Chemical and phase equilibrum (CPE) calculations are indispensable to the geochemical simulation of natural systems, such as freshwater, groundwater, and mineral formations. In natural environments, many chemical reactions occur, both at the interface between rocks and fluids (e.g., dissolution reactions) and in bulk phases (e.g., aqueous speciation). Moreover, the typical ionic species found in nature require thermodynamic models for electrolytes, increasing the calculation complexity. In this work, we present RAND-based algorithms, which originate from Gibbs energy minimization, for geochemical CPE problems for closed systems and open systems. The open system problems specify fixed chemical potentials for non-charged species, as in a constant partial CO${}_2$ pressure problem, or for charged ionic species, as in a constant pH problem. We showcase the robustness and efficiency of these algorithms using the mineral system Mg-Si-Ca-CO${}_2$-H${}_2$O because of its relevance to CO${}_2$ underground geological storage. The algorithms show quadratic convergence and the coupled tangent plane distance analysis can determine the most stable phase assemblage. The algorithms generate results in agreement with PHREEQC, whereas they are much faster than PHREEQC. The described algorithms can be potentially used for reliable and fast simulation of CO${}_2$ storage in geological formations, and of other processes in natural environments involving geochemical equilibrium.

化学和相平衡（CPE）计算对于诸如淡水，地下水和矿层等自然系统的地球化学模拟是必不可少的。在自然环境中，在岩石和流体之间的界面（例如，溶解反应）和整体相（例如，水的形态形成）中都会发生许多化学反应。此外，自然界中发现的典型离子物种需要电解质的热力学模型，从而增加了计算复杂性。在这项工作中，我们提出了基于RAND的算法，该算法源自Gibbs能量最小化，用于封闭系统和开放系统的地球化学CPE问题。开放系统问题规定了不带电物质的固定化学势，例如恒定的部分CO${}_{\mathrm{2个}}$压力问题，或带电离子物种的问题，例如持续的pH问题。我们展示了使用矿物系统Mg-Si-Ca-CO的这些算法的鲁棒性和效率${}_{\mathrm{2个}}$-H${}_{\mathrm{2个}}$O，因为它与CO相关${}_{\mathrm{2个}}$地下地质储藏。该算法显示出二次收敛性，并且相切平面距离耦合分析可以确定最稳定的相位组合。该算法产生的结果与PHREEQC一致，但是它们比PHREEQC快得多。所描述的算法可潜在地用于CO的可靠和快速仿真${}_{\mathrm{2个}}$ 储存在地质构造中，以及在涉及地球化学平衡的自然环境中的其他过程。