Calculation guidelines for Rotary Dryer.pdf
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The document outlines the design procedure for a rotary dryer used to dry fertilizer from 5% to 1.5% moisture content. The key steps are: 1) Performing mass and heat balance calculations to determine moisture evaporated, dry solid mass, and total heat duty of 4.4 MJ/hr. 2) Sizing the dryer using the heat duty to calculate required air flow of 14.8 kg/hr, diameter of 2.3 m, volumetric heat transfer coefficient of 398 kJ/hr-m3-K, and length of 18 m. 3) Checking that the outlet air humidity is below saturation and selecting design parameters like number of flights based on sol
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Calculation guidelines for Rotary Dryer.pdf
- 1. DESIGN PROCEDURE FOR A ROTARY DRYER:
- 2. ROTARY DRYER DESIGN 1. Heat and mass balance in a rotary dryer 1.1 Mass Balance To calculate the heat duty, a mass balance must be established. General mass balance around the dryer is given in the equation below. (1.1) (1.2) Mass of feed is equivalent to the mass of solids and the moisture it contains. This can be used in calculating the heat balance around the dryer. (1.3) (1.4) 1.2 Heat Duty of dryer Heat transferred in direct-heat rotary dryer is expressed as follows: (1.5) Q is the rate of heat transfer, Ua is the volumetric heat transfer coefficient, V is the dryer volume, and Δt is the true mean difference between the drying air and the material. The heat supplied by the drying air is used for five different operations: a. To heat the dry solid from its inlet temperature to its final temperature. (1.6) b. To heat moisture to vaporization temperature (inlet wet-bulb temperature). (1.7) c. Heat to evaporate moisture. (1.8) d. To heat residual moisture to final temperature. (1.9) e. To superheat the evaporated moisture (1.10) The overall heat transfer to the product is given by the equation. 𝑄 = (1 + 𝛼)( 𝑄1 + 𝑄2 + 𝑄3 + 𝑄4 + 𝑄5) (1.11) Q=UaV(ΔT)lm 𝑄1 = 𝑚𝑠 × 𝐶𝑠 × (𝑇𝑓2 − 𝑇𝑓1) 𝑄2 = 𝑚𝑤 × 𝐶𝑤 × (𝑇𝑤 − 𝑇𝑓1) 𝑄3 = 𝑚𝑒 × λ𝑙𝑣 𝑄4 = 𝑚𝑟𝑤 × 𝐶𝑤 × (𝑇𝑓2 − 𝑇𝑤) 𝑄5 = 𝑚𝑒 × 𝐶𝑣 × (𝑇𝑓2 − 𝑇𝑤) 𝑚𝑓 = 𝑚𝑒 + 𝑚𝑝 𝑚𝑓 (1 − 𝑋1) = 𝑚𝑝 (1 − 𝑋2) 𝑚𝑠 = 𝑚𝑓 (1 − 𝑋1) 𝑚𝑤 = 𝑚𝑓 (𝑋1)
- 3. where 𝛼 is a factor that presents heat loss due to convection and radiation which ranger to 7- 10%. 1.3 Air mass rate The air mass rate required to transfer sufficient heat for the drying is (1.12) Density of air can be estimated using the psychrometric chart or with the equation below (1.13) 1.4 Gas mass velocity Gas mass velocity must be determined before modelling a rotary dryer. Allowable mass velocity, G, of the gas in a direct-contact rotary dryer depends on the dusting characteristic of the material being dried and usually ranges from 2000-25000 kg/m2 h. 1.5 Air humidity The humidity of the exit air must be checked to verify that it does not exceed