Ottawa’s anaerobic digester produces 13 m^3/day of sludge with a suspended solids concentration of 7.8%. What volume of sludge must they dispose of
each year if their sand drying beds yield a solids concentration of 35%.
To find the volume of sludge that Ottawa must dispose of each year, we need to first calculate the annual production of sludge.
Given:
- Daily sludge production = 13 m^3/day
- Suspended solids concentration of the sludge = 7.8%
Step 1: Calculate the total sludge production per year.
Since we know the daily sludge production, we can multiply it by the number of days in a year.
Total sludge production per year = Daily sludge production * Number of days in a year
Number of days in a year = 365
Daily sludge production = 13 m^3/day
Total sludge production per year = 13 m^3/day * 365 days/year
Total sludge production per year = 4745 m^3/year
Step 2: Calculate the volume of sludge at a solids concentration of 35%.
We need to find the final volume of sludge after it is dried on the sand drying beds and reaches a solids concentration of 35%.
To calculate this volume, we use the equation:
Volume of sludge at 35% solids concentration = Total sludge production per year * (100 / % solids concentration)
Total sludge production per year = 4745 m^3/year
% solids concentration = 35%
Volume of sludge at 35% solids concentration = 4745 m^3/year * (100 / 35)
Volume of sludge at 35% solids concentration = 13585.71 m^3/year
Therefore, Ottawa must dispose of approximately 13,585.71 m3 of sludge each year.
To find the volume of sludge that needs to be disposed of each year, we need to calculate the total mass of the sludge produced and then divide it by the final solids concentration.
1. Calculate the daily mass of sludge produced:
Sludge_production = 13 m^3/day
2. Calculate the mass of suspended solids in the sludge:
Mass_suspended_solids = Sludge_production * Suspended_solids_concentration
Mass_suspended_solids = 13 m^3/day * 7.8% = 1.014 kg/day
3. Calculate the daily volume of sludge required to achieve a solids concentration of 35%:
Desired_solids_concentration = 35%
Mass_sludge = Mass_suspended_solids / (Desired_solids_concentration / 100)
Mass_sludge = 1.014 kg/day / (35% / 100) = 2.897 kg/day
4. Calculate the annual volume of sludge required:
Volume_sludge = Mass_sludge / Desired_solids_concentration
Since we know that volume = mass / concentration, we can rearrange the equation to solve for the volume:
Volume_sludge = Mass_sludge / Desired_solids_concentration
Volume_sludge = 2.897 kg/day / (35% / 100) = 8.277 m^3/day
5. Finally, calculate the annual volume of sludge required:
Annual_volume_sludge = Volume_sludge * 365 days/year
Annual_volume_sludge = 8.277 m^3/day * 365 days/year = 3019.805 m^3/year
Therefore, Ottawa's anaerobic digester needs to dispose of approximately 3019.805 m^3 of sludge each year.