Question

In wastewater treatment, microorganisms are often used to convert dissolved organic compounds to more microorganisms, which are then removed from the flow stream by such processes as thickening. The production of microorganisms in the aeration tank is estimated to be 17,438lb/ day. Hint: mgd= million gallons per day

(a) Calculate the mass flow rate of influent in unit of lbs/day? Take 1 decimal place for solution.
(b) What is the conversion factor for converting mgdmg/L to lbs/day? Take 3decimal places for solution.
(c) Set up the mass balance equation(s) for the system: 1. Mass balance equation for water flow; 2. Mass balance equation for the activated sludge (microorganisms); ( 3 marks) 3. Solve for QE​ and QW​ (take 2 decimal places for your answer).
d) Find the reaction rate constant (k) for the microorganisms, assuming the reaction is firstorder.

Answer 1

The mass flow rate of influent in lbs/day is 145.01 lbs/day. The conversion factor for converting mgd/mg/L to lbs/day is 8,340 lbs/day. The mass balance equations for the system are QE = QW and Production rate = Removal rate.

Step-by-step explanation:

(a) To calculate the mass flow rate of influent in lbs/day, we need to convert the given value in million gallons per day (mgd) to lbs/day. The conversion factor for water is 8.34 lbs/gal. Therefore, the mass flow rate in lbs/day = (17,438 lbs/day) * (1 mgd / 1.0e+6 gal) * (8.34 lbs/gal) = 145.01 lbs/day.

(b) The conversion factor for converting mgd/mg/L to lbs/day is calculated using the formula: conversion factor = (1.0e+6 / 1 day) * (8.34 lbs/gal) = 8,340 lbs/day.

(c) The mass balance equations for the system are:

1. Mass balance equation for water flow: QE = QW, where QE is the effluent flow rate in mgd and QW is the influent flow rate in mgd.
2. Mass balance equation for the activated sludge (microorganisms): Production rate - Removal rate = 0. Therefore, Production rate = Removal rate.

(d) To find the reaction rate constant (k) for the microorganisms, assuming the reaction is first-order, we need more information. The first-order reaction rate equation is ln(Nt/N0) = -kt, where Nt is the concentration of microorganisms at time t, N0 is the initial concentration of microorganisms, k is the reaction rate constant, and t is time. If you can provide more information, we can calculate the value of k.