18.10.11 I am only updating the published papers section of this web-page. I don't have time to update the content!
Work in this area is concentrating on the following areas
We are investigating the yield and productivity of reactions occurring in a reactor system that consists of a cascade of two well-stirred reactors arranged in series.
There has been extensive research aimed at improving product yields in chemical reactors. Many studies, both experimental and theoretical, have shown that periodic forcing is an appropriate engineering tool to improve the conversion or selectivity of a desired product (Silveston et al 1995; Stankiewicz & Kuczynski 1995). However, the additional complications and costs associated with implementing external periodic operation have limited the uptake of this technique within industry (Silveston et al 1995; Stankiewicz & Kuczynski 1995).
The possibility of combining the advantages of periodic operation with the benefits of using two reactors arranged in series through the use of `natural oscillations' has been investigated in [ Yang & Su 1993; Chen et al 1995; Ray 1995; Balakrishnan & Yang 1998 Jianqiang & Ray 2000]. By `natural oscillations' it is meant that the process parameters are chosen so that a steady input of reactants into the first reactor generates self-sustained oscillations in its output. This output then forces the second reactor.
The attraction of this method is that no external energy is required to generate the oscillations. Improvements in reactor performance are therefore achieved without the additional costs associated with external periodic forcing. Consequently, this approach harnesses the advantages of periodic forcing without the expense of implementing such perturbations.
Using this approach, significant increases in product yields for various biochemical processes have been shown to be theoretically possible (Ray 1995; Yang & Su 1993; Balakrishnan & Yang 1998) These results were obtained through extensive computations: the governing equations were integrated for numerous values of the process parameters to find the values giving the best reactor performance. This approach is time consuming. More importantly, regions of parameter space may easily be missed. Balakrishnan & Yang (1998) found that such an omission occurred in the work reported by Yang & Su (1993), despite the simplicity of the system investigated. As the system complexity increases (through more detailed chemistry and/or systems with more than two reactors) the likelihood of similar omissions increases when investigations relies upon direct integration. Hence there is a need for a more efficient and systematic approach to investigating these systems.
Our approach is to use techniques from nonlinear dynamical systems theory, in particular bifurcation analysis and singularity theory, to obtain practical insights into this novel operational strategy. For instance, it is important to identify the regions of parameter space in which natural oscillations occur. On a bifurcation diagram the regions in which a steady input of reactants into reactor 1 may produce a periodic input of reactants into reactor 2 are defined by parameter values that represent degenerate Hopf bifurcations. Within these regions the values of the primary bifurcation parameter over which periodic behaviour occurs are defined by Hopf and/or double-zero bifurcation points. As noted by Balakrishnan & Yang (1998) the optimal yield may not be associated with a limit-cycle, but rather may occur at a stable steady-state. Thus it is important to investigate both the dynamic and static multiplicity of the reactor model.
Previous researchers have compared the performance of a two-reactor system against a single reactor with the same total residence time. Using such a comparison Yang and Su (1993) concluded that "the performance of two-CSTB-in-series system is always better than that of one CSTR of equal dilution rate" . Similarly, Balakrishnan and Yang (1998) "speculate that the performance of a two-chemostat-in-series system may in general be better than a single chemostat system with the same total residence time". We have shown that the performance of a two-reactor cascade should not be gauged by comparing it to the performance of a single reactor having the same residence time; comparisons using this criterion can give grossly misleading results [Sidhu & Nelson 2005]. Our analysis shows that before maximising the performance of a cascade, we must first consider the performance of a single reactor system as a benchmark.
For instance, for one particular biochemical system the total residence time of the cascade was set at 7.5 (in dimensionless units). The performance of a single reactor with a residence time of 7.5 was found to be 35.88 (in dimensionless units). (The performance was defined to be the concentration of microorganisms leaving the system). The performance of a cascade with equal residence times in each reactor was 67.34, an improvement of 88% over the single reactor. As the residence time in the first reactor was varied the maximum system performance was found to be 542.12, an improvement of 1420% over the single reactor, which happened when the residence time in the first and second reactors was 1.1 and 6.4 respectively. However, the best performance of a single reactor occurs when the residence time is 1.10 and is 535.04. This is only marginally smaller than the optimal performance of the cascade but significantly occurs at a much lower residence time; recall that we are comparing against a cascade with a total residence time of 7.5.