the maximum vapor the exit air can hold. (1.13) 2. Number of Heat Transfer Unit and Log-Mean Temperature NTU is the ratio of the overall thermal conduction to the smaller heat capacity. It is a combination of overall heat transfer coefficient, transfer area, fluid flow rate, and heat capacity parameters which is combined to form this one-dimensional parameter. This can be used to calculate the wet-bulb temperature if exit gas temperature is given and vice versa. (2.1) Rotary dryers are operated most economically when Nt is between 1.5 to 2.5. Log-mean temperature can be calculated using the equation (2.2) 𝑚𝑎 = 𝑄 𝐶𝑎(𝑇𝑎2 − 𝑇𝑎1) 𝑌2 = 𝑌1 + 𝑚𝑒 𝑚𝑎 Nt=ln(Ta1-Tw/Ta2-Tw) (ΔT)lm= (𝑇𝑎1 − 𝑇𝑤) − (𝑇𝑎2 − 𝑇𝑤) ln(Ta1-Tw/Ta2-Tw) 𝑣ℎ = 22.41𝑇 273.15 × ( 1 28.97 + 𝐻 18.02 )
- 4. 3. Diameter Dryer diameter is a function of the amount of materials that will be subject to drying. The gas mass velocity is also a factor in determining the ideal dryer diameter. (3.1) To calculate the diameter of the dryer (3.2) 4. Overall heat transfer coefficient The volumetric heat-transfer coefficient itself consists of a heat-transfer coefficient Uv based on the effective area of contact between the gas and the solids, and the ratio a of this area to the dryer volume. An empirical equation is to calculate volumetric heat transfer is given as follow: (4.1) Optimum value for the constant k by AICHE ranges from 3.75-5.25 and is dependent on the materials, flight geometry, rotational speed, and dryer holdup. Values for n are suggested by various authors. Friedman and Marshall (1949) 0.16 Aiken and Polsak (1982) 0.37 Miller et al. (1942) 0.60 McCormick (1962) 0.67 Myklestad (1963) 0.80 5. Length of Dryer Dryer length is a function of the calculated values above. It highly affects the residence time of the material and one of the bases of effective dryer. Length is calculated based on the heat transfer coefficient (equation 1.5). (5.1) Volume can be calculated after length is determined. (5.2) 𝐴 = 𝑚𝑎 𝐺 𝑑 = √ 4𝑚𝑎 𝜋𝐺 𝑈𝑎 = 𝑘𝐺𝑛 𝐷 𝐿 = 4𝑄 𝜋𝐷2𝑈𝑎 ∙ (ΔT)lm V=A×L
- 5. 6. Peripheral Speed and Rotational Speed Peripheral Speed P is the distance travelled by a point in a perpendicularly rotating body over a period of time. Peripheral speed ranges from 0.1 – 0.5 m/s. Rotational speed is calculated (6.1) 7. Flights design Flights help to increase the surface area of contact between the material and drying air. Its dimension is based on the percent loading of the solid in the dryer. An ideal solids loading is said to be optimum between 10-15%. With this, the number and height of flights can be calculated using the equations below. (7.1) (7.2) For more accurate design procedure, see flights designing. 8. Residence Time Residence time equation is given by Friedmann and Marshall. The second terms is the drag friction caused by the gas. (8.1) where S is the slope in rad, F is the solids feed rate per minute. B is dependent on particle diameter in microns. 