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Joshi Horizontal Well Critical Rate for Gas Coning Formula

qo=1.535×103(ρoρg)kh[h2(hlv)2]Boμoln(re/rw)q_o=1.535\times10^{-3}\frac{(\rho_o-\rho_g)k_h[h^2-(h-l_v)^2]}{B_o\mu_o\ln(r_e/r_w)}

Joshi Horizontal Well Critical Rate for Gas Coning 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_o, rho_g, r_e, r_w, l_v, h, mu_o, B_o, k_h) 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_o equals 9.566847 STB/day.

rho_og/cc

0.85

rho_gg/cc

0.1

r_eft

1000

r_wft

0.328

l_vft

20

hft

50

mu_ocP

2

B_oRB/STB

1.2

k_hmD

100

Inputs

rho_o

g/cc

Oil Density

rho_g

g/cc

Gas Density

r_e

ft

Effective Drainage Radius

r_w

ft

Wellbore Radius

l_v

ft

Distance Between Gas-Oil Interface and Perforated Top of Vertical Well

h

ft

Oil Column Thickness

mu_o

cP

Oil Viscosity

B_o

RB/STB

Oil Formation Volume Factor

k_h

mD

Horizontal Permeability

Outputs

q_o

STB/day

Critical Oil Rate

k_h

mD

Horizontal 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, gas-coning critical-rate method, pages 286-295.

Source

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