一个计算机模拟水-岩反应过程的数学模型

本文对计算机模拟水-岩反应过程的地球化学背景作了详细的讨论,指出偏平衡假设对于水-岩反应过程是合理的,因而可用一准平衡过程逼近于一真实的地球化学过程。根据热力学原理和地质概念模型,作者建立了一个完整的数学模型,它可以模拟不同的地球化学过程。该模型由一组非线性方程构成,其中包括质量守恒方程和化学平衡方程。为了求解,作者将非线性方程组化为最小平方和形式,然后采用改进的牛顿迭代法进行数值求解。作者还采取了初始值初步改善和变量替换等措施,避免了求解水-岩反应方程组常遇到的两个问题,即初始值选取和负浓度的出现。本文所给出的算法具有很好的数值稳定性。作者模拟了黄铁矿型矿床的形成过程,计算结果与矿床的实际典型分带相一致。

A Mathematical Model Of Computer Simulation For Water-Rock Reactions

In this paper the authors have discussed the background of the computer simulation in geochemistry. It is pointed out that a natural geochemical process can be approximated by a series of equilibrium states with the partial equilibrium assumptions. Based on thermodynamics and geological conceptual models, a mathematical model to simulate water-rock reactions has been well established. A geochemical process is governed by a set of nonlinear equations composed of mase balance and chemical equilibrium equations which, in turn, are transformed into an optimization problem convenient to solution. Moreover, the authors have employed the techniques of initial value improvement and variable transforms to prevent the negative concentrations and avoid encountering the difficulties in initial value selection, which are inherent in solving water-rock reaction equations. The algorithms proposed here have good numerical stability and, in consequence, the model can be solved by computer. As an example, a massive sulfide rnineralization has been simulated. The authors have calculated the reaction between basalt and seawater, the mixing of hydrothermal solution and seawater, and the aqueous speciation of Cu and Fe at varying temperatures. By setting suitable initial conditions and factors controlling the mineralization p1ocess, the authors have achieved further results than those of Reed. What is more. the calculated zonation of the massive sulfide deposit is well accordant with the typical natural one.