One of the primary goals of igneous petrology is the definition and evaluation of the roles of the processes responsible for chemical differentiation. Quantitative simulation of these processes not only requires an understanding of the systematics of mineral-liquid equilibria in natural systems but also some understanding of how different processes interact. The programs presented here consist of empirically calibrated expressions of mineral-melt equilibria that are built around a thermodynamic framework. The framework of the programs (which are designed to model phase equilibria based igneous differentiation) have been published in earlier works (Nielsen and Dungan, 1983; Nielsen, 1985; Nielsen, 1988 a, b; Nielsen et al., 1988). This presentation is to show how modeling can be used to gain otherwise unobtainable insights into the mechanics of igneous differentiation, in particular, for processes that are difficult to simulate in the laboratory. In this chapter we will simulate the major differentiation processes that are characteristic of shallow igneous magma chambers. These processes include crystallization, recharge, assimilation .and eruption. In each example, we will examine how observations of natural systems can be converted into the mathematical constraints necessary for the construction of computer based models. Since our primary goal is to model natural igneous systems, the examples show how phase equilibria modeling can be used to help solve problems related to interpretation of the chemical and mineralogic diversity of suites of natural lavas.

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