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Champagne, soapy water and a respectable pint of beer have one thing
in common – bubbles. Next time you are faced with a brimming glass or a
bowl of washing-up, look closely at the froth. Even better, shake up an
almost empty beer bottle so that it fills up with foam. The bubbles are
no longer spherical, as they are in isolation, but join together in simple
curving networks as the bubbles compete for space. The shapes that the froth
takes up have more than aesthetic value, however. They help us to understand
how fluid moves deep in the Earth, when rocks melt, ores form and metamorphic
reactions produce new minerals.

Advertisements for mineral water extol the virtues of the years that
the contents of the bottles spend trickling through the rocks that lie beneath
scenic countryside. It is easy to imagine that water moves in a similar
way, in fractures and caves, throughout the Earth’s crust. But this ignores
the effects of pressure, steadily growing as the depth increases, faster
than water pressure builds up in the depths of the sea. Caves would collapse
and fractures close more than about 10 kilometres below ground. Fluids do
still move deep in the crust, but not through such obvious pathways; instead
the flow of fluids depends on the tiny pores that lie between mineral grains.

Rocks are a complex mixture of many chemical elements; they are distributed
between different minerals, and in some cases, fluids in tiny pores within
and between grains. Different minerals need not have different compositions.
If the way in which their atoms are arranged vary, then two minerals will
not have the same physical and chemical properties despite having the same
chemical composition. If a substance such as a mineral or a fluid is homogeneous,
with distinct physical and chemical properties, and can be separated physically
from the rock, it is known as a ‘phase’. For example, quartz, mica, water
or homogeneous molten rock are all phases. The interactions between solid
and fluid phases in rocks determine how the fluids – whether oil, water
or molten rock – seep through rocks where fractures cannot form.

Energy locked up in the contacts between crystals and fluids on their
boundaries has a particular role in controlling this flow. Surface tension
is the most familiar example of how energy is held at the edges of a phase;
a droplet of water does not spread out across a dry surface because the
molecules at its edge are pulled in towards the centre of the drop. The
same forces can be seen in action when oil and water are mixed, pulling
droplets into round shapes, which have the minimal surface area for a given
volume. This distortion cuts down on the energy held at the edges of each
phase. The same drive to cut down on the energy locked up in boundaries
affects solids. Followed to a logical conclusion, this results in a distinctive
pattern of grains known as an equilibrium texture. This is the three-dimensional
configuration of its various phases that gives the material as a whole the
lowest possible internal energy. It looks like the beer froth we started
with; the film of beer surrounding the bubbles represents the network of
boundaries between crystals, and the shapes of the bubbles, the shapes taken
up by the mineral grains.

For a rock made of just one mineral, such as a limestone, and for other
crystalline solids made of one phase, an equilibrium texture is distinctive.
Grain boundaries are either straight or gently curving, and meet at 120
degrees at ‘edges’, where three grains are involved, and at about 109 degrees
at junctions between four grains, the ‘corners’. If you took a slice through
the rock, you would see a pattern of grain boundaries meeting at 120 degrees.
Individual grains of calcite – the dominant mineral in limestone – are all
the same size.

But few rocks are made of just one mineral. The characteristic equilibrium
texture of a rock containing more than one mineral phase is more complicated.
The grain boundaries are still smoothly curved or straight, and the grains
of each mineral are all roughly the same size. But the angles at the junctions
between grains of different minerals are no longer the uniform 120 degrees.
They vary, depending on the surface energies – like surface tension – of
the two phases. But the theory comes into its own when it is applied to
rocks that also contain fluids.

Jean Verhoogen, at the University of California at Berkeley, was among
the first to apply the ideas of textural equilibrium to geology. In 1948
he realised that the forces of surface tension may play an important part
in determining the course of deep geological processes. Among the processes
that Verhoogen considered were the onset of crystallisation of mineral phases
from solution, the formation of ore deposits, how individual crystals grow
within solid rock, as happens in metamorphic reactions, and the development
of gas bubbles in lava flows.

In the late 1970s, following an article written by the metallurgist
W. Beere working for the Central Electricity Generating Board in Gloucestershire,
geologists such as Harve Waff at the University of Oregon realised that
textural equilibrium could help them to understand the role of fluids in
rocks, important for processes in the interior of the Earth. In this case,
theorists have to consider what an equilibrium texture becomes in wet, porous
rock; they found that the fluid fills the space available along the grain
boundaries in a particular pattern, depending on the particular fluid and
solid. And the pattern that this fluid takes up determines whether the rock
is permeable or impermeable. Rather than calculate the energy distribution
for all sorts of different materials from first principles, materials scientists
at first concentrated on experiments to show how the boundaries looked.
They found that the angle between two mineral grains when both are in contact
with a fluid – known as the fluid-solid-solid dihedral angle – was a good
indicator of what the texture would look like, and how the fluid would flow,
at equilibrium.

In 1948, Cyril Smith, a materials scientist from the Massachusetts Institute
of Technology, in Cambridge, Massachusetts, showed that if the dihedral
angle is less than 60 degrees, the fluid in the pores of a solid will spread
into an interconnected network along the network of grain edges, no matter
how little fluid is there. By contrast, if the dihedral angle is greater
than 60 degrees, the fluid will settle into isolated pores at the ‘corners’,
the junctions between four grains; it will not link into a network.

This 60 degrees angle acts as a criterion to predict fluid flow paths
in rocks that have reached textural equilibrium: fluid can flow between
grains only if the fluid occupies a continuous network of pores throughout
the rock – in other words, if the dihedral angle is less than 60 degrees.
If the fluid lies only in isolated pores at the corners of grains – if it
has a dihedral angle greater than 60 degrees – the solid will be impermeable
to this type of flow.

If such impermeable rocks contain a lot of fluid, the isolated blobs
of fluid in the pores may grow so large that they join up along grain edges.
But this pore structure is not stable; it collapses to form large isolated
reservoirs of fluid surrounded by more than four grains of the solid. These
volumes of fluid are unlikely to form in most cases, because pressure is
usually enough to distort or fracture the rock and squeeze it out.

Because rocks in general contain so little fluid, the dihedral angle
provides a way to tell whether a rock will be permeable or impermeable when
its texture achieves equilibrium. But these ideas are useful only if you
understand the conditions under which rocks can reach this ideal state.
Temperatures, pressure and so on must allow processes that lead to equilibrium
to happen faster than those that destroy it.

An equilibrium texture results from grain boundaries moving – as individual
phases dissolve and precipitate elsewhere – and the elements that make up
the different phases diffuse along grain boundaries. All these processes
happen fastest when a solid is highly soluble in the fluid, or when the
rocks are hot enough to speed diffusion significantly.

The main process that destroys an equilibrium texture is deformation.
Cool rocks at shallow depths in the crust (rocks that are reservoirs for
oil and gas, for example) are unlikely to have flow paths controlled by
the dihedral angle, because as such rocks come under stress, