Updated: November  27, 2001.
Copyright © 2000 by Walt W McNab, Concord, CA, U.S.A. 
All Rights Reserved.

Computer-Mediated Distance Learning

Course on

 

MULTISPECIES 

REACTIVE TRANSPORT IN 

GROUNDWATER

INSTRUCTOR:

WALT W. McNAB

Senior Scientist
Exponent-Failure Analysis Associates
Oakland, California

TOPIC A: BASIC PROCESSES AND EQUATIONS

 Lecture 4: Phase Equilibria

 Introduction

Previously, in Lecture 2, we touched briefly on the subject of equilibration of aqueous species concentrations in the presence of a mineral phase. The example problem cited in that lecture entailed a single mineral phase, calcite (CaCO3), present as an "infinite" solid, and its effect on carbonate equilibria and pH. In this lecture, we will see  that phase equilibria can be much more complex than just this simple scenario. In fact, they may involve multiple co-existing mineral phases, gases, and phases that appear or disappear as a result of changing conditions. Because many types of reactive transport problems involve phase equilibria responses to changes in water chemistry, as a result of transport, an understanding of the processes involved is an important aspect of this course. In this lecture, we will explore the subject of phase equilibria, starting with some of the most basic concepts, moving on to certain situations that must be considered when modeling aqueous systems entailing phase equilibria,. Finally , we'll conclude with an example that covers a particularly instructive problem in phase equilibria: the reaction path model.

 Basic concepts

As a first step, letís define what we mean precisely by the word "phase." One common definition of a phase in a purely physical context is in reference to a particular state of matter, such as a liquid, solid, or gas. In the case of natural geologic materials constituting an aquifer, our definition of a phase refers to a part of a system that is physically and chemically homogeneous and is separated from other parts of the system by sharp boundaries. Thus, for a typical groundwater reactive transport problem, there may be many phases present. Each mineral within the solid (e.g., calcite, quartz, feldspar, clay minerals) constitutes a phase (although, in flow problems, we often refer to the "solid phase". The aqueous solution is a phase in itself (including all of its dissolved cations and anions). The gas in the void space constitutes another phase (composed of various components, e.g., CO2, CH4, etc.). There is always only one gaseous phase in the void space, but there may be a number of liquid phases, e.g., an aqueous phase and a non-aqueous liquid phase (NAPL).

Heterogeneous chemical reactions between the solid phase minerals and the aqueous solution introduce changes in the masses of the mineral phases present, and the concentrations of various aqueous species, through precipitation and dissolution reactions. The use of the term "precipitation" in both geochemistry and meteorology is not just a coincidence. Just as rainfall is associated with a critical water content developing in a portion of the atmosphere, precipitation of a mineral phase occurs (or is at least favored to occur thermodynamically) when its constituent components reach critical activities in the aqueous solution. Taking the meteorological analogy a bit further, we can easily argue that the dissolution process is very much the geochemical analog of evaporation. In this case, the activities of the mineralís constituent components in the aqueous solution are below some critical threshold, so that the mineral is no longer stable and begins to dissolve.

             (Eq.-2) 

The product of the components on the left-hand-side of Eq.-2, divided by the equilibrium constant on the right-hand-side, is known as the saturation index. A saturation index of less than one implies that the mineral does not favor precipitation; rather, if physically present in the system, it will favor dissolution . The mineral phase is said to be undersaturated. Conversely, a saturation index greater than one implies that precipitation of the mineral phase is favorable (i.e., the mineral phase is supersaturated). It should be noted that calculated saturation indices are usually reported in logarithmic form, so that a value that is less than zero favors dissolution while a value that is  greater than zero favors precipitation.

We must recognize that the concept of saturation index is an artifact of the equilibrium model and all of the associated assumptions. In reality, the rates of precipitation and dissolution reactions may be relatively slow (i.e., kinetically inhibited). In other words, just because the saturation index indicates a mineral phase is strongly favored to dissolve or precipitate, it may not necessarily do so at a measurable rate. Furthermore, things can get very complicated when a number of mineral phases are supersaturated at the same time, as only a few of them may be true members of the real mineral assemblage. We will discuss this point in more detail in a moment. Nevertheless, an important point in the solubility product/saturation index relationships holds true regardless of kinetic considerations: in the absence of external sources or sinks of components to a system, precipitation and dissolution reactions are self-limiting. In other words, any precipitation reaction will deplete the aqueous phase of constituent components, lowering the saturation index. Conversely, dissolution reactions enrich the aqueous phase in the relevant components, raising the saturation index.

 Reaction Path Modeling: An Example

 

Letís use an example problem  to further explore in more detail some of the concepts that we have developed above about mineral equilibration reactions.. 

The mineral phase microcline, KAlSi3O8, a member of the feldspar group, is a common constituent of igneous rocks such as granite. Given that microcline is created from very hot magma derived from the Earthís interior, one might imagine that it may not be very stable chemically when exposed at the Earthís surface, where the ambient environment is very different in terms of temperature and pressure, and where water is present to facilitate chemical weathering. Indeed, feldspars, such as microcline, are usually observed to weather into clean minerals in rocks that have been exposed at the surface for long (geologic) periods of time. A possible weathering reaction for microcline may be written as:

             (Eq.-3)

Now letís examine the question as to what can happen to microcline from an equilibrium modeling

         (Eq.-5)

         (Eq.-6)

Now, suppose we were to introduce microcline into pure water (pH =7) as an experiment. What would happen? 

