Sliding fugacity path

Fig. 2.4. Example of a sliding-fugacity path. Deep groundwaters of a geopressured zone in a sedimentary basin migrate upward to lower pressures. During migration, CO2 exsolves from the water so that its fugacity follows the variation in total pressure. The loss of CO2 causes carbonate cements to form.

Fig. 2.10. Use of the dump option to simulate scaling. The pore fluid is initially in equilibrium with minerals in the formation. As the fluid enters the wellbore, the minerals are isolated (dumped) from the system. The fluid then follows a polythermal, sliding-fugacity path as it ascends the wellbore toward lower temperatures and pressures, depositing scale.

Sliding activity and sliding fugacity paths are similar to fixed activity and fixed fugacity paths, except that the model varies the buffered activity or fugacity over the reaction path rather than holding it constant. Once the equilibrium state of the initial system is known, the model stores the initial activity a° or initial fugacity / / of the buffered species or gas. (The modeler could set this value as a constraint on the initial system, but this is not necessary.)... 

In an example of a sliding fugacity path, we calculate how CO2 fugacity affects the solubility of calcite (CaC Os). We begin by defining a dilute solution in equilibrium with calcite and the CO2 fugacity of the atmosphere... 

Fig. 14.6. Effect of C02 fugacity on the solubility of calcite (top) and on pH (bottom), calculated at 25 °C using a sliding fugacity path.

Fig. 14.7. Species concentrations (mmolal) in the sliding fugacity path shown in Figure 14.6.

In fixed and sliding fugacity paths, the model transfers gas into and out of an external buffer to obtain the fugacity desired at each step along the path (see Chapter 14). The increment Anr is the change in the total mole number Mm of the gas component as it passes to and from the buffer (see Chapter 3). When... 

Fixed-activity and sliding-activity paths (Sections 14.2-14.3) are analogous to their counterparts in fugacity, except that they apply to aqueous species instead of gases. Fixed-activity paths are useful for simulating, for example, a laboratory experiment controlled by a pH-stat, a device that holds pH constant. Sliding-... 

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. 

The resulting fluid has a pH of about 8.3. To vary the CO2 fugacity, we set a path in which fco2 slides from the initial atmospheric value... 

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