Mass balance calculation is a fundamental approach in geosciences. In petrology and geochemistry, it is widely used for quantitative characterization of phase transition and mass transfer. In a routine petrological practice, this method is commonly used to calculate proportions of the minerals formed from initial or parental bulk composition, or to quantify the reaction coefficients for minerals involved in a chemical reaction that achieves equilibria. In this paper, we present a new mass balance calculation program, GeoBalance, which is written with Visual Basic for Applications (VBA) and built in a macro-enabled Excel™ worksheet. The working algorithm is based on solving the least square problem using pseudo-inverse of matrix and singular value decomposition (SVD) of matrix. Both unconstrained and constrained solution methods are implemented in the program and can be chosen by the user. In addition, input data (e.g. compositions of the minerals) can be different data types, such as cations, oxides, moles of oxides, or moles of mineral endmembers. As a result of calculation, phase proportions are presented as percentages on 100%-normalized basis with residuals (for each chemical component), and a sum of squared estimate of errors (SSE). Monte Carlo simulation of error propagation for evaluating calculation uncertainty is also implemented as an optional function. An additional advantage of our program is that it enables users to perform mass balance calculations for complicated systems with a flexible number of phases and/or chemical components.

质量平衡计算是地球科学中的基本方法。在岩石学和地球化学中，它广泛用于相变和传质的定量表征。在常规的岩石实践中，此方法通常用于计算由初始或母体总体组成形成的矿物的比例，或量化实现平衡的化学反应中涉及的矿物的反应系数。在本文中，我们提出了一个新的质量平衡计算程序GeoBalance，它是用Visual Basic for Applications（VBA）编写的，并内置在启用宏的Excel™工作表中。该工作算法基于使用矩阵的伪逆和矩阵的奇异值分解（SVD）求解最小二乘问题。不受约束和受约束的求解方法都在程序中实现，并且可以由用户选择。另外，输入数据（例如，矿物的成分）可以是不同的数据类型，例如阳离子，氧化物，氧化物的摩尔数或矿物端基的摩尔数。计算的结果是，相比例以百分数归一化的百分比表示，带有残差（对于每个化学成分）以及误差平方估计值的总和（SSE）。用于评估计算不确定性的误差传播的蒙特卡洛模拟也作为可选功能实现。