacos, and Skjaeveland Formula

QoD=651.4μoBo(qoh2(ρwρo)kh)Q_{oD} = 651.4 \cdot \mu_o \cdot B_o \cdot \left( \frac{q_o}{h^2 \cdot (\rho_w - \rho_o) \cdot k_h} \right)

Dimensionless Vertical Well Critical Rate Correlations – Hoyland, Papatzacos, and Skjaeveland calculates dimensionless critical oil rate for pressure transient analysis workflows in reservoir engineering.

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How engineers use this formula

Use this formula when the listed inputs (mu_o, B_o, q_o, h, rho_w, rho_o, k_h) 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, Q_oD equals 1.421236 dimensionless.

mu_ocP

0.25

B_obbl/STB

1.2

q_oSTB/day

500

hft

50

rho_wg/cc

1.025

rho_og/cc

0.75

k_hmD

100

Inputs

mu_o

cP

Oil Viscosity

B_o

bbl/STB

Oil Formation Volume Factor

q_o

STB/day

Critical Oil Flow Rate

h

ft

Oil Column Thickness

rho_w

g/cc

Water Density

rho_o

g/cc

Oil Density

k_h

mD

Horizontal Permeability

Outputs

Q_oD

dimensionless

Dimensionless Critical Oil Rate

q_o

STB/day

Oil Flow Rate (rearranged)

mu_o

cP

Oil Viscosity (rearranged)

B_o

bbl/STB

Oil Formation Volume Factor (rearranged)

h

ft

Reservoir Thickness (rearranged)

rho_w

g/cc

Water Density (rearranged)

rho_o

g/cc

Oil Density (rearranged)

k_h

mD

Horizontal Permeability (rearranged)

Source and review

reviewed

Hoyland, Papatzacos, and Skjaeveland (1989). SPE 19823. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas.

Source

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