Geochemical Constraints on Mass Transfer

Here we will use a simplified example to illustrate some basic aspects of the mass transport process for carbonates that avoids most of the more complex relationships. In this example, the calcium and carbonate ion concentrations are set equal, and values of the activity coefficients, temperature, and pressure are held constant. The carbonate ion concentration is considered to be independent of the carbonic acid system. The resulting simple (and approximate) relation between the change in saturation state of a solution and volume of calcite that can be dissolved or precipitated (Vc) is given by equation 7.4, where v is the molar volume of calcite. 

This relationship can be modified to calculate (equation 7.5) the commonly used concept of the number (N) of pore volumes of water necessary to cause a given change in porosity ( ). If an ion activity product of 0.4, a change in saturation state 

Let us now consider the problem from the standpoint of calcite precipitation kinetics. At saturation states encountered in most natural waters, the calcite reaction rate is controlled by surface reaction kinetics, not diffusion. In a relatively chemically pure system the rate of precipitation can be approximated by a third order reaction with respect to disequilibrium [( 2-l)3, see Chapter 2]. This high order means that the change in reaction rate is not simply proportional to the extent of disequilibrium. For example, if a water is initially in equilibrium with aragonite ( 2c=1.5) when it enters a rock body, and is close to equilibrium with respect to calcite ( 2C = 1.01), when it exits, the difference in precipitation rates between the two points will be over a factor of 100,000 The extent of cement or porosity formation across the length of the carbonate rock body will directly reflect these 

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