A new efficient framework for reduced two-dimensional nonlinear aggregation population balance models

Two-dimensional (2D) nonlinear population balance models are inherently complex due to their high computational demands and sensitivity to the choice of grid type. To address the challenge of tracking multiple properties and to provide an alternative to full 2D population balance models, we consider a reduced model that efficiently captures moisture content (tracer) and size distributions of granule in aggregation population balance equations (PBEs), under the assumption that the aggregation kernel depends solely on granule volume and time, and is independent of tracer volume. This reduced model is formulated as a tracer population balance equation (TPBE), for which we present a new and efficient discretization method that ensures conservation of tracer mass. The proposed formulation is versatile and applicable to any grid type, making it suitable for both continuous and batch particulate systems. We validate its performance using two benchmark applications: (a) batch systems and (b) mixed-suspension mixed-product removal systems. The formulation is tested across various kernels and compared against the cell average technique (CAT) to confirm its effectiveness. Results show that the proposed method achieves accuracy comparable to CAT while requiring approximately 50–60% less computational time. Overall, this approach offers a computationally efficient alternative to standard 2D models, with broad applicability in systems where reduced computational cost is critical for particle process modeling.

Content

Subjects

34A12

35Q70

45K05

Aggregation process

Grids

Moisture content and size distributions

Reduced population balance model

Weighted finite volume scheme

DDC Class

620: Engineering