9. Dryer Hold-up volume Hold-up volume is volume occupied by the solids inside the dryer within the residence time. This is important since it can identify if the dryer is underloaded or overloaded. It is also used for load computations. (9.1) (9.2) N=P/πD Fd =D/8 Nf =3D τ= 0.3344𝐿 S𝑁0.9D + 0.608BLG F B=5𝑑𝑝−0.5 %𝐻𝑉 = 𝑉𝑠𝑜𝑙𝑖𝑑𝑠 𝑉𝑑𝑟𝑦𝑒𝑟 𝑉𝑠𝑜𝑙𝑖𝑑𝑠 = 𝐹 × 𝑅 ρb
- 6. Design procedure for rotary dryer
- 7. Case Study: Solids drying at AFC Granulation Plant 1 Step 1: Specification of Duty Fertilizer from a granulator with a temperature of 80 0 C and at a rate of 30000 kg/hr containing moisture of 5% (w.b.) will be dried in a rotary dryer to a final product containing 1.5% moisture. Drying air from the burner is available at 400 0 C and 0.0188 kg/kg dA humidity. Material must not be heated above 130 0 C. Maximum air mass velocity is set at 9000 kg/hr-m2. Step 2: Collection of physical and thermophysical data Data for Process Design Calculation Product Specification: Parameter Data Symbol Unit Feed Rate 30000 F Kg/hr Initial Moisture content wb 5% X1 Kg/kg wb Final Moisture content wb 1.5% X2 Kg/kg wb Inlet Temperature feed 333 Tf1 K Final Temperature feed 370 Tf2 K Product average diameter 4 dp mm Thermophysical Properties: Parameter Data Symbol Unit Specific heat of product 1.188 Cs Kg/hr Specific heat of water 4.18 Cw Kg/kg wb Specific heat of vapor 1.89 Cv Kg/kg wb Specific heat of air 1.048 Ca K Latent heat of vaporization 2300 λl kJ/kg Bulk Density feed 970 ρb Kg/m3 Properties of Air Parameter Data Symbol Unit Gas Mass flow rate 9000 G Kg/hr m2 Atmospheric air temperature 303 Ta K Air humidity 0.0188 Y1 Kg H2O/kg dA Temperature of air after burner 673 Ta1 K
- 8. Step 3: Determination of temperature profiles With the given properties of air, identify wet-bulb temperature using psychrometric chart. Calculate the outlet air temperature using equation 2.1. At 673K and 0.0188 kg/kg dA, wet-bulb temperature is 343 K. Using equation 2.1 with Nt say 2, estimate the outlet air. The outlet air temperature is estimated to be 387 K. Calculate the log mean temperature using equation 2.2. Step 4. Perform Mass balance Step 5: Perform Heat Duty Calculation using equation (1.5-11) Nt=ln(Ta1-Tw/Ta2-Tw) 2=ln(673-343/Ta2-343) Ta2 = 387 (ΔT)lm= (𝑇𝑎1 − 𝑇𝑤) − (𝑇𝑎2 − 𝑇𝑤) ln(Ta1-Tw/Ta2-Tw) (ΔT)lm= (673 − 343) − (387 − 343) ln(673-343/387-343) = 142.669 𝑚𝑓 = 𝑚𝑒 + 𝑚𝑝 𝑚𝑓 (1 − 𝑋1) = 𝑚𝑝 (1 − 𝑋2) 30000 = 𝑚𝑒 + 𝑚𝑝 30000(1 − .05) = 𝑚𝑝 (1 − .015) 𝑚𝑝 = 28934.02 me = 1065.98 𝑄1 = 𝑚𝑠 × 𝐶𝑠 × (𝑇𝑓2 − 𝑇𝑓1) 𝑄2 = 𝑚𝑤 × 𝐶𝑤 × (𝑇𝑤 − 𝑇𝑓1) 𝑄3 = 𝑚𝑒 × λ𝑙𝑣 = 30000 × 0.95 × 1.188 (370 − 333) = 1252746 𝑘𝐽/ℎ𝑟 = 30000 × .05 × 4.184(343 − 333) = 62760 𝑘𝐽/ℎ𝑟 = 1065.98 × 2400 = 2558375.635 𝑘𝐽/ℎ𝑟
