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Carbon dioxide ( C O 2 ) is an undesirable component present in natural gas composition. The supersonic separator is a new and potential technology for natural gas treatment, which expands the gas through supersonic velocities until a shock wave formation. The modeling capacity to predict the shock wave position inside the device is analyzed considering parametric uncertainties. Results from four real gas models were compared in computational fluid dynamic modeling. Uncertainties that affect coefficients in the real gas models were propagated through the carbon dioxide flow solver using the Latin Hypercube Sampling approach. It was observed that the shock wave introduces non-linearity in the local standard deviation. Soave-Redlich-Kwong and Aungier-Redlich-Kwong are slightly affected by input parametric uncertainties. On the other hand, the Peng-Robinson model results are strongly affected.

The Direct Dual Quadrature Method of Generalized Moments (D2uQMoGeM) was formulated for the solution of the population balance equation. It mixes the properties of the Direct Quadrature Method of Moments (DQMoM) and the Dual Quadrature Method of Generalized Moments (DuQMoGeM). The weights and weighted abscissas are tracking directly as in DQMoM and the quadrature errors are controlled by an adaptive quadrature as in DuQMoGeM. The D2uQMoGeM was implemented and tested for several different problems with analytical solutions. It was shown to be more accurate than DQMoM with a reasonable increase in computational time.

The Dual Quadrature Method of Generalized Moments (DuQMoGeM) is an accurate moment method for solving the population balance equation (PBE). The drawback of DuQMoGeM is the high computational cost associated with numerical integrations of the PBE integral terms in which each integrand can be integrated independently and, therefore, amenable to parallelization on GPUs. In this work, two parallel adaptive cubature algorithms were implemented on a hybrid architecture (CPU–GPU) to accelerate the DuQMoGeM. The speedup and scalability of these parallel algorithms were studied with different types of Genz's test functions. Then, we applied these parallel numerical integration algorithms in the DuQMoGeM solution of the PBE for three bivariate cases, obtaining speedups between 11 and 15.