GPS-X Technical Reference

19 Modelling Fundamentals
The process of dynamic modelling of facilities involves the solution of thousands
of coupled nonlinear ordinary differential equations. The formulation and
solution of this type of problem is facilitated through the use of Continuous
Simulation Languages (CSL). CSLs date back to the late 1960s when IBM
introduced the language called CSMP (Continuous System Modelling Program).
Of the number of very specialized simulation languages that are available, GPS-
X uses ACSL for conducting simulations.
BENEFITS OF MATHEMATICAL MODELLING
Mathematical models assist in developing a thorough understanding of the behaviour of a system
and in evaluating various system operating strategies. A proposed system can be evaluated
without building it. A costly or unsafe system can be experimented with by using a model rather
than disturbing the real system.
Why COD is Important to Know
One of the most important ways to check the operation of a wastewater treatment plant,
the consistency of the analytical procedures and the integrity of the mathematical model
is to perform mass balances around the system for the different compounds. This task is
not always simple as components transform into other substances, bacterial cells grow,
respire and decay.
With regard to the organic substances, a commonly measurable parameter is the
Chemical Oxygen Demand (COD). We could measure organic carbon as Total Organic
Carbon (TOC) in the plant, but we would miss the fraction which was removed in the
form of CO 2 gas after oxidation. It is difficult to determine the oxygen requirement based
on TOC, as different substances require different amounts of oxygen depending on their
chemical composition. The influent wastewater is truly a non-homogenous mixture in this
respect.
We could measure the 5-day Biochemical Oxygen Demand (BOD 5) and suspended solids
as most plants in North America do. Suspended solids have the same problem as TOC
with respect to oxidation. BOD 5 seems to give relevant information, but it is
inappropriate for continuous monitoring, and the accuracy of the results is not
comparable to other analytical methods. BOD 5 measures only the part of organics which
were used for respiration in the BOD test during 5 days, and does not give information
about the amount converted into bacterial cells. Ultimate BOD (BOD u) corrects this
problem but the analytical time and sometimes the accuracy is unacceptable. The BOD
test completely ignores a very important fraction of the influent wastewater (inert
particulates), which contributes in a major way to excess sludge production.
GPS-X Technical Reference