Models polythermal reaction

Polythermal reaction models (Section 14.1), however, are commonly applied to closed systems, as in studies of groundwater geothermometry (Chapter 23), and interpretations of laboratory experiments. In hydrothermal experiments, for example, researchers sample and analyze fluids from runs conducted at high temperature, but can determine pH only at room temperature (Fig. 2.2). To reconstruct the original pH (e.g., Reed and Spycher, 1984), assuming that gas did not escape from the fluid before it was analyzed, an experimentalist can calculate the equilibrium state at room temperature and follow a polythermal path to estimate the fluid chemistry at high temperature. 

Polythermal reactions paths are those in which temperature varies as a function of reaction progress, . In the simplest case, the modeler prescribes the temperatures T0 and Tf at the beginning and end of the reaction path. The model then varies temperature linearly with reaction progress. This type of model is sometimes called a sliding temperature path. 

To model the problem, we take a packet of water in contact with the fracture walls over a polythermal reaction path. The fact that the packet moves relative to the walls is of no concern, since the fracture surface area exposed to the packet is approximately constant. Since the system contains 1 kg of water, we can show from geometry that the surface area 4s (in cm2) of the fracture lining is,... 

Reaction paths can be traced at steady or varying temperature the latter case is known as a polythermal path. Strictly speaking, heat transfer occurs even at constant temperature, albeit commonly in small amounts, to offset reaction enthalpies. For convenience, modelers generally define polythermal paths in terms of changes in temperature rather than heat fluxes. 

As an example of how the dump option might be used, consider the problem of predicting whether scale will form in the wellbore as groundwater is produced from a well (Fig. 2.10). The fluid is in equilibrium with the minerals in the formation, so the initial system contains both fluid and minerals. The dump option simulates movement of a packet of fluid from the formation into the wellbore, since the minerals in the formation are no longer available to the packet. As the packet ascends the wellbore, it cools, perhaps exsolves gas as it moves toward lower pressure, and leaves behind any scale produced. The reaction model, then, is a polythermal, sliding-fugacity, and flow-through path combined with the dump option. 

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