Construct and detail fully worked design sheet exercises for the following set of problems.

Course Title: Air Pollution Control Technologies      

Coursework 1: Individual Design Calculation Assessment Sheet

Please read the following carefully for things to take note of!!!

Construct and detail fully worked design sheet exercises for the following set of problems. As part of your answers, detail any assumptions made, catalogue the data given, and the full detail of the workings conducted to derive further data required for your calculations. Be careful to make full reference to extracted data from design book tables and graphs used. Reference all bibliographical/lecture notes slides or published data tables employed as part of your answer. Be careful to state the SI units of each quantity used in your calculation.

Where spreadsheets have been used to obtain an optimal design solution, detail the various stages of your iterative solution method in full.

Particle Sizing

The following data were obtained from a cascade impactor:

Size Range, [mm]	0-4	4-8	8-16	16-30	30-50	>50
Mass, [mg]	30	125	95	65	20	5

Is the distribution log-normal? If so, estimate d₅₀ and σ_g. [12 marks]

Consider an ESP that has the following theoretical efficiency versus particle size relationship:

Calculate the overall efficiency of this ESP for the particle distribution in question 1. [12 marks]

A gas stream with a particulate loading of 50.0 g/m³ passes through a 65%-efficient cyclone followed by a 96%-efficient ESP. Calculate the overall efficiency of the system. [8 marks]

Cyclone Design

The size distribution of a particle-laden gas stream is given below. Calculate the overall collection efficiency of a High Efficiency Lapple Cyclone with a body diameter of 1.2 metre. The volumetric flow rate of the carrier gas is 150 m³/min at 350K and 1 atm. The mass density of the particulates is 1,600 kg/m³.

Particle Size	Mass
Range, (mm)	%
0-2	1.0
2-4	9.0
4-6	10.0
6-10	30.0
10-18	30.0
18-30	14.0
30-50	5.0
50-100	1.0

Assume that a scroll modification to the inlet increases N_e to 9 turns, what will happen to the overall collection efficiency? [26 marks]

Calculate the pressure drop for the cyclone of Problem 4 assuming K=16. [8 marks]

Design a Lapple standard cyclone to function as a pre-cleaner for the particle size distribution below. The carrier gas is dry air is at 65.6 °C and 1 atm, and is flowing at 0.5664 m³/min. The cyclone need only be 65-75% efficient. Specify your final choice of body diameter and the corresponding efficiency. The mass density of the particulates is 1,200 kg/m³

Particle Size Range, (mm)	Mass percent in Size Range
0-2	4.0
2-6	16.0
6-12	20.0
12-20	20.0
20-40	20.0
40-80	18.0
>80	2.0

As part of your answer show in detail the iterative series of calculations employed to derive your answer. (Show at least 2 iterations with justification leading to the next) [50 marks] 

Estimate the annual electricity cost to run a fan to push 800 m³/min of air through a device that has a pressure drop of 3,570 Pa. Assume a fan/motor efficiency of 0.65. Electricity costs $ 0.28/kWh, and the fan runs 7,800 hours per year. [8 marks]

ESP Design

A 98% efficient ESP follows the Deutsch equation. If the gas flow rate changes and the efficiency drop to 94%, calculate the ratio of the new gas flow rate to the old gas flow rate. [12 marks]

Provide a reasonable design for a 99.3 % efficient ESP treating 30,000 m³/min of gas. The fly ash has a resistivity of 7.1 X 10¹⁰ ohm-cm.

Specify the following:

(a) total plate area,

(b) channel width,

(c) number and size of plates,

(d) number of electrical sections (total and in the direction of flow),

(e) and total corona power to be supplied.

Then, estimate the overall dimensions. [34 marks]

A coal burning power plant is required to remove fly ash from its stack gases. The treatment method should achieve a total efficiency of 99.5% for a total flow rate of 33,980 m³/min of gas. The suggested design is as follows:

Use a multi-cyclone pre-cleaner with an 85% collection efficiency and a pressure drop of 750 Pa, followed by an ESP with a pressure drop of 50 Pa. Because the cyclone will remove most of the larger particles, assume an effective drift velocity of 0.09144 m/s for this ESP.

Determine:

(a) Collection area of the ESP (assume the Deutsch equation is applicable)

(b) Total capital cost (TIC) in 1988 dollars

(c) Total power consumption (Fan + Corona power)

(d) Total annual power costs (assume 7800 hours of operation per year)

(e) Annual operating costs (include only power costs and depreciation; exclude labour, taxes, and all other costs)

Assume the following cost data:

Installed cyclone costs = $10.59/m³/min(1988 dollars)

Electrical costs = $0.06/kWh

Fan efficiency = 60%

Depreciation of capital investment = 15 years straight line method [32 marks]

Fabric Filter Design

1. From the following test data, estimate the values of K_S and K_e for the filter drag model.

                                        Limestone Dust Loading   1.00 g/m³

                                        Fabric Area                   1.00 m²

                                        Air Flow Rate                 0.80 m³/min

Time, min	5	10	15	20	25	30
Filter,DP, Pa	330	490	550	600	640	700

Give your answers in units of N-min/kg-m and (Pa-min)/m, respectively.

[Hint: Perform and evaluate a five-point linear regression] [18 marks]

12. Using the data of Problem 11, design a shaker bag house to filter 4,000 m³/min of air that contains 1.50 g/m³ of limestone dust.  Assume that the cleaning time for one compartment is 3.0 minutes and that the available DP is 2,000 Pa.  In your design, specify the filtering velocity, the number of compartments, the cloth area per compartment, and the filtration time t_f. [30 marks]

13. A pulse-jet bag house is desired for a finished cement plant.  Calculate the number of bags required to filter 8000 m³/min of air with a dust loading of 3.0 g/m³.  Each bag is 3.0 m long with a 0.3-m diameter.  If the average pressure drop is 1.0 kPa and the main fan is 60% efficient, calculate the fan power in kW. If the pulse air volumetric flow rate is 0.5% of the filter airflow rate and the pulse air pressure is 6.0 atm, calculate the power drawn by a 50% efficient compressor (in kW). [20 marks]