pbepack

Status

pbepack is currently being developed and not yet ready for use.

Description

pbepack is a modern-Fortran package to solve population balance equations (PBE) for one- and two-component aggregation processes using the (extended) fixed pivot method. For single component systems, the code implements the method of Kumar & Ramkrishna (1996), and for bivariate aggregation the method of Vale & McKenna (2005).

Underlying PBE

If the system is spatially homogeneous, a two-component aggregation process is described by the following PBE:

$\large \begin{align*} & \frac{{\partial n(x,y,t)}}{{\partial t}} = \\ & \frac{1}{2}\int_0^x {\int_0^y {\beta (x - x',y - y';x',y';t)n(x - x',y - y',t)n(x',y',t) d x' d y'}} \\ & -n(x,y,t)\int_0^\infty {\int_0^\infty {\beta (x,y;x',y';t)n(x',y',t)d x' d y'}} \end{align*}$

where is the number of particles of state per unit volume at time and $\beta (x,y;x',y';t)$ is the aggregation rate coefficient. The internal coordinates and denote the amount (mass, moles, etc.) of each component in the particle.

Getting started

Build

The easiest way to build/test the code and run the examples is by means of fpm. To run a given example, just do:

fpm run --example "example-filename"

and the numerical results will be stored in the output subfolder. You can then use the provided Python script to read the data and plot the results.

Usage

comming soon...

Examples