Most of the experienced chemical engineers know about the Darcy-Weisbach equation for frictional pressure drop using the Darcy friction factor values from Moody's chart. The Moody chart provides the Darcy friction factor values for a given Reynold's number and a given relative roughness for conduits with a circular cross-section (circular pipes).

For newcomers to pressure drop calculations the references provided for Darcy-Weisbach and Moody's chart below could be great starting points:

http://en.wikipedia....isbach_equation

http://en.wikipedia....iki/Moody_chart

Today's blog entry is related to some empirical equations for pressure drop calculations in Crude Oil & Petroleum products (Gasoline, Naphtha, Kerosene) pipelines. Let us get to the equations straight away:

**Shell-MIT Equation - Pressure Drop in Heavy Crude Oil & Heated Liquid Pipelines (USC Units)**

R = 92.24*Q / (v*D

_{i})

where:

R = Reynolds no, dimensionless

Q = Flow Rate, bbl / day

v = Kinematic Viscosity, cSt

D

_{i}= Pipe internal diameter, inches

R

_{m}= R / 7742

where:

R

_{m}= modified Reynolds number, dimensionless

*Pressure Drop*

P

_{m}= 0.241*f*S

_{g}*Q

^{2}/ D

_{i}

^{5}

where:

P

_{m}= Frictional Pressure Drop, psi / mile

S

_{g}= Liquid Specific Gravity, dimensionless (water = 1.0)

f = friction factor, dimensionless (calculated as below)

Laminar Flow:

f = 0.00207 / R

_{m}

Turbulent Flow:

f = 0.0018 + 0.00662*(1 / R

_{m})

^{0.355}

**Shell-MIT Equation - Pressure Drop in Heavy Crude Oil & Heated Liquid Pipelines (Metric Units)**

R = 353,678*Q / (v*D

_{i})

where:

R = Reynolds no, dimensionless

Q = Flow Rate, m

^{3}/ h

v = Kinematic Viscosity, cSt

D

_{i}= Pipe internal diameter, mm

R

_{m}= R / 7742

where:

R

_{m}= modified Reynolds number, dimensionless

*Pressure Drop*

P

_{m}= 6.2191E10*f*S

_{g}*Q

^{2}/ D

_{i}

^{5}

where:

P

_{m}= Frictional Pressure Drop, kPa / km

S

_{g}= Liquid Specific Gravity, dimensionless (water = 1.0)

f = friction factor, dimensionless (calculated as below)

Laminar Flow:

f = 0.00207 / R

_{m}

Turbulent Flow:

f = 0.0018 + 0.00662*(1 / R

_{m})

^{0.355}

**T R Aude Equation - Pressure Drop in Refined Petroleum Products (Gasoline, Naphtha, Kerosene) Pipelines (6" and 8" line size only) (USC units)**

P

_{m}= (Q*µ

^{0.104}*S

_{g}

^{0.448}/ (0.871*K*D

_{i}

^{2.656}))

^{1.812}

where:

P

_{m}= Pressure drop due to friction, psi / mile

Q = flow rate, bbl / hr

D

_{i}= pipe internal diameter, inches

S

_{g}= Liquid specific gravity, dimensionless

µ = Liquid Viscosity, cP

K = pipe roughness / efficiency factor (usually 0.9 to 0.95)

**T R Aude Equation - Pressure Drop in Refined Petroleum Products (Gasoline, Naphtha, Kerosene) Pipelines (6" & 8" line size only) (Metric units)**

P

_{m}= 8.888E8*(Q*µ

^{0.104}*S

_{g}

^{0.448}/ (0.871*K*D

_{i}

^{2.656}))

^{1.812}

where:

P

_{m}= Pressure drop due to friction, kPa / km

Q = flow rate, m

^{3}/ h

D

_{i}= pipe internal diameter, mm

S

_{g}= Liquid specific gravity, dimensionless

µ = Liquid Viscosity, cP

K = pipe roughness / efficiency factor (usually 0.9 to 0.95)

Reference: Liquid Pipeline Hydraulics by E. Shashi Menon

It is important to note that these equations cannot be generalized for any liquid flow and are specifically meant for the liquids mentioned in the titles of these equations. Also note that the T. R. Aude equation is targeted for 6" & 8" pipelines for white oil products. Apparently these equations were developed for specific products, line sizes and for long distance pipelines and would provide more accurate pressure drop values than the Darcy-Weisbach equation for pipe friction loss. The interpretation behind these equations being more accurate would be based on their being developed based on actual field tests for the mentioned liquids and line sizes. An important thing to note for liquid transmission in long-distance pipelines is that, the liquid density and viscosity is not constant along the entire length of the pipeline. Another aspect of long-distance pipeline transmission of liquids is that, liquids generally considered to be incompressible, are not so over the long transmission distances encountered in pipelines. In fact for pipeline transmission of liquids, liquids are considered to be partially compressible which would explain the development of these empirical equations.

If high accuracy is not a pre-requisite for pressure drop calculations for the mentioned liquids and line sizes then my advice to all would be to use the Darcy-Weisbach equation which should provide conservative pressure drop values.

Hope to get quite a few comments on this blog entry from the readers of my blog.

Regards,

Ankur.

This is useful!