*Report Revision on 15 November 2025*

# TBP-Diluent-H$_2$O-HNO$_3$ Solvent Extraction

`Stage` is a [Cortix](https:cortix.org) module developed at Cortix Tech to model and simulate system-level physicochemical phenomena in a single stage of a solvent extraction contactor process. This module integrates into the Cortix architecture of network dynamics HPC simulation and can be coupled with many other instances to model a contactor bank in future developments of this project. Therefore the module and simulation tool design followed here applies to a multi-stage process and it is based on a network dynamics simulation as described in [Cortix](https:cortix.org).

The focus of this document is to describe the development of the stand-alone `Stage` which is aimed at providing superior modularity and flexibility to account for all possible scenarios of interest to the user when modeling and simulating uranium solvent extraction processes. Therefore `Stage` has been developed for any chemical reaction mechanism. The modularity for reaction mechanisms is provided by Cortix.

## Elements

The concerns of `Stage` are to 

 + Implement the mixing and disengagement of immiscible phases, 
 + Apply balance laws and thermodynamic constitutive constraints, 
 + Build the system of governing equations, and 
 + Solve the resulting time-dependent, coupled, non-linear, stiff (algebraic) ordinary differential equations.

`Stage` considers 3 phases, namely organic, aqueous, and vapor. If one phase is neglected, it appears as
an empty Cortix `phase` container. There are great differences in the way disengagement occurs in contactors
in practice, therefore a central design and implementation of `Stage` is to handle all practical types of mixing and disengagement. Currently both mixing and disengagement are of type: *instantaneous*.

The flows of the organic and aqueous phases are always countercurrent to each other, however at this 
moment it is unknown the direction of the vapor phase, therefore it is assumed each of the aqueous and 
organic phases drag the vapor phase. Hence the vapor flow is cocurrent to other phases. This assumption will
be revisited once collaboration with experimental colleagues takes place.

| | |
|:--:|:--:|
| <img width="650" src="pics/contactor.png" title="Solvex Artist Sketch"> | <img width="800" src="pics/solvex-module.png" title="Solvex Module Diagram"> |
| <p style="text-align:center;"><b>Solvex Contactor Sketch</b></p> | <p style="text-align:center;"><b>Solvex Module Diagram</b></p> |

[*Stage* Cortix module source](https://github.com/dpploy/solvex/blob/main/src/solvex/stage.py)

## Development Path

The `Stage` module is being developed in a progression of usecases:

  1. Water-air contact (empty organic phase)
  1. Water extraction in TBP/n-dodecane (w/o and w/ air)
  1. Aqueous nitric acid extraction in TBP/n-dodecane (w/o and w/ air)
  1. Uranyl nitrate, nitric acid, water extraction in TBP/n-dodecane (w/o and w/ air)
  1. Metal impurities, uranyl nitrate, nitric acid, water extraction in TBP/n-dodecane (w/o and w/ air)

aimed at elucidating many aspects of the modeling and simulation of solvent extraction of interest to the user. Each of the usecases will be individually studied and documented starting with the current case through the use of reproducible electronic notebooks.

## Sponsor

 This project is funded by Cortix Tech, Lowell, MA.

## Participants at Cortix Tech

 + Dr. Valmor F. de Almeida, Techical Lead, is the principal developer of [Cortix](https:cortix.org) and derived modules including `Stage`. He leads the coding efforts at Cortix Tech.

 + Viggo F. de Almeida, BS student in Nuclear Engineering, U of Tennessee Knoxville, is the maintainer of the website for usecases testing and documentation.