(57a) Dynamic Simulation of Interconnected Solids Processes

A novel flowsheet simulation system, aimed at the dynamic modelling of complex production processes mainly in the area of solids processing, is being developed within the Priority Program SPP 1679 “Dynamic simulation of interconnected solids processes (DYNSIM-FP)” of the German Research Foundation (DFG) since July 2013 [1]. The Priority Program consists of 29 separate projects from different German universities and is thematically divided into four main groups:

- A: Development and implementation of new dynamic models of individual apparatuses and process substeps;

- B: Calculation of material parameters and development of models to describe properties of solids materials;

- C: Development of advanced algorithms and methods for dynamic simulation of complex process structures;

- Z: Development of a novel framework for the flowsheet simulation of dynamic processes.

This flowsheet simulation framework, named Dyssol (acronym for the DYnamic Simulation of SOLids processes), is presented in this contribution. The main objective of the system is to combine models, methods and algorithms, developed within the whole SPP 1679 program, into a single modelling framework that allows performing dynamic modelling of complex process structures involving solid, liquid and gaseous phases as well as their mixtures.

2. Calculation algorithm and applied methods

The Dyssol simulation system implements a sequential-modular approach [2] (SMA), where each unit is relatively independent from others and can be computed separately by its own numerical method or calculation algorithm using an individual simulation time step. Obtained results after computation of each unit are transferred between units according to the flowsheet structure. This approach leads to a relative independence between models and provides high flexibility of the simulation system itself.

The SMA implies sequential computation of models in a certain order, so it is necessary to know all inlets of a model to start calculation. Flowsheets, which consist solely of serially connected modules, satisfy this condition by default. On the other hand, applying of SMA is complicated if there are recycle streams in a process structure. In this case a flowsheet must be additionally converted into sequential form by tearing recycle streams [3]. Tearing here means search for recycle streams and setting some initial values into them.

For the dynamic simulation a modified waveform relaxation method (WRM) [4] is used. The whole simulation time is divided into smaller non-constant time intervals, on which convergence can be reached faster. Units are solved separately on each time window using some initial guess for the solution. Calculations are repeated on the current time interval until the convergence is reached. Then, the system proceeds to the calculations on the next time window. To initialize each next time window extrapolated values from the previous time intervals are used. The number of WRM iterations, needed to reach convergence, depends on the difference between the extrapolated and actual results. A set of extrapolation algorithms has been implemented in Dyssol to initialize the first iteration on each time interval.

3. Parallelization methods

Dynamic flowsheet simulation is a computationally demanding process. Sequential-modular algorithm of the Dyssol makes it relatively easy to implement different parallelization mechanisms [4] that can significantly reduce calculation time. Several strategies are implemented in the simulation system Dyssol:

- Parallelization of basic functions of the simulation system, such as matrix transformation and mixing of material streams.

- Parallel calculation of the model itself. Feasibility of this approach depends on the particular model, and the specific implementation is the task of a model’s developer.

- Simultaneous calculation of individual time points for steady-state models. If the outlet parameters of model are independent of its internal state, and are determined only by the input parameters, model state at different time points can be computed in parallel.

- Parallel calculation of models, which are located on independent branches of a flowsheet and thereby are not directly dependent from each other.

4. Handling of multidimensional distributed parameters

One of the main challenges during the simulation of solids processes is related to the dispersity of granular materials: the solid phase can be distributed along several interdependent properties, such as size, shape, moisture content, density, etc. forming a multidimensional set of distributed parameters. On the other hand, each operation on the material flow, such as separation, mixing, agglomeration, etc. may require a change in one or more distributed parameters. In this case it may be necessary to calculate all dimensions from a multidimensional set even if the value of a single parameter had been changed. Therefore, it should be considered that during the simulation interdependency between all parameters should not be lost. This means that applying the same methods for calculation of solids as for liquid-gaseous systems is impossible or can lead to their incorrect handling.

All parameters of the granular materials are represented in the simulation system Dyssol in the discretized form. The entire interval, on which the parameter is determined, is represented as a set of shorter intervals. To describe the distribution each such interval is associated with the number or mass of particles whose parameters fall within this interval. The discretization scheme must be fine enough that the numerical errors were small compared to the accuracy of the used models.

To represent interdependency between several distributed parameters multidimensional matrixes [4, 5] are used, where the number of dimensions is equal to the number of parameters. Each cell of such matrix contains the mass fraction of the solid material with certain combination of parameters, whereas the total sum of all entities of the matrix is equal to one.

For storing of such discretized multidimensional distributed parameters a sparse data format is used. The multidimensional matrix is represented by a flat tree data structure, where each level of this tree is one of the dimensions. If there are some classes, which are empty (contain zeroes), there is no need to store data on lower levels. This approach provides an opportunity to reduce memory consumption and calculation time. For more efficient usage of this structure dimensions are arranged in such a way, that the more zeroes a dimension contains, the higher it is placed in the structure.

For correct handling of solids an approach with transformation matrices is used [4, 5]. Each cell of a transformation matrix describes the mass fraction of material that passes from one class with a particular combination of parameters to some other class with another combination of parameters. This concept allows preserving information about all parameters, even those which are not considered or not changed in the current model. Thus, instead of an explicit calculation of the model's parameters transformation matrix can be generated and applied to obtain output stream in each unit.

When using this approach, the model of each particular unit is slightly complicated because not the final distribution of parameters is being calculated, but the laws of their transformation. However, this concept ensures that all information about the distributed parameters of granular materials will be retained during the computation and properly considered.

Acknowledgement

We gratefully acknowledge the financial support of the German Research Foundation (DFG) within the priority program SPP 1679 “Dynamic simulation of interconnected solids processes DYNSIM-FP”.

References

[1] www.dynsim-fp.de (2017).

[2] Hillestad, M., Hertzberg, T.: Convergence and stability of the sequential modular approach to dynamic process simulation. Comput. chem. Engng. 12, 1988, 407-414.

[3] Towler, G., Sinnott, R.: Chemical engineering design: principles, practice, and economics of plant and process design. Second edition. Butterworth-Heinemann Press, 2013.

[4] Dosta, M.: Hamburg-Harburg, Techn. Univ., Diss., 2012.

[5] Pogodda, M.: Hamburg-Harburg, Techn. Univ., Diss., 2007.