(49d) Parallel GPU-Based Monte Carlo Techniques for the Flowsheet Simulation of Solid Processes

The description of particle processing and production in the scope of a flowsheet simulation poses a subject of great difficulty, hence several particle properties have to be taken into account for the complete characterization of the particulate material. The corresponding particle dynamics may exhibit strong non-linear dependencies on these multi-variate properties and are mostly described by the population balance equation (PBE) (see e.g. [1,2]). The Monte Carlo (MC) technique poses a solution method for the PBE, which allows to take several particle properties into account. Such multivariate modelling requires normally a large amount of computational resources, if a sectional method is used for the solution of the PBE (see e.g. [3]).

The modelled particle size distributions (PSD) can describe differences in particle concentrations spanning several orders of magnitudes. The computationally efficient description of such large differences of particle concentrations becomes possible by the application of weighted MC simulation particles [4,5]. Recent algorithms for the nucleation, coagulation [6], condensational growth/evaporation [7] and breakage [8] of particles by means of weighted MC simulation particles have been formulated specifically for graphic processing units (GPU). It has been shown that the parallel computation on GPUs could be exploited for the accelerated solution of the PBE, making thus the incorporation of this stochastic technique for the simulation of flowsheet processes suitable.

Production processes on plant scale can be mostly formulated as a sequence of coupled unit operations (with possible tear streams), which in turn can be described by the PBEs. There exist several approaches, to solve such a system, next to the sequential modular approach, a (simultaneous) equation-oriented approach can be chosen to describe such a coupled system (see e.g. [9,10]). The parallel formulation of the solution of the PBEs by means of the MC method is best suited for the equation-oriented approach.

We present in the following some basic application examples for the parallel solution of systems describing different unit operations. These dynamic unit operations are described as PBEs, so that the aforementioned particulate processes of coagulation, condensational growth, evaporation, nucleation and breakage may be simulated simultaneously by the means of the parallel MC method.

We present a parallel simulation algorithm, which makes the incorporation of these several mechanisms in an operator splitting technique (see e.g. [11]) possible. It is shown how the parallel computational architecture of the GPU can be used in order to simulate such a system in a computationally efficient way, the application of synchronized and asynchronous kernel launches on the GPU is investigated in this context.

In the scope of this algorithm, several MC simulations are performed for each unit operation in parallel. The different units can be launched in parallel, too. The dependency of the accuracy (as well as the computational time) of the MC technique as a function of the number of used simulations per unit is investigated.

The computational complexity (i.e. simulation time) is investigated in dependency on the ‘heterogeneity’ of the system, as well. This means that the computational times for ‘more homogeneous’ systems (comprising unit operations, which describe the same processes (e.g. coagulation) for different parameters (e.g. temperature)), with ‘more heterogeneous’ systems (for which one unit operation may comprise different processes than another unit operation (e.g.: unit 1 describes agglomeration and unit 2 describes breakage of the particulate material)). The computational time and accuracy are presented as a function of simulated units and the ‘heterogeneity’ of the system.

The financial support of DFG (Deutsche Forschungsgemeinschaft) within the priority program SPP 1679 "Dynamic flowsheet simulation of interconnected solids processes" is gratefully acknowledged.

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