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### Shell-MIT Equation

Fluids Engineering and Design Resources

Shell-MIT Equation

The Shell-MIT equation, also known as the MIT equation, was initially used by the Shell pipeline company for modeling the flow of high viscosity heated crude oil pipelines. This equation for pressure drop uses a modified Reynolds number*R*, which is a multiple of the normal Reynolds number. From

_{m}*R*a friction factor is calculated depending on whether the flow is laminar or turbulent. The calculation method is as follows. The Reynolds number of flow is first calculated from

_{m}Equation 1

*R = 92.24 Q / ( D v)*

From the preceding, a modified Reynolds number is defined as

Equation 2

R_{m} = R / 7742

where R= Reynolds number, dimensionless

*R _{m}* = modified Reynolds number, dimensionless

Q = flow rate, bbl/day

D = pipe inside diameter, in

ν = liquid kinematic viscosity, cSt

Next, a friction factor is calculated from one of the following equations:

Equation 3

*F = 0.00207 / R _{m} -> for laminar flow*

*or *

Equation 4

*0.0018 + 0.00662 ( 1 / R _{m} )^{0.355} -> for turbulent flow*

The laminar flow limit is the same as before: Reynolds number R < 2100 approximately.

The friction factor f in Eqs. (3) and (4) is not the Darcy friction factor we have used so far with the Colebrook equation. Therefore we cannot directly use it in the Darcy equation to calculate the pressure drop.

The pressure drop due to friction with the Shell-MIT equation is then calculated as follows:

Equation 5 *
*P

_{m}= 0.241 ( f Sg Q

^{2}) / D

^{6}

where

*P _{m}* = pressure drop due to friction, psi/mi

f = Shell-MIT equation friction factor, dimensionless

Sg = liquid specific gravity

Q = liquid flow rate, bbl/day

D = pipe inside diameter, in

With flow rate in bbl/h, the pressure drop due to friction is calculated using the following modified version of the Darcy equation:

Equation 6*
*

*P*

_{m}= 138.82 ( f Sg Q^{2}) / D^{5}where

*P _{m}* = pressure drop due to friction, psi/mi

f = Shell-MIT equation friction factor, dimensionless

Sg = liquid specific gravity

Q = liquid flow rate, bbl/h

D = pipe inside diameter, in

In SI units the MIT equation is expressed as follows:

*P _{m} = ( 6.2191 x 10^{10} ) ( f Sg Q^{2} ) / D^{5} *

where

*P _{m}* = frictional pressure drop, kPa/km

f = Shell-MIT equation friction factor, dimensionless

Sg = liquid specific gravity

Q = liquid flow rate, m

^{3}/h

D = pipe inside diameter, mm

Related:

- Babcock Steam Flow Rate Formula and Calculator
- Swamee-Jain Friction Factor Equation and Calculator
- Churchill Friction Factor Formulae and Calculator
- Harris Formula Pressure and Fluid Flow Equation and Calculator
- Liquid Pressure Drop in Pipe and Pipe Fittings Spreadsheet Calculator
- Friction Loss - Fluid Flow Hydraulic and Pneumatic
- Darci's Equation Fluids Flow Equation
- Pipe Flow/Friction Factor Calculations with Excel Training - 3 PDH
- Unwin Gas Change of Pressure Calculator and Formulas
- Gas Flow Rate Through Orifice Equations and Calculator per. ISO 5167
- Low Pressure Flow Oliphant and Spitzglass Formula and Calculator

Reference:

- Piping Calculations Manual,

E. Shashi Menon

SYSTEK Technologies, Inc