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Hoyland Papatzacos Skjaeveland Isotropic Vertical Well Critical Rate Formula

Qoc=(ρwρo)koBoμo10822[1(hph)2]1.325h2.238(lnre)1.99Q_{oc}=\frac{(\rho_w-\rho_o)k_o}{B_o\mu_o10822}\left[1-\left(\frac{h_p}{h}\right)^2\right]^{1.325}h^{2.238}(\ln r_e)^{-1.99}

Hoyland Papatzacos Skjaeveland Isotropic Vertical Well Critical Rate calculates critical oil rate for well performance workflows in reservoir engineering.

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How engineers use this formula

Use this formula when the listed inputs (rho_w, rho_o, k_o, B_o, mu_o, h, h_p, r_e) are known and the assumptions behind the cited well performance 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_oc equals 76.673282 m^3/day.

rho_wkg/m^3

1000

rho_okg/m^3

850

k_omD

100

B_oRB/STB

1.2

mu_ocP

2

hm

50

h_pm

20

r_em

500

Inputs

rho_w

kg/m^3

Water Density

rho_o

kg/m^3

Oil Density

k_o

mD

Effective Oil Permeability

B_o

RB/STB

Oil Formation Volume Factor

mu_o

cP

Oil Viscosity

h

m

Oil Column Thickness

h_p

m

Perforated Interval

r_e

m

Drainage Radius Used by the Correlation

Outputs

Q_oc

m^3/day

Critical Oil Rate

k_o

mD

Effective Oil Permeability

mu_o

cP

Oil Viscosity

B_o

RB/STB

Oil Formation Volume Factor

Source and review

reviewed

Joshi, S.D. 1991. Horizontal Well Technology, Page 257; Hoyland, Papatzacos, and Skjaeveland vertical-well critical-rate correlation.

Source

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