Total dissolved carbon

Chapter 8 describes a similar one-dimensional chain of identical reservoirs, but one that contains several interacting species. The example illustrated here is the composition of the pore waters in carbonate sediments in which dissolution is occurring as a result of the oxidation of organic matter. I calculate the concentrations of total dissolved carbon and calcium ions and the isotope ratio as functions of depth in the sediments. I present... 

The concentrations of the different carbon species depend on total dissolved carbon and the requirement that the solution be electrically neutral, that is, that there be as many negative charges per unit volume as there are positive charges. The total dissolved carbon concentration (frequently called sigma C) is... 

The calculation of the concentrations of dissolved carbon species from total dissolved carbon and alkalinity is carried out in subroutine CARBONATE, presented in program DGC09. I have specified the equilibrium constants as functions of water temperature by fitting straight lines to the values tabulated by Broecker and Peng (1982, p. 151). 

In order to calculate the partial pressure of carbon dioxide, it is necessary to figure the total dissolved carbon and alkalinity as well. I consider three reservoirs—atmosphere, surface sea, and deep sea—as illustrated in Figure 5-1. I distinguish between the concentrations in the surface and deep reservoirs by using a terminal letter. v for the surface reservoir and d for the deep reservoir. 

The total dissolved carbon and alkalinity in the deep sea are given by... 

The difference between the total dissolved carbon in the surface and in deep-sea reservoirs depends on productivity. And the difference between the alkalinity in these reservoirs depends on productivity and also corat, the calcium-carbonate-to-organic-carbon ratio. The carbon dioxide partial pressure depends on the difference between total carbon and alkalinity in the surface reservoir, and all these depend on the total amount of carbon and alkalinity at the start of the calculation in the three reservoirs combined. By adjusting the values of these various parameters and repeating the calculation, I arrive at the following values for a steady-state system that is close to the present-day ocean with a preindustrial level of atmospheric carbon dioxide ... 

I consider a system in which organic matter is oxidized at a steady rate that is a specified function of depth in uniform calcium carbonate sediments. The oxidation of organic matter increases the total dissolved carbon in the pore water of the sediment. The resultant increase in acidity causes the dissolution of calcium carbonate and a consequent increase in alkalinity as well as another increase in total dissolved carbon. The total dissolved carbon and alkalinity are transported by diffusion between different depths in the sediment. 

Odd numbers are total dissolved carbon, even are calcium... 

Figure 8-2 shows the depth profiles of the saturation index omegadel), the solution rate, and the respiration rate. At the shallowest depths, the saturation index changes rapidly from its supersaturated value at the sediment-water interface, corresponding to seawater values of total dissolved carbon and alkalinity, to undersaturation in the top layer of sediment. Corresponding to this change in the saturation index is a rapid and unresolved variation in the dissolution rate. Calcium carbonate is precipitating... 

Fig. 8-1. The evolution of the depth profile of total dissolved carbon. The curves are labeled with the time in years since the beginning of the calculation.

Like the climate system described in Chapter 7, this diagenetic system consists of a chain of identical reservoirs that are coupled only to adjacent reservoirs. Elements of the sleq array are nonzero close to the diagonal only. Unnecessary work can be avoided and computational speed increased by limiting the calculation to the nonzero elements. The climate system, however, has only one dependent variable, temperature, to be calculated in each reservoir. The band of nonzero elements in the sleq array is only three elements wide, corresponding to the connection between temperatures in the reservoir being calculated and in the two adjacent reservoirs. The diagenetic system here contains two dependent variables, total dissolved carbon and calcium ions, in each reservoir. The species are coupled to one another in each reservoir by carbonate dissolution and its dependence on the saturation state. They also are coupled by diffusion to their own concentrations in adjacent reservoirs. The method of solution that I shall develop in this section can be applied to any number of interacting species in a one-dimensional chain of identical reservoirs. 

Fig. 8-9. The evolution of total dissolved carbon (solid lines) and alkalinity (dashed lines) at various depths, specified in centimeters.

I imagine that respiration adds total dissolved carbon at an isotope ratio of delcorg, specified by subroutine SPECS. I further assume that dissolution adds total carbon at an isotope ratio delcarb, also specified in subroutine SPECS. The precipitation of calcium carbonate removes total carbon at an isotope ratio equal to the isotope ratio of the pore water. There is no fractionation associated with either dissolution or precipitation in this system. Because the isotopic value associated with precipitation is different from that associated with dissolution, I have to test the sign of diss before adding the dissolution term to the equation for the rate of change of the isotope ratio in subroutine EQUATIONS. This test is made in the IF statements in this subroutine. 

Fontes, J. -C., Gamier, J. M., Determination of the initial 14C activity of the total dissolved carbon, A review of the existing models and a new approach, Water Resour. Research, 15(2), 399-413 (1979). 

Fig. 3.23 Carbon isotopic composition of total dissolved carbon in some large river systems. Data source Amazon LongineUi and Edmond (1983), Rhine Buhl et al. (1991), St Lawrence Yang et al. (1996)...

In a nuclear waste repository located in basalt, solution pH is controlled by interactions between groundwater and the reactive glassy portion of the Grande Ronde basalt (10). In situ measurements and experimental data for this system indicate that equilibrium or steady-state solutions are saturated with respect to silica at ambient temperatures and above. Silica saturation and the low, total-dissolved carbonate concentration indicate the pH may be controlled by the dissolution of the basalt glass (silica-rich) with subsequent buffering by the silicic acid buffer. At higher temperatures, carbonate, sulfate, and water dissociation reactions may contribute to control the final pH values. 

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