Calcite equilibrium model

Two geochemical models were used to quantify the exchangeable C reservoir (1) a theoretical model based on calcite equilibrium control (calcite equilibrium model), and (2) an empirical model based on measured losses of CO2 from a surrogate unsaturated zone atmosphere to unsaturated water-sediment mixtures (CO2 retention model). 

According to the calcite equilibrium model, Pick s second law for C02 diffusion in the unsaturated zone can be generalized as ... 

III. P C02 values that were calculated using the calcite equilibrium model (column A) were within 1 standard deviation (S.D.) of onsite mean P C02 data (column B) only at the piezometers located in the borehole nearest the trench. Simulated P C02 values for piezometers at the second and third borehole were substantially larger than measured values. Decreasing the source term for C02 at the trench produced a fit to the onsite data at either the second or third borehole, but simulated P C02 values at the two remaining boreholes were unlike the onsite data. 

The simulated C02 fugacity matches the initial reservoir C02 content and indicates that the pH is buffered by C02-calcite equilibrium. Further modelling was carried out using the Geochemists Workbench React and Tact modules with the thermodynamic database modified to reflect the elevated P conditions and kinetic rate parameters consistent with the Waarre C mineralogy. The Waarre C shows low reactivity and short-term predictive modelling of the system under elevated C02 content changes little with time (Fig. 1). 

For the calculations, averages of the results of the two 5. -equilibrium models of Ca2+ = 35 p.p.m., Mg2+ = 7 p.p.m., and alkalinity = 1.55 X 10 3 equiv./liter are used. Solubility data of Larson and Buswell (11), carbon dioxide solubility data of Hamed and Davies (2), and the carbonate ionization data of Hamed and Hammer (3) and Hamed and Scholes (4) are used. Linear interpolations are made for dolomite between pK(soly) = 16.3(5°C.) and 17.0(25°C.). Equations outlining the calcite and dolomite calculations are ... 

To display the secondary Y-axis for the calcite saturation index besides the primary Y-axis with the concentrations for Ca and C, Chart options / Show secondary y-axis must be chosen by click on the right mouse button in the graph. The result of the modeling can be seen in Fig. 72. The figure depicts a convergence to the calcite equilibrium. However, the saturation index shows that... 

Most natural water systems in contact with calcite (oceans, rivers, lakes, carbonate rock aquifiers) are, however, near equilibrium, and PCO2 dependence cannot be ignored. According to our model, the rate of backward reaction is a significant function of surface pH, and surface pH is determined by calcite equilibrium at the surface PCO2. At the relatively high pH, low PCO2 conditions of most natural waters, the surface pH is least well defined and may depend, in part, on the flux of CO2 between the surface and bulk fluid. 

Thus the surface seawater, at 25°C (p = 1 atm), is oversaturated by a factor of 7 with respect to calcite. The model equilibrium system has a slightly higher pH value and a [Caj] approximately seven times smaller than that of the surface seawater. 

Modelling calculations were performed for Crooks Gap and Bonanza to determine how much calcite could dissolve given sufficient time to reach equilibrium between calcite and the added CO2. The purpose of the calculations was to determine how far from equilibrium the natural systems were, and to assess the potential for using a thermodynamic equilibrium modelling program to predict well bore scale (discussed in the next section). 

Laboratory measurements of the losses of CO2 and C02 from a surrogate unsaturated zone atmosphere to unsaturated sediments indicate the presence of an adsorbed C phase that can retard C02 transport in the unsaturated zone. Measured losses of CO2 from the atmosphere were 8 to 17 times greater than those predicted by calcite equilibrium calculations. Modeled predictions of C02 transport in a cross section near buried low-level radioactive waste support the presence of the adsorbed C phase distribution of P C02 was more accurately simulated using a model of C02 retention based on measured CO2 -loss isotherms than with a model based on calcite equilibrium control. Failure to account for the adsorbed C phase can lead to substantial errors when using models to estimate C transport and exchange in the unsaturated zone. 

Fig. 15.3 Geochemical model calculation using the program PHREEQC. To an oxic seawater with calcite in equilibrium (cf. Table 15.4) an organic substance is gradually added automatically leading to a redox reaction. The system should continue to be open to calcite equilibrium, but sealed from the gaseous phase...

Fig. 15.4 Geochemical model calculation using the program PHREEQC. In an anoxic system (state at the end of the model calculation from Fig. 15.3), the gradual addition of organic matter to the redox reaction is continued, whereby the system is kept open for calcite equilibrium and sealed from the gaseous phase. Initially, the dissolved sulfate will be consumed, in the course of which low amounts (logarithmic scale) of methane will emerge. Only after the sulfate concentration has become sufficiently low, will the generation of methane display its distinct increase.

By this reaction, we can expect the modeled fluid to be rather acidic, since it is rich in potassium. We could have chosen to fix pH by equilibrium with the siderite, which also occurs in the veins. It is not clear, however, that the siderite was deposited during the same paragenetic stages as the fluorite. It is difficult on chemical grounds, furthermore, to reconcile coexistence of the calcium-rich ore fluid and siderite with the absence of calcite (CaCOs ) in the district. In any event, assuming equilibrium with kaolinite leads to a fluid rich in fluorine and, hence, to an attractive mechanism for forming fluorite ore. 