If we regard the flowrate into the single and cascade reactors as being the same, then the total volume of a cascade system with a total residence time of 7.5 is 7.5/1.1 (\approx 6.8) times larger than a single-reactor system with a residence time of 1.1. Thus a 6.8 fold increase in reactor volume has improved the reactor performance by only 1.9%. It may be that, in practice, an increase in the system performance of 1.9% merits a 6.8 fold increase in the total volume. But on our comparison, the improvement should be 1.9% not 1420%.
In view of these results we suggest that the performance of a cascade should be compared against the optimal performance of a single reactor having a residence time no greater than that of the cascade. Using this approach we have shown that there are parameter regimes in which the performance of an optimally designed cascade is not superior to that achieved in a single reactor.
We have also investigated the performance improvement in a cascade of two non-isothermal CSTRs [Sidhu et al 2007]. It has been assumed that in a suitable designed cascade natural oscillations generated in the first reactor will improve the yield leaving the second reactor. In this study we showed that in some circumstances the maximum yield is obtained when a steady input into the first reactor produces a steady input into the second reactor that generates periodic behaviour in the second reactor via a Hopf bifurcation.
Many industrial processes produce wastewaters or slurries typically contain high concentrations of biodegradable organic matter. Before the wastewater/slurry can be discharged the pollutant concentration must be reduced. One way to achieve this is through the use of a biological species (`biomass') that consumes the organic matter (`substrate').
We have investigated biological reactor models in which the growth rate is given by a Contois expression with a variable yield coefficient [Nelson and Sidhu, 2007; Nelson et al, 2008]. (The justification for the use of this expression for modelling the cleaning of slurries/wastewaters from the food processing industries is given elsewhere on this site).
In (Nelson and Sidhu, 2007) the reduction in pollutant concentration was investigated when wastewaters are passed through one of two reactor configurations: a single reactor and a two-reactor cascade. In the latter scenario, the total residence time is fixed and the residence time in the first reactor is taken to be a design parameter. At sufficiently small residence times there is little difference between an optimised cascade and a single reactor. However, at higher residence times an optimised cascade can outperform the single reactor by two orders of magnitude. Alternatively, the performance of a single reactor can sometimes be replicated by a double reactor cascade having a much shorter residence time. Under such circumstances, a cascade has a considerably greater throughput of wastewater.
Along the no-washout branch the substrate concentration is a strictly decreasing function of the residence time. Thus it appears that an increase in the residence time should always lead to a decrease in the pollutant concentration leaving the reactor. However, we showed that when Hopf bifurcations are present in the system there are circumstances in which an increase in the residence time can lead to a decrease in the pollutant concentration leaving the reactor. This happens when the time-averaged effluent concentration associated with a stable limit cycle is higher than the steady-state effluent concentration associated with the corresponding unstable steady-state solution. Thus periodic behaviour is undesirable. If the Hopf bifurcation is subcritical then the reactor exhibits bi-stability. This has the potential to cause a deterioration in the performance of the reactor as instead of operating at the stable no-washout solution the reactor may evolve to a stable periodic solution.
We also showed that, under some circumstances, a cascade can have an inferior performance to that of a single reactor having the same residence time.
In (Nelson et al, 2008) the optimal performance of a single membrane reactor and a double membrane reactor cascade was determined. In a membrane bioreactor, a membrane filtration process is used to separate the effluent from the biomass. This process retains biomass within the bioreactor, increasing its concentration and allowing for a more efficient treatment of contaminated wastewater. This produces a higher quality effluent than is obtained using conventional reactors. Consequently, membrane reactors are increasingly being used as elements of advanced water processing schemes.
It was found that in many cases the cascade membrane reactor outperforms the single membrane bioreactor by two orders of magnitude. For both the single and cascade reactor configurations, it was found that periodic behaviour did not improve the performance of the reactor.
Some papers dealing with reactor cascades are also listed in the section: Ethanol production: Published papers.
