4 Component Model Calculator

Inputs

Fractions of components that make up the slurry. The sum of the fractions must equal 1

"Carrier Fluid" (Xf) Xf Fraction (Xf)

"Pseudo-homogeneous" (Xp) Xp Fraction (Xp)

"Heterogeneous" (Xh) Xh Fraction (Xh)

"Stratified" (Xs) Xs Fraction (Xs)

d50 for Xh Fraction

V_sm,h m/s

V_sm,s m/s

V_t m/s

Where:
- V_sm,h : Max. stationary deposition velocity for Xh particles.
- V_sm,s : Max. stationary deposition velocity for Xs particles.
- V_t : Particle terminal settling velocity for Xh particles.

Internal Diameter (Di) Int. Diameter (Di)

Flow Rate (Q) Flow Rate (Q)

Darcy Friction Factor (f) Darcy f Factor (f)

Liquid SG (SG_L) Liquid SG (SG_L)

Solids SG (SG_S) Solids SG (SG_S)

Volume Concentration (Cv) Vol. Concent. (Cv) %

Dynamic viscosities (Use same units for both values)

DV Carrier Fluid (μf)

DV Water (μw)

Results

Head Loss per meter of pipe (m water/m pipe) for each fraction.

Head Loss Xf - mWater/m

Head Loss Xp - mWater/m

Head Loss Xh - mWater/m

Head Loss Xs - mWater/m

Total Head Loss - mWater/m

Total Head Loss - mSlurry/m

About

What is the 4 Component Model (4CM)?

The 4CM allows the user to precisily estimate friction losses in pipelines transporting slurries. The model was first introduced in the 3rd edition of the book "Slurry Transport Using Centrifugal Pumps" by K. C. Wilson, G. R. Addie, A. Sellgren and R. Clift, and has since gone through extensive validation and revisions.

How does the model work?

The model subdivides the slurry into four basic components, each based on their particle size. Then, the friction losses are calculated for each component using the most appropriate model for their corresponding particle size. Once all values have been computed, they are unified into one final friction loss for the entire slurry, using a weighted average.

Can the 4CM be applied to any slurries?

This model was developed for use with slurries of any grading profile, from broad to narrow to bimodal.
Please keep in mind that this model is only valid for flow velocities above the LDV. You can read more about the LDV and find our calculators in the following article: LINK TO ARTICLE