- 9. 𝑄 = (1 + 𝛼)( 𝑄1 + 𝑄2 + 𝑄3 + 𝑄4 + 𝑄5) At an allowance of 10% for heat loss 𝑄 = (1 + .1)( 𝑄1 + 𝑄2 + 𝑄3 + 𝑄4 + 𝑄5) 𝑄 = 4414178.044 𝑘𝐽/ℎ𝑟 Step 6: Calculate air requirements Using equation 1.12 Calculate volumetric flow of air using equation 1.13 𝑉 = 𝑚𝑎 ∗ 𝑣ℎ 𝑄4 = 𝑚𝑟𝑤 × 𝐶𝑤 × (𝑇𝑓2 − 𝑇𝑤) 𝑄5 = 𝑚𝑒 × 𝐶𝑣 × (𝑇𝑓2 − 𝑇𝑤) = 28934.02 × .015 × 4.184(370 − 343) = 49029.26 𝑘𝐽/ℎ𝑟 = 1065.98 × 1.89 × (370 − 343) = 89978.24 𝑘𝐽/ℎ𝑟 𝑚𝑎 = 𝑄 𝐶𝑎(𝑇𝑎2 − 𝑇𝑎1) 𝑚𝑎 = 4414178.044 1.048(673 − 387) = 14761.36488 𝑘𝑔/ℎ𝑟 𝑣ℎ = 22.41𝑇 273.15 × ( 1 28.97 + 𝐻 18.02 ) = 22.41 ∗ 673 273.15 × ( 1 28.97 + 0.0188 18.02 ) = 1.9635 𝑚3 𝑘𝑔 𝑑𝐴 𝑌2 = 14761.365 × 1.9635 = 28984.4714 𝑚3 /ℎ𝑟
- 10. Step 7: Calculate outside air humidity Using equation The outlet humidity is below the saturation humidity at outlet air properties. Step 8: Calculate diameter Assuming a Gas Mass Velocity of 3420 kg/hr m2, calculate the diameter using equation Step 9: Calculate volumetric heat transfer coefficient Using equation 4.1, setting k as 4 (optimum range 3.75-5.25) and n as 0.67 as McCormick suggested. Step 10: Dryer Length and Volume Calculation Using equation 5.1, calculate the length of the dryer. Equation 5.2 is used to calculate dryer volume. 𝑌2 = 𝑌1 + 𝑚𝑒 𝑚𝑎 𝑌2 = 0.0188 + 1065.98 14761.36488 = 0.0910 kg H2O/kg dA 𝐴 = 𝑚𝑎 𝐺 𝑑 = √ 4𝑚𝑎 𝜋𝐺 𝐴 = 14761.36488 3420 = 4.316 𝑚2 𝑑 = √ 4 × 14761.36 𝜋 × 3420 = 2.344 𝑚 𝑈𝑎 = 𝑘𝐺𝑛 𝐷 = 4 × 3420.67 2.344 = 397.97𝑘𝐽 ℎ𝑟 − 𝑚3 − 𝐾 = 4 × 4414178.044 𝜋 × 2.3442 × 397.97 ∙ 142.669 = 18.012 𝑚 V=A×L 𝐿 = 4𝑄 𝜋𝐷2𝑈𝑎 ∙ (ΔT)lm = 4.316 × 18.012 = 77.7439 𝑚3
- 11. Step 11: Estimate Number of flights and flight design (See flights design procedure) Step 12: Estimate peripheral speed and Calculate rpm Peripheral speed of dryers is typically between 0.1-0.5 m/s. Say the speed is 0.5 m/s, using equation 6.1, calculate the rotational speed. Step 13: Estimate slope and calculate residence time Most dryers operate at a slope of 1ᵒ-5ᵒ, say for example that this dryer operates at 2ᵒ. General equation for estimating the residence time of a material in a rotary dryer is given by Friedmann and Marshall. Equation 8.1. The drag of the gas in parallel operation pushes the material towards the outlet, thus, the negative sign is used and results in a shorter residence time. Step 14: Calculate hold up volume Using equation 9.2 Holdup volume is calculated using 9.1. N=P/πD =0.5/π*2.344 = 4.07 rpm B=5𝑑𝑝−0.5 τ= 0.3344𝐿 S𝑁0.9D + 0.608BLG F =5*4000−0.5 = 0.07906 = 0.3344 ∗ 18.012 ( 𝜋 180 × 2) 4.070.92.344 - 0.608*0.07906*18.012*28984.4714/60 30000/60 = 19.958 𝑚𝑖𝑛𝑠 𝑉𝑠𝑜𝑙𝑖𝑑𝑠 = 𝐹 × 𝑅 ρb 𝑉𝑠𝑜𝑙𝑖𝑑𝑠 = 30000 × 19.958 × 1/60 970 = 10.28762 𝑚3 %𝐻𝑉 = 𝑉𝑠𝑜𝑙𝑖𝑑𝑠 𝑉𝑑𝑟𝑦𝑒𝑟 %𝐻𝑉 = 10.28762 77.7489 × 100 = 13.23%
- 12. This value is within optimum holding volume value of 10-16%. Thus, design can be considered as appropriate. Step 15: Estimation of Mechanical works Proceed to the calculation of insulation if applicable. Consult mechanical department for motor specifications.