analysis of a pilot-scale anaerobic baffled reactor treating domestic ...

introduction to characterisation of reactor hydrodynamics and how reactor hydrodynamics impact on
anaerobic digestion processes.
2.3.1 Theory of flow modelling
A flow model of a reactor requires an appreciation of the flow patterns within the reactor; it is
relatively easy to develop a flow model for a reactor design that may be approximated by mixed flow
or plug flow when there is a single fluid phase present. Analytical solutions for a number of cases are
readily available in the literature (Levenspiel, 1999 pp. 90-119). However in many cases, certainly in
the case of multi-stage digesters, flow patterns can deviate widely from these ideal flow patterns due
to channelling of fluid, recycling of fluid, existence of stagnant regions in the reactor, or the presence
of a different phase (Levenspiel, 1999 pp. 257-277).
Although the advent of computational fluid dynamics software and ever-increasing computing speed
and power allows for the generation of complete velocity maps for complex reactor analysis problems
(given sufficient experimental data), it is often only necessary to know how long individual molecules
stay within the reactor, i.e. the distribution of residence times of defined sub-divisions of the flowing
fluid. This approach to incorporating the effects of flow on reactor dynamics is called residence time
distribution modelling. This information can be obtained using a stimulus-response experiment
(Levenspiel, 1999).
2.3.1.1 Residence time distribution modelling
In a continuous reactor operated at (or approaching) steady state with non-ideal flow properties, the
flow patterns cannot be satisfactorily described with either a completely mixed tank reactor or plug
flow reactor model. The degree of deviation from an ideal model of flow can be determined by
applying a disturbance to the input into the system, and measuring the response in the output of the
system. A common method is to apply a tracer to the reactor feed in either a pulse signal or a step
input signal. Levenspiel (1999) recommended that any material that can be detected and which does
not disturb the normal flow pattern in the reactor can be used as a tracer. By measuring the
concentration of tracer that appears in the outflow over time, Cout, it is possible to calculate the exit age
distribution Et to be equal to the normalised exit concentration curve:
E
t
= C
t
=
t
∫0 ∞
∫
0
C
C
out
out
dt
dt
26
Eq. 2-12
If the tracer used can be assumed to have the same exit age distribution, or residence time distribution
(RTD) as other liquid or dissolved components, then the form of Et calculated above applies equally to
liquid and dissolved species. Thus residence time distribution of the tracer pulse in the reactor system
provides information on residence time distribution of other liquid or soluble components in the
system.
In a non-ideal reactor with a homogenous (single phase) conversion process (substrate product), it
is possible to predict the yield of an isothermal process from batch kinetic data and knowledge of the
residence time distribution. For a first order reaction, the prediction is unique, i.e. a single solution will
emerge irrespective of the flow patterns within the reactor that result in the observed RTD
(Danckwerts, 1953). For other orders of reaction kinetics, bounds on the extent of conversion may be
calculated by considering the cases of maximum mixedness (i.e. a continuous stirred tank reactor,
CSTR) and maximum segregation (i.e. a plug flow reactor, PFR) (Zwietering, 1959). This is due to the