PO.VFP.HagedornBrown.dPdL
Description
Calculates pressure gradient for multiphase pipe flow using Hagedorn and Brown (1965) correlation with Griffith modification, [psi/ft]. Developed for vertical, upward flow and recommended only for near-vertical wellbores.
Syntax
=PO.VFP.HagedornBrown.dPdL(Ql, Qg, P, Rho_l, Ul, Bl, Rho_g, Ug, Bg, IFT_gl, Rs, pipe_ID, pipe_roughness)Parameters
| Parameter | Description |
|---|---|
| Ql | Liquid rate, [bbl/D]. |
| Qg | Gas rate, [mmscf/D]. |
| P | Pressure, [psi]. |
| Rho_l | Liquid density at in-situ conditions, [lb/ft3]. |
| Ul | Liquid viscosity at in-situ conditions, [cP]. |
| Bl | Liquid formation volume factor, [bbl/STB]. |
| Rho_g | Gas density at in-situ conditions, [lb/ft3]. |
| Ug | Gas viscosity at in-situ conditions, [cP]. |
| Bg | Gas formation volume factor, [rcf/scf]. |
| IFT_gl | Liquid-gas interfacial (surface) tension, [dynes/cm]. |
| Rs | Solution gas-oil ratio, [scf/STB]. |
| pipe_ID | Pipe inner diameter, [in]. |
| pipe_roughness | Pipe relative roughness, [dimensionless]. |
SI Unit Version
Lambda Name
PO.VFP.HagedornBrown.dPdL.SIFormula
=LAMBDA(Ql, Qg, P, Rho_l, Ul, Bl, Rho_g, Ug, Bg, IFT_gl, Rs, pipe_ID, pipe_roughness, LET(
Ql_bbld, PO.UnitConverter(Ql, "m3/d", "bbl/d"),
Qg_mmscfd, PO.UnitConverter(Qg, "sm3/d", "mmscf/d"),
P_psi, PO.UnitConverter(P, "kPa", "psi"),
Rho_l_lbft3, PO.UnitConverter(Rho_l, "kg/m3", "lb/ft3"),
Rho_g_lbft3, PO.UnitConverter(Rho_g, "kg/m3", "lb/ft3"),
IFT_gl_dynecm, PO.UnitConverter(IFT_gl, "mN/m", "dyne/cm"),
Rs_scfSTB, PO.UnitConverter(Rs, "sm3/sm3", "scf/STB"),
pipe_ID_in, PO.UnitConverter(pipe_ID, "cm", "in"),
result_psift, PO.VFP.HagedornBrown.dPdL(Ql_bbld, Qg_mmscfd, P_psi, Rho_l_lbft3, Ul, Bl, Rho_g_lbft3, Ug, Bg, IFT_gl_dynecm, Rs_scfSTB, pipe_ID_in, pipe_roughness),
PO.UnitConverter(result_psift, "psi/ft", "kPa/m")))SI Parameters
| Parameter | Unit | Description |
|---|---|---|
Ql |
m3/d | Liquid rate, [m3/d] |
Qg |
sm3/d | Gas rate, [sm3/d] |
P |
kPa | Pressure, [kPa] |
Rho_l |
kg/m3 | Liquid density at in-situ conditions, [kg/m3] |
Ul |
- | Liquid viscosity at in-situ conditions, [cP] |
Bl |
- | Liquid formation volume factor, [m3/sm3] |
Rho_g |
kg/m3 | Gas density at in-situ conditions, [kg/m3] |
Ug |
- | Gas viscosity at in-situ conditions, [cP] |
Bg |
- | Gas formation volume factor, [rm3/sm3] |
IFT_gl |
mN/m | Liquid-gas interfacial (surface) tension, [mN/m] |
Rs |
sm3/sm3 | Solution gas-oil ratio, [sm3/sm3] |
pipe_ID |
cm | Pipe inner diameter, [cm] |
pipe_roughness |
- | Pipe relative roughness, [dimensionless] |
How to save as a reusable Excel function
LAMBDA is a built-in Excel feature (Microsoft 365) that lets you create custom functions without VBA. The formula above works as-is when pasted into a cell.
To save a LAMBDA as a reusable named function:
- Go to Formulas → Name Manager → New
- Enter a name, e.g.
PO.VFP.HagedornBrown.dPdL.SI - In Refers to, paste the LAMBDA formula without the trailing invocation
(...) - Click OK
Now use =PO.VFP.HagedornBrown.dPdL.SI(...) anywhere in your workbook.