Testing the Favourability of Periodic Reactor Operations Based on the Second Order Frequency Response Function
Systematic methods and tools for managing the complexity
Process Operation, Monitoring & Analysis (T4-2)
Keywords: Periodic reactor operation, Frequency response functions, Perfectly mixed and plug-flow reactors, Homogeneous and heterogeneous reactors
Periodic operations of different chemical engineering processes, especially of chemical reactors, have been attracting attention of a number of research groups in the last 20-30 years. The attractiveness of the periodic operations lies in the fact that the average process performance corresponding to the periodic operation can be superior to the optimal steady-state operation, i.e., that the process productivity can be increased by cycling one or more inputs. The source of this improvement lies in the process nonlinearity. Nevertheless, the improvement is obtained only in some cases, while in some others the periodic operation can be unfavourable.
Testing whether a potential periodic process is favourable or unfavourable generally demands long and tedious experimental and/or numerical work. This paper presents a new, fast and easy method for this testing, based on the Volterra series approach, nonlinear frequency response and the concept of higher order frequency response functions.
Without going into details, let us just remind that the frequency response (quasi-steady state response to a sinusoidal input change) of a nonlinear system, in addition to the basic harmonic, contains a non-periodic (DC) term, and an indefinite sequence of higher harmonics.
On the other hand, any nonlinear model with polynomial nonlinearity (G), can, in the frequency domain, be replaced by an indefinite sequence of frequency response functions of different orders (G1(w), G2(w1,w2), G3(w1,w2,w3),…), which are directly related to the DC component and different harmonics of the response. The DC component, which is responsible for the average performance of the periodic process, has a dominant term which is proportional to the asymmetrical second order function G2(w,-w):
In principle, the sign of the function G2(w,-w) defines the sign of the DC component, and, accordingly, whether the periodic operation is favourable or unfavourable. In that way, in order to decide on the favourability of a particular periodic operation, it is enough to set up its nonlinear mathematical model and derive and analyse the asymmetrical second order function G2(w,-w).
The method has been tested for several simple homogeneous and heterogeneous reaction mechanisms, with input concentration variation, and for both perfect mixed and plug-flow reactors. An important result of this analysis is that, for one reaction mechanism, the periodic operation in both reactor types is either favourable or unfavourable. Consequently, the analysis for the perfectly mixed reactor, which is generally simpler, can be used in order to investigate the justifiableness of the periodic operation, no matter which type of reactor would be used in practice.
The proposed method can be also be used for rough estimation of the average performance of the periodically operated reactors.
See the full pdf manuscript of the abstract.
Presented Tuesday 18, 09:05 to 09:25, in session Process Operation, Monitoring & Analysis (T4-2).
