Design method for dense phase pneumatic conveying lines
Scale-up calculation from pilot tests
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| Section summary |
|---|
| 1. Method and limitations |
| 2. Calculation procedure of dense phase conveying system from pilot plant results |
| 3. Example of design of dense phase conveying system |
| 4. The Konrad method |
| 5. Dense phase Excel calculation tool (scale up) |
| 6. Published methods for dense phase pneumatic conveying design - Dense phase pressure drop calculation |
1. Method and limitations
How to design and size a dense phase pneumatic transport line ?
There are few existing methods published to calculate dense phase pneumatic conveying systems but most of the knowledge here stays with specialized suppliers. Anyway, if dilute phase pneumatic conveying lines can be sized pretty confidently thanks to models, it is less true for dense phase conveying, thus pilot plant tests are almost every time conducted in order to design a new installation and to control / adjust model results.
Figure 1 : Typical dense phase conveying system
The calculations below are showing how to scale up - or scale down in some cases - the pilot plant results in order to design an industrial line, it focuses especially on the parameters to be kept constant.
2. Calculation procedure : dense phase conveying design from
pilot plant results
In order to have meaningful test results, the following must be ensured :
- The test line's pipe has a similar length, but most importantly a similar number of bends as the industrial line
- The solids load ratio is similar to what is planned for the industrial line
- The pick-up speed and end of line speed are determined and kept equal for both test line and industrial line
Solids load and air velocity are thus the constant for the scale up. The pipe diameter and the air volumetric flow thus need to be adjusted in consequence.
From there, the pressure observed during the tests should be the same industrially if the constant above are respected, thus industrial pipe diameter and the industrial air flow rate can be calculated the following way :
Pipe Diameter
The mass flow by unit of pipe cross sectional area is kept constant :
mpindus/Sindus =
mppilot/Spilot
The air flow can then be calculated by
Qair_indus_N = Sindus * upick-up * ρ / ρN in Nm3/h
With :
mpindus = mass flow of the
product SCALED UP in kg/h
mppilot = mass flow of the product OBSERVED in pilot
plant in kg/h
Sindus = pipe section SCALED up in m2
Spilot = pipe section USED in pilot plant in m2
D = diameter of the pipe SCALED up in m
d = diameter of the pipe USED in pilot plant in m
Qair_indus_N = air flow SCALED up in Nm3/h
upick_up = air velocity
at beginning of pipe OBSERVED in pilot plant, parameter kept
constant for scale up
ρ = specific weight of air a the beginning of the conveying pipe,
from pressure OBSERVED in the pilot plant and ASSUMED constant in
the industrial scale, in kg/m3
ρN = specific weight of air at normal conditions in kg/m3
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3. Example of calculation to design a dense phase conveying
system
Example of sizing of dense phase conveying line from pilot plant results
A trial is organized to design an industrial dense phase pneumatic conveying line for a material that is sensitive to breakage. The industrial line must be able to convey 8 t/h, the pipe layout is 50 m including 15 m vertical and has 5 bends.
The design needs to know the following :
| Industrial line |
|---|
| Diameter D = ? |
| Solids load ratio %τ = ? |
| Air flow = ? |
| Upickup =
? Uend = ? |
| Conveying pressure =
? |
A pilot plant test is carried out on a line featuring a diameter 60 mm. The layout is 50 m, with only 5 m elevation but 5 bends. The tests confirm the possibility to convey dense phase the materials. The tests results are given below :
| Pilot Plant results |
|---|
| Product conveying rate = 2000 kg/h |
| Conveying pressure =
1.2 bar g, temperature = 20c |
| Air flowrate = 67 Nm3/h |
The following calculation can then be performed :
- Qair = 67*1/2.2 = 30.5 m3/h
- Upickup = 30.5/(π*0.062/4) / 3600 = 3 m/s
- mair = 67*1.2 = 80 kg/h
- τ = 2000/80 = 25
The air conveying velocity is conserved in between the pilot test and the industrial installation, thus the air flow can be calculated :
Qair = Upickup * Sindus = 3 * π * D2 /4 = 122 m3/h at 1.2 bar g
This gives 267 Nm3/h
In summary
| Pilot Plant test results | Industrial line design |
|---|---|
| Pneumatic conveying line capacity = 2000 kg/h | Pneumatic conveying line capacity = 8000 kg/h |
| d = 60 mm | D = 120 mm |
| Upickup = 3 m/s Uend = 6 m/s |
Upickup = 3 m/s Uend = 6 m/s |
| Pressure = 1.2 bar g | Pressure = 1.2 bar g |
| Solids load ratio = 25 | Solids load ratio = 25 |
| Air flow = 67 Nm3/h | Air flow = 267 Nm3/h |
| Layout = 50 m incl 5 m vertical and 5 bends | Layout = 50 m inlc 15 m vertical and 5 bends |
Note that the industrial line having a higher elevation than the test plant, the designer should consider an additional pressure generated by the column of product to lift and adjust the calculation - not detailed here.
