https://github.com/hugomvale/pbepack
Package to solve population balance equations for particulate processes.
https://github.com/hugomvale/pbepack
aggregation breakage coagulation fortran pbe population-balance-equation
Last synced: 4 months ago
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Package to solve population balance equations for particulate processes.
- Host: GitHub
- URL: https://github.com/hugomvale/pbepack
- Owner: HugoMVale
- License: mit
- Created: 2022-09-18T14:26:30.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2024-08-24T22:05:06.000Z (over 1 year ago)
- Last Synced: 2024-08-24T23:21:55.741Z (over 1 year ago)
- Topics: aggregation, breakage, coagulation, fortran, pbe, population-balance-equation
- Language: Fortran
- Homepage: https://hugomvale.github.io/pbepack/
- Size: 481 KB
- Stars: 1
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE.md
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README
# pbepack
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[](https://codecov.io/gh/HugoMVale/pbepack)
[](https://github.com/topics/fortran)
## 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)](https://doi.org/10.1016/0009-2509(96)88489-2), and for bivariate aggregation the method of [Vale & McKenna (2005)](https://doi.org/10.1021/ie050179s).
## Underlying PBE
If the system is spatially homogeneous, a two-component aggregation process is described by the following PBE:
}}{{\partial&space;t}}&space;=&space;\\&space;&&space;\frac{1}{2}\int_0^x&space;{\int_0^y&space;{\beta&space;(x&space;-&space;x',y&space;-&space;y';x',y';t)n(x&space;-&space;x',y&space;-&space;y',t)n(x',y',t)&space;d&space;x'&space;d&space;y'}}&space;\\&space;&&space;-n(x,y,t)\int_0^\infty&space;{\int_0^\infty&space;{\beta&space;(x,y;x',y';t)n(x',y',t)d&space;x'&space;d&space;y'}}&space;\end{align*} "\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 &space;dx&space;dy "n(x,y,t) dx dy")
is the number of particles of state  "(x,y)")
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`](https://fpm.fortran-lang.org/en/index.html). To run a given example, just do:
```
fpm run --example "example-filename"
```
and the numerical results will be stored in the [`output`](/output) subfolder. You can then use the provided Python script to read the data and plot the results.
### Usage
comming soon...
## Examples
comming soon...