Fig. 24.1. Volumes of minerals (amorphous silica, calcite, and sepiolite) precipitated during a reaction model simulating at 25 °C the evaporation of Sierra Nevada spring water in equilibrium with atmospheric C02, plotted against the concentration factor. For example, a concentration factor of x 100 means that of the original 1 kg of water, 10 grams remain.

In fact, the choice of CO2 fugacity has little effect on the mineralogical results of the mixing calculation. In the model, the critical property of the Fountain fluid is that it is undersaturated with respect to calcite, so that calcite dissolves when the fluid mixes into the Lyons. Because we assume equilibrium with dolomite and magnesite, the saturation index (log Q/K) of calcite is fixed by the reaction... 

To set up the calculation, we specify initial isotopic compositions for the fluid and calcite. We choose a value of —13 %c for r) 18 Os mow of the Lyons fluid, reflecting Tertiary rainfall in the region, and set the calcite composition to +11 %o, the mean of the measured values (Fig. 25.4). We further set S13C pi)B for the fluid to — 12 %o. We do not specify an initial carbon composition for the calcite, so the model sets this value to — 11 %c, in isotopic equilibrium with the fluid. Again, this value is near the mean of the measurements. 

In a final application of kinetic reaction modeling, we consider how sodium feldspar (albite, NaAlSisOs) might dissolve into a subsurface fluid at 70 °C. We consider a Na-Ca-Cl fluid initially in equilibrium with kaolinite [Al2Si20s (OF )/ ], quartz, muscovite [KAl3Si30io(OH)2, a proxy for illite], and calcite (CaC03), and in contact with a small amount of albite. Feldspar cannot be in equilibrium with quartz and kaolinite, since the minerals will react to form a mica or a mica-like... 

To see how this process works, we construct a model in which reaction of a hypothetical drainage water with calcite leads to the precipitation of ferric hydroxide [Fe(OH)3, which we use to represent HFO] and the sorption of dissolved species onto this phase. We assume that the precipitate remains suspended in solution with its surface in equilibrium with the changing fluid chemistry, using the surface com-plexation model described in Chapter 10. In our model, we envisage the precipitate eventually settling to the stream bed and hence removing the sorbed metals from the drainage. 

Lafon, G. M., G. A. Otten and A. M. Bishop, 1992, Experimental determination of the calcite-dolomite equilibrium below 200 °C revised stabilities for dolomite and magnesite support near-equilibrium dolomitization models. Geological Society of America Abstracts with Programs 24, A210-A211. 

Estimates of storage capacity based on simple flow and equilibrium geochemical models indicate that the Rose Run Sandstone, by itself, potentially can store 30 years of emissions from the five largest coal-burning power plants in eastern Ohio. Ultimately the injected C02 can dissolve into the brine and be converted to the stable, immobile, carbonate mineral phases, primarily siderite, dawsonite, and calcite. 

The activities of Mg++ and Ca++ obtained from the model of sea water proposed by Garrels and Thompson have recently been confirmed by use of specific Ca++ and Mg++ ion electrodes, and for Mg++ by solubility techniques and ultrasonic absorption studies of synthetic and natural sea water. The importance of ion activities to the chemistry of sea water is amply demonstrated by consideration of CaC03 (calcite) in sea water. The total molality of Ca++ in surface sea water is about 10 and that of COf is 3.7 x 1C-4 therefore the ion product is 3.7 x 10 . This value is nearly 600 times greater than the equilibrium ion activity product of CaCO of 4.6 x 10-g at 25°C and one atmosphere total pressure. However, the activities of the free 10ns Ca++ and COj = in surface sea water are about 2.3 x 10-3 and 7.4 x 10-S, respectively thus the ion activity product is 17 x 10 which is only 3,7 rimes greater than the equilibrium ion activity product of calcite. Thus, by considering activities of sea water constituents rather than concentrations, we are better able to evaluate chemical equilibria in sea water an obvious restatement of simple chemical theory but an often neglected concept in sea water chemistry. 

Fig. 2. Logarithmic activity diagram depicting equilibrium phase relations among aluminosilicates and sea water in an idealized nine-component model of tire ocean system at the noted temperatures, one atmosphere total pressure, and unit activity of H20. The shaded area represents (lie composition range of sea water at the specified temperature, and the dot-dash lines indicate the composition of sea water saturated with quartz, amotphous silica, and sepiolite, respectively. The scale to the left of the diagram refers to calcite saturation foi different fugacities of CO2. The dashed contours designate the composition (in % illite) of a mixed-layer illitcmontmorillonitc solid solution phase in equilibrium with sea water (from Helgesun, H, C. and Mackenzie, F T.. 1970. Silicate-sea water equilibria in the ocean system Deep Sea Res.).

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