The activated sludge process is widely used in wastewater treatment plants to reduce effluent levels in contaminated wastewaters originating from both the municipal and industrial sectors. It uses naturally occurring micro-organisms to remove pollutants, such as organic matter and nitrogen compounds, from wastewaters (sewage). The process generally consists of two units: an aerated biological reactor, in which bacteria are used to degrade pollutants, and a settling unit (or clarifier), in which the activated sludge settles to the bottom of the unit. The settling of the sludge, which contains most of the bacteria, at the bottom of the settling unit clarifies the treated wastewater, allowing it to be separated from the bacteria. The water is then discharged whilst most of the activated sludge, along with mixed liquor, is recycled from the bottom of the clarifier into the biological reactor. The settling process concentrates any microorganisms that are not discharged with the water. The activated sludge that is not recycled is disposed of using standard methods.
A key feature of the process is that large quantities of air are bubbled through the wastewater in open aeration tanks. The oxygen contained in the air is required by the bacteria, and other microorganisms present in the system, to live, grow and multiply.
We have investigated a model for the treatment of wastewater in the activated sludge process due to Curds. The biochemical model assumes that the incoming sewage is broken down by two types of bacteria, sludge bacteria and sewage bacteria, and two types of ciliated protozoa, free-swimming ciliates and ciliates attached to sludge flocs. The recycling process is assumed to concentrate the sludge bacteria and the attached and crawling protozoa. The wastewater reactor is assumed to be well mixed, so the mathematical formulation for this process can be represented by a continuously stirred tank reactor with recycle.
Curds originally investigated the model through numerical integration to obtain steady-state solutions for one particular set of parameter values. Our analysis combines steady-state analysis with path-following techniques. We have shown that such methods enable the dependence of the system efficiency upon the residence time for a single reactor with recycle [Watt et al 2006] and two reactors with recycle [Sidhu et al 2006] to be readily obtained. For the cascade the total residence time in the two reactors was fixed, and the residence time in the first reactor was then treated as the primary bifurcation parameter. The optimal performance of the single reactor is used as a benchmark for comparison with performance of a cascade. For sufficiently low total residence times, an optimised single reactor was found to outperform a cascade. At sufficiently high total residence times, an optimised cascade outperforms an optimised single reactor. In some cases the improvement in the cascade performance may be small, however it was seen that to achieve the same level of efficiency as in the cascade, a single reactor would have to be operated for a significantly larger residence time.
The ASM1 model contains 13 differential equations. However, four equations, pertaining to inert soluble organic material, particulate inert organic material, non-biodegradable particulate products arising from biomass decay and alkalinity, uncouple from the remaining nine equations, and therefore do not affect the dynamics of the system.
We have analysed the ASM1 in a single reactor without recycle using continuation methods to determine the steady-state behaviour of the system (Sidhu & Nelson; 2007). In particular, we determine bifurcation values of the residence time, corresponding to branch points, that are crucial in determining the performance of the plant. The first branch point marks a transition at which the washout solution becomes unstable. Thus the residence time must be higher than that at this branch point. Although the system performance, as defined by total chemical oxygen demand, always increases with residence time, the second branch point marks a transition above which improvement in reactor performance with increasing residence time are much more marginal. If the reactor performance is to be significantly improved over that obtained at the second branch point then either very large residence times or a different reactor configuration, such as a cascade, must be used.
Used path-following methods to find cascade designs where the product yield exceed 0.48, which is the yield currently obtained in industry. (Sidhu et al, 2008). This performance could not be achieved with a single reactor. For a double reactor cascade with equal (unequal) residence times in each stage the total residence time required was 16.22 (15.23) hours. For a triple reacor cascade with equal residence times in each stage the total residence time required was 16.29 hours.
|Professor A.A. Adesina||2006-Present||Membrane reactors|
|Mr R.T. Alqahtani (PhD student)||2010-Present||Cascades||Simple models|
|Dr E. Balakrishnan||2006-Present||Simple models|
|Professor X. Dong Chen||2001-Present||Membrane reactors||Simple models||Stomach models|
|Dr J. Kavanagh||2007-Present||Ethanol production|
|Professor A.K. Ray||2006-Present||Cascades||Ethanol production|
|Dr M.J. Sexton.||2003-2005||Membrane reactors|
|Dr H.S. Sidhu.||2002-Present||Membrane reactors||Cascades||Activated Sludge||Simple models||Ethanol production||Stomach models|
|Dr S.D. Watt.||2005-Present||Activated Sludge||Ethanol production|
|Dr A.L. Worthy||2010-Present||Cascades||Simple models|