According to one reference (Robie, R.A., Hemingway, B.S., and Fisher, J.R., U.S. Geological Survey Bulletin 1452, 1978) the log equilibrium constants for the reactions given by Eqs. 3 - 6 are 0.875, 8.049, 5.708, and 12.970, respectively. We know that the dissolution of microcline in pure water  will occur in accordance with Eq.-3, but from left to  right, because none of the reaction products (Al3+, H4SiO4, K+) is present at the beginning of the modeling ìexperiment.  Since the

So, how do we figure out whatís going to happen? Reaction path modeling provides a means for studying the sequence of minerals that may appear (and disappear) during incongruent dissolution. Briefly, a reaction path is a path drawn on a phase diagram that depicts the stability fields of various mineral phases as a function of the activities of their constituent components in the aqueous phase (phase diagrams are a very useful tool in geochemical thermodynamics and, again, are discussed in many textbooks). The path reflects changes in the water chemistry resulting from the precipitation and dissolution reactions as mineral phase stability relationships change. We are interested in reaction paths from a reactive transport modeling perspective because the changes induced in the thermodynamically stable mineral assemblages in a given system by reactions, versus those induced by transport, will be an important consideration for many problems.

At this point, weíll have our first look at a geochemical speciation model, one that is capable of simulating a reaction path, for application to our microcline dissolution problem. The model we will be using is PHREEQC, available as a downloadable public domain software package. We will make extensive use of

PHREEQC 

Later in this course as we investigate full-blown reactive transport problems. For this present example, we will not be addressing the numerical model or its user interface for now (this will come later in the course). We will simply take it for granted that we can describe a problem such as the incongruent dissolution of microcline to the model and know that it will solve it for us.

Our reaction path model is fairly straightforward: we start adding microcline to a beaker of pure water at pH =7 in small increments, watching the response of the solution at each step, and continue until the solution will not take anymore microcline (weíll see what this means in a moment). Suppose this happens after we have added 200 micromoles of microcline to the pure water. The only mineral phases we allow the model to consider are those listed in the reactions given by Eqs. 3 - 6.

The results of our simulation ñthe incremental addition of a total of 200 micromoles of microcline to the pure water ñ are shown on Figures 1-3. 

 Let us summarize this process in detail:

At first, as microcline dissolved, the release of Al3+ quickly leads to saturation with gibbsite, Al(OH)3, which begins to precipitate. 

Meanwhile, the concentration of K+ continues to rise unabated until saturation is reach with muscovite, KAl3Si3O10(OH)2, at which point {\em kaolinite} becomes undersaturated and begins dissolving. 

Finally, because the ratio of Al to Si in muscovite exceeds that of microcline, H4SiO4 continues accumulating in solution fails to remove, saturation is eventually reached with microcline itself. At this point, the addition of more microcline will not change the aqueous phase composition and the simulation ends.

Figure 1. Quantities of various minerals present in the system in response to the addition of microcline.

Figure 2. Component activities in the aqueous phase in response to the addition of microcline.

Figure 3. Mineral log saturation indices during in response to the addition of microcline.

 The Gas Phase

Before we wrap up this lecture, letís consider one additional topic: the gas phase. Relationships between component activities in the aqueous phase and the presence of gas phases in contact with the aqueous phase can be addressed using methodologies similar to those applied to mineral phases. The important difference to bear in mind is that while individual mineral phases are always characterized by an activity of one, gas phase activities directly reflect the partial pressure of individual gas species in the gas mixture. 

Thus, unlike the case for solid phase minerals, the solubility product in an equilibrium expression between a gaseous species and its constituent components in the aqueous phase is does not yield a saturation index. Rather, it implies a partial pressure of the gas phase with which the aqueous phase is, theoretically, in equilibrium. This calculated partial pressure is referred to as the fugacity of the gas phase. The concept of fugacity is illustrated as an exercise below.

 PROBLEMS

Problem 1.

 The equilibration of oxygen gas with the aqueous phase can be described by the reaction,

where the log equilibrium constant is 86.08. Given a pH of 7, what is the oxygen fugacity in a water composition with an assumed equilibrium pE of ñ4.5, corresponding roughly to methane-producing conditions? Comment on the result ñ do you think this quantity is physically measurable? If not, can you think of why it may be useful anyway for characterizing certain types geochemical problems. Try

ANSWER

Problem 2.

 Consider what would happen if quartz, SiO2, were included in the reaction path model for the incongruent dissolution of microcline, as characterized by the reaction,

Qualitatively, what changes would you expect to the mineral reaction sequence is the equilibrium constant for the above reaction is very high? Or very low?

ANSWER

You are now ready to continue to

LECTURE 5: Ion Exchange and Surface Complexation.

You may e-mail me questions and comments.

Walt W. McNab
E-mail address: Walt McNab <WaltMcNab@prodigy.net>

Copyright Notice

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANSWER TO PROBLEM 1.

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At pH 7 and pE ñ4.5, the logarithm of the oxygen fugacity is ñ73.1.  Clearly, 10-73.1 is not a physically measurable quantity and is illustrative from a theoretical standpoint only.  Also, from this expression, it follows that at {O2(g)} = 0.21 and at pH 5, pE = 15.6, whereas at pH 8, pE = 12.6.  If oxygen is the only oxidizing agent in the system, then the capacity of the system to oxidize reduced species is fixed.  That is why oxygen fugacity is sometimes a more satisfactory measure of the redox capacity of a system; it is absolute, whereas pE is always coupled with pH.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANSWER TO PROBLEM 2.

The presence of quartz in the modeled microcline dissolution problem would remove H4SiO4 from solution upon saturation if the equilibrium constant is were very small (a large equilibrium constant would favor formation of the product as the reaction is written).  This would interfere with the ability of kaolinite and muscovite to form.