3.4 Essential Model Preparations & Adaptations
3.4.4 Model Outputs
As a consequence of the model adaptations and the later requirements for the implementation of the surrogate models, the model outputs are defined as:
XCO= Z H 0 − Robs,CO A·n˙0,CO in molCO s m2·molCO m2·s , (3.49) YCH∗ 4= Z H 0 Robs,CH4 A·n˙0,CO in molCH4 s m2·molCO m2·s . (3.50) HFB in m, (3.51) dBmax in m, (3.52) am = A ˙ mgas in m 2·s kg . (3.53)
The outputXCOrepresents the total conversion of CO andYCH∗
4 represents the amount of
generated methane per mole of initial CO. The outputsHFB,dBmax, andam are representing
the final fluidised bed height, the maximum bubble diameter, and the specific cross-sectional area of the reactor, respectively.
To give an overview, figure 3.12 illustrates a scheme of the input and output variables of the fluidised bed methanation reactor model.
Cooling Agent
Raw SNG
Clean Producer Gas
Inputs
Outputs
χH2 χCH4 χH2O χN2 χCO2 TR PR xoilout Scat= ˙ NCO+CO2 mcat xoilin m2 kg s m3 std. m2·s m s am=m˙A gas Um fR =uum f m3 std.,CO+CO2 s·kgcat XCO Y∗ CH4 dBmax HF BFIGURE3.12:Scheme of the fluidised bed reactor with illustration of the input and output variables.
3.5 Conclusions
Predictions of a fluidised bed methanation reactor model were compared to experimental data at different operation conditions varying three factors; the catalyst hold-up, the gas flow rate, and the dilution by nitrogen. By applying three different Langmuir-Hinshelwood rate expressions to the fluidised bed model and by comparing the performance of predicting the selectivity of the reaction system of the model with experimental data, the kinetics 3m were identified as the best performing one with the model definition.
The reaction selectivity as performance indicator was determined using the freeboard con- centration measurements. This was suitable since, for the subsequent process design & optimisation methodology, the outlet concentrations and not the measured profiles are the relevant properties of the process unit. Furthermore, these values are most probably less affected by measurement biases. It was found that it is advantageous to use the chemical selectivity of the reactions as performance indicators if the reactions are very fast and there- fore total conversion is nearly always reached. Furthermore, the reaction selectivity is a good approach to normalise the results and to make them comparable in case of analysing volume contracting or expanding reactions.
The selectivity of the reactions was found to differ for the most experiments clearly from the equilibrium. This shows that the fluidised bed methanation is a rate limited process at nearly all tested operating conditions. The rate based model was able to predict satisfactorily the experimental results although room is left for improvements. For instance the model may be improved by determining experimentally the pressure dependency of the kinetics in a broader range than it was done before. Uncertainties inside the reactor model according the hydrody-
3.5. Conclusions
namics and mass transport (e.g., bubble size distribution, bubble size growth, characteristics of phase separation) are probable since most applied correlations from literature are based on experiments utilising non reactive fluidised beds without any internals (e.g. heat exchanger tubes). Therefore, better bubble growth correlations with bubble size distribution and better approximation of the bubble hold-up and the mass transfer area for reactive fluidised beds with internals should be developed and implemented into the model.
Irrespective of these issues, which may be improved with future experiments, the rate based model is suitable for the application in the process design & optimisation methodologies for predicting the behaviour of the fluidised bed methanation reactor. Applying it enables the process design & optimisation methods to calculate economic properties of the process designs more accurately. It allows more detailed unit sizing and energy integration calculations while considering the aspects of the rate limitations inside the fluidised bed methanation reactor.
4
Surrogate Modelling
In sections 4.1 and 4.3 parts of sentences, full sentences or whole paragraphs are contributed by Ivo Couckuyt in the course of collaborative work on the following publication in preparation:
Sinan L Teske, Ivo Couckuyt, Tilman J. Schildhauer, Serge M. A. Biollaz, and François Marechal. “Integrating Rate Based Models into Multi-Objective Optimisation of Process Designs us- ing Surrogate Models”. In: 26th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems. 2013
4.1 Introduction
The idea of surrogate modelling or often also called meta-modelling is based on the techniques of mathematical approximation of any kind of data. It can be real world experimental data or data from computer models which are then called computer experiments. Surrogate modelling techniques are a commonly applied approach in engineering design processes to reduce computational complexity and computation time for existing high fidelity computer models like most finite-element computer models are. Especially in case of optimisation tasks of complex multi-scale problems, there is the need of simplifying models, since optimisation methods mostly require the calculation of many different states of the involved models. This rapidly raises the computational costs. Such an approach of constrained optimisation in expensive simulation was presented by Kleijnen et al. [59]. Kleijnen also reviewed the general use of surrogate modelling in simulation [58]. A panel discussion held in the year 2002 and summarised in [95] shows that surrogate modelling is applied widely in different engineering fields to reduce complexity and computational costs of modelling and optimisation problems. Further, Simpson et al. [95] highlights the needs of industry and academics to improve the application of surrogate models.
As described in chapter 2, the multi-objective optimisation of the superstructure based process model involves the calculation of several ten-thousand sets of decision variable combinations. The originally applied model of the fluidised bed methanation reactor is based on thermody- namic equilibrium calculations, hence the impact of this process unit model on the overall calculation time is small. The goal in this thesis is to replace this unit model with the rate based fluidised bed model described in chapter 3. Replacing this model directly would increase the calculation time of the multi-objective optimisation exceedingly. A single computation of the rate based model needs several seconds. For CFD (computational fluid dynamics) calculated process units, the calculation time could even cost much more time. Such an increase in computational cost is inappropriate for many problems. In comparison to that, the calculation with surrogate models mostly need only a fraction of a second to calculate the same process states. The advantage of using surrogate models is not only the reduction of computational costs, however, it also provides the engineer a tool for rapid design space exploration and more importantly with visualisation capabilities [96]. These fast visualisation capabilities are of paramount importance for engineers to examine the problem and to support their decision making.
It is important to note the difference between local and global surrogate models. Local surrogates involve building small, relatively low fidelity surrogates for use in optimisation tasks where they are applied as rough approximates of the (costly) optimisation surface. They guide the optimisation algorithm towards optimal extrema while minimising the number of simulations of the original model [74]. Once the optimum is found, the surrogate is discarded. In contrast to that, by applying global surrogate modelling, the objective is to construct a high fidelity approximation model that is as accurate as possible over the complete design space of interest while using as few simulation points as possible. Once constructed, the