A projected Newton algorithm based on chemically allowed interval for chemical equilibrium computations

Abstract

The chemical equilibrium equations utilized in reactive transport modeling are complex and nonlinear, and are typically solved using the Newton-Raphson method. Although this algorithm is known for its quadratic convergence near the solution, it is less effective far from the solution, especially for ill-conditioned problems. In such cases, the algorithm may fail to converge or require excessive iterations. To address these limitations, a projected Newton method is introduced to incorporate the concept of projection. This method constrains the Newton step by utilizing a chemically allowed interval that generates feasible descending iterations. Moreover, we utilize the positive continuous fraction method as a preconditioning technique, providing reliable initial values for solving the algorithms. The numerical results are compared with those derived using the regular Newton-Raphson method, the Newton-Raphson method based on chemically allowed interval updating rules, and the bounded variable least squares method in six different test cases. The numerical results highlight the robustness and efficacy of the proposed algorithm.

Graphical abstract

Keywords

chemical equilibrium / reactive transport modeling / numerical methods / projected Newton method

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Competing interests

The authors declare that they have no competing interests.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 22178190 and 22008129).

Electronic Supplementary Material

Supplementary material is available in the online version of this article at https://doi.org/10.1007/s11705-024-2390-8 and is accessible for authorized users.

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