Calculator 1: David Mills Dense Phase Scale-Up Sizer
FOR EDUCATIONAL PURPOSES ONLY — NO WARRANTY — ALWAYS CONSULT A REPUTABLE SUPPLIER1. Pilot Plant Baseline Data
2. Target Industrial Requirements
3. Pilot Intermediate Parameters
| Actual Pilot Air Flow (Q_actual): | - m³/h |
| Inlet Pick-up Velocity (u_pickup): | - m/s |
| Solids Loading Ratio (Φ / τ): | - kg/kg |
4. Industrial Sizing Outputs
- mm
equivalent to - inches (Nearest Nominal Bore)
| Required Industrial Air Flow (Q_air_indus): | - Nm³/h |
| Anticipated Operating Pressure: | - bar g |
| Preserved Solids Loading Ratio: | - kg/kg |
4. The Konrad Method: Step-by-Step Sizing & Calculation Example
The Konrad horizontal slug flow model is an analytical force-balance model that describes the pressure drop across moving plugs of cohesive-less bulk solids [1]. It evaluates the shear force required to slide the material along the pipe wall against both dynamic wall stress transmission and the static weight of the moving bed [1, 2].
Step-by-Step Sizing Procedure:
- Step 1: Calculate Active Slug Length ($L_{slugs}$): Multiply the total pipe length ($L$) by the fraction of the pipe occupied by active moving slugs ($r$): $$L_{slugs} = L \times r$$
- Step 2: Calculate Dynamic Wall Friction Gradient ($\text{Grad}_{wall}$): Compute the pressure drop gradient (Pa/m) resisting the dynamic wall shear using particle stress transmission ($K_w$), internal voidage ($\phi$), slug velocity ($v_p$), and wall-particle friction ($\mu_w$): $$\text{Grad}_{wall} = 2.168 \cdot \mu_w \cdot \rho_b \cdot K_w \cdot \frac{\sqrt{g}}{\sqrt{D}} \cdot v_p \cdot \frac{1 - 2\phi}{1 - \phi}$$
- Step 3: Calculate Static Weight Friction Gradient ($\text{Grad}_{weight}$): Compute the sliding friction gradient (Pa/m) resisting the gravity weight of the horizontal bed: $$\text{Grad}_{weight} = 2 \cdot \mu_w \cdot \rho_b \cdot g$$
- Step 4: Sum the Gradients: Obtain the total pressure drop gradient per meter of active slug: $$\text{Grad}_{total} = \text{Grad}_{wall} + \text{Grad}_{weight}$$
- Step 5: Calculate Total Pressure Drop ($\Delta P_{slugs}$): Multiply the total gradient by the active slug length: $$\Delta P_{slugs} = \text{Grad}_{total} \times L_{slugs}$$
Numerical Sizing Example:
An engineer is sizing a dense phase horizontal line conveying a standard bulk solid with the following parameters:
- Loose Bulk Density ($\rho_b$): $800\text{ kg/m}^3$
- Internal Pipe Diameter ($D$): $100\text{ mm} \rightarrow 0.1\text{ m}$
- Mean Slug Velocity ($v_p$): $1.5\text{ m/s}$
- Wall-Particle Friction ($\mu_w$): $0.40$
- Stress Transmission Ratio ($K_w$): $0.45$
- Slug Internal Porosity ($\phi$): $0.40$
- Total Line Length ($L$): $50\text{ m}$
- Active Slug Fraction ($r$): $0.40$ ($40\%$)
Calculation Results:
- 1. Active Slug Length: $$L_{slugs} = 50\text{ m} \times 0.40 = \mathbf{20.0\text{ m}}$$
- 2. Dynamic Wall Friction: $$\text{Grad}_{wall} = 2.168 \times 0.40 \times 800 \times 0.45 \times \frac{\sqrt{9.81}}{\sqrt{0.1}} \times 1.5 \times \frac{1 - 0.80}{1 - 0.40} = \mathbf{1,546.1\text{ Pa/m}}$$
- 3. Static Weight Friction: $$\text{Grad}_{weight} = 2 \times 0.40 \times 800 \times 9.81 = \mathbf{6,278.4\text{ Pa/m}}$$
- 4. Total Sizing Gradient: $$\text{Grad}_{total} = 1,546.1 + 6,278.4 = \mathbf{7,824.5\text{ Pa/m}} \text{ (or } \mathbf{78.2\text{ mbar/m}})$$
- 5. Total Projected Line Friction Drop: $$\Delta P_{slugs} = 7,824.5\text{ Pa/m} \times 20\text{ m} = \mathbf{156,490\text{ Pa}} \text{ (or } \mathbf{1.565\text{ bar}})$$
Source & Reference:
Konrad, K. (1980). Dense Phase Pneumatic Conveying of
Cohesive-less Solids in Horizontal Pipes (Ph.D. Thesis).
University of Cambridge, UK.
Calculator 2: Konrad Analytical Horizontal Slug Flow Sizer
FOR EDUCATIONAL PURPOSES ONLY — NO WARRANTY — ALWAYS CONSULT A REPUTABLE SYSTEM SUPPLIER1. Physical Slug Properties
2. Pressure Gradient Sizing
| Estimated Active Slug Length (L_slugs): | - m |
| Single Slug Pressure Gradient: | - Pa/m (- mbar/m) |
3. Sizing Gravity/Friction Loss Output
- Pa
equivalent to - mbar (- bar)
5. Dense phase Excel calculation tool (scale up)
Please access here the Free Excel calculator for dense phase scale up calculation : calculator download (click here)
As mentionned above, dense phase conveying is always a delicate conveying process and a design should always be done with a recognized company, the procedure above being only for awareness, to have a rough idea of the scale up, and not detail design.
This scale-up procedure can also be used in dilute phase.
Download Dense Phase Scale-up Excel Sizing Spreadsheet
Get the professional scale-up calculation template offline. Verify industrial pipe diameters, air volume flow rates, and preserve velocity constants from pilot plant trial results.
6. Published methods for dense phase pneumatic conveying design - Dense phase pressure drop calculation
Design calculation methods for dense phase conveying, which comes back to calculating the pressure drop of a dense phase pneumatic conveying system given a pipe layout, materials properties and flowrate, is usually not detailed in bulk solids handling books, with few exceptions, at least from what the author of this website could read. It is therefore particularly difficult for Engineers outside of specialized companies producing those system, to perform even some rough designs of dense phase pneumatic conveying systems. This paragraph attempts to perform a literature review of the published method or research for dense phase pneumatic conveying that may interest Engineers working on this field :
| Author | Book, article title or thesis | Year | Description |
| Sprouse and Schuman | Dense-Phase Feeding of Pulverized Coal in Uniform Plug Flow (AICHE Journal) | 1983 | Specifically for dense phase continuous flow (piston flow) |
| Luis Sancheza, Nestor A. Vasqueza, George E. Klinzing, Shrikant Dhodapkarb |
Evaluation of models and correlations for pressure drop
estimation in dense phase pneumatic conveying and an experimental analysis (Powder Technology) |
2005 | Review several models, the Mi model is the one most in accordance with the set of data |
| Bo Mi | B. Mi, Low-velocity pneumatic transportation of bulk solids | 1994 | Proposes a model for horizontal dense phase conveying |
| Geldart and Ling | Dense Phase Conveying of Fine Coal at High Total Pressures (Powder Technology) | 1990 | Model for dense phase conveying |
| G.E. Klinzing, F. Rizk, R. Marcus, L.S. Leung | Pneumatic Conveying of Solids: A theoretical and practical approach (Springer) | 2010 | Parts of the book are touching the dense phase pneumatic conveying of solids |
| Mills | Pneumatic Conveying Design Guide (Butterworths) page 421 | 2013 | Mills is applying the Universal Conveying method to dense phase conveying, these are relatively high capacity and pressure though |
Frequently Asked Questions (FAQ)
What is the scale-up method in dense phase pneumatic conveying?
The scale-up method is an empirical design procedure that uses trial results from a small-scale pilot plant to size a full-scale industrial conveying line. Because purely analytical formulas suffer from massive errors in non-homogeneous dense phase flows, system designers run short tests to establish baseline flowrates and pressures [Calculation_Dense_Phase.html]. These parameters are then scaled proportionally to the industrial pipe cross-sectional area while keeping conveying velocities and solids loading ratios constant [Calculation_Dense_Phase.html].
What is Konrad's horizontal slug flow model?
Konrad's model is a fundamental force-balance model that calculates the friction pressure drop gradient of low-velocity, cohesive-less plug/slug flows in horizontal pipes. The equation relates the pressure drop per meter of active slug ($\Delta P / L_{slug}$) to wall-particle friction, bulk density, stress transmission coefficients, voidage, pipe diameter, and mean slug velocity [Calculation_Dense_Phase.html]. It is mathematically expressed as: $\Delta P / L_{slug} = 2.168 \cdot \mu_w \cdot \rho_b \cdot K_w \cdot (\sqrt{g}/\sqrt{D}) \cdot v_p \cdot ((1 - 2\phi) / (1 - \phi)) + 2 \cdot \mu_w \cdot \rho_b \cdot g$.
How does pipeline length affect dense phase pressure drop?
In dense phase conveying, pressure drop scales linearly with straight pipeline length as more moving slugs are actively dragged along the pipe wall. Under David Mills' scale-up guidelines, if the solids loading ratio is kept constant, the solids pressure drop component must be adjusted proportionally by multiplying the test loop's solids pressure drop by the length ratio ($L_{industrial} / L_{test}$).