Modeling ore generation in a magmatic context

[Display omitted] •Review of available models.•Direct, inverse, iterative processes.•Difficulties in elaborating a model for ore generation.•Suggested model based on metal enrichment. Magmatic ore deposit models are constructed from a set of measurables (e.g., ore grade, fluid composition, structure) from which important parameters (temperature, pressure, chemistry) can be estimated and possible genetic processes can be constrained. Such models include direct, inverse or iterative problems. Direct problems separately consider an Eulerian and a Lagrangian formulation. In the first case, an analytical approach describes the bulk system from an external frame, whereas the Lagrangian approach provides a description from a discrete element attached to the system. Conversely, inverse problems mostly rely on a system of equations or differential equations. Their solution requires a matrix inversion, using statistical criteria to bracket errors. Subsequently, an iterative approach is adopted, commencing with an initial bulk model that is successively refined to fit the observations. The direct problem always results in a unique solution, though the formulation is highly overdetermined. Such unique solution highly depends on the input parameters, and multiple solutions vary with the initial imposed conditions. Conversely, the inverse problem is underdetermined by construction. Accordingly, it provides a set of solutions, generally identified and separated by statistical tests, as exemplified by the least squares approximation. Both methods intrinsically ignore feedback loops. Iterative methods are weak in quantifying the results. Based on the insights gained from this review, we developed a new integrative model for porphyry deposits that relies on the magmatic segregation of metals through a fluid sparging process. A formulation under the direct problem basically considers the enrichment factor for groups of metals (e.g., Cu, Mo, Au). A Lagrangian approach using a lattice Boltzmann model examines metal diffusion from the melt toward an immiscible phase, commonly a salty aqueous fluid. Metals first diffuse in the melt, the motion of which slows down when the mush development reduces the porosity, thus tapping the mobile fluid phase. Gas bubbles turn to tubes. They offer more mobility and allow the progression of the fluid phase, leading to metal advection, followed by metal precipitation. The quantitative results are poorly constrained owing to the large uncertaint