02-26 & 02-28 - Assume that the rate of which organics...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Assume that the rate of which organics are consumed is directly proportional to their conc. in solution. i.e . What type of kinetics? _____________________ then: where k 1 is a rate constant for the reaction (we've assumed the cell conc., X , remains approximately constant for the test) Note: k 1 depends (among other things) on - type of organics in the waste - type of bacteria used for test - physical and chemical test conditions (pH, temp., etc.) first order 1 k dL L dt Note that this is similar to our empirical model for substrate utilization @ the limiting case where S << K S s dS kXS dt K S so, k 1 = kX/K S
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
To get L as a function of time integrate the rate equation. Use as boundary conditions L = L o @ t = 0 L = L @ time = t separate variables and integrate to get L =   o Lt 1 L0 ln L k t   1 kt o Le 1 o L L e L O t o 1 L o L dt k L dL plot of the result Note that the decay of BOD has the same exponential form as the decay of a radioisotope t L Instantaneous rate of change = Slope = dL/dt = -k 1 L
Background image of page 2
Since the organic concentration is conveniently expressed in units of mg O 2 demand (i.e. mg BOD L ), it is easy to extend the above L L results to describe O 2 consumption. Define: = O 2 consumed at time = t = BOD "exerted" at time = t y i.e., y L y = L O - L = BOD exerted But, 1 kt o L L e 1 o y L (1-e ) so time L L O @ time = 0, BOD exerted = 0
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
plot y vs. time | | | y | | | time This model can (and has) be used to describe the time course of oxygen utilization in a natural stream, a reactor, or a BOD test bottle. 1 kt o y L (1-e ) Note: y = BOD L = L o at time = L L O =BOD L
Background image of page 4
Sources of Confusion : 1. Some texts use k 1 for a base 10 log system i.e. L= L o 10 -k 1 t . We'll stick to base "e" natural log system. i.e. L=L o e -k 1 t for homework and exams. 2. the term BOD is ambiguous, since it refers to the concentration of something remaining (L) as well as the amount of O 2 consumed (y). It is helpful to be careful with nomenclature and to speak in terms of "BOD exerted" = y vs. "BOD concentration" = L [ or just use "L" and "y" to make it clear what you mean] Substrate concentration (expressed in units of O 2 needed to oxidize it).
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Some comments on BOD • Note that BOD L (or L o ) is a Limiting Value for both BOD concentration ( L ), and BOD exerted ( y ). L L e o k t 1 for BOD concentration : At time = 0, L = L o y L e o k t ( ) 1 1 for BOD exerted : At time = , y = L o
Background image of page 6
Temperature effects on BOD kinetics In general, an increase in temperature increases the rate of a reaction. We take care of this by adjusting the rate constant using the following form of the Arrhenius equation: where k 1 is the rate constant in the BOD equation and   1.047 (text value) [other values have been suggested up to = 1.14] 20) (T C) (20 1 (T) 1 θ k k
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
By running a BOD test and sampling at different times, it is possible to determine k 1 for laboratory conditions and the waste of interest.
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/13/2010 for the course CEE 3510 taught by Professor Lion during the Spring '10 term at Cornell University (Engineering School).

Page1 / 28

02-26 & 02-28 - Assume that the rate of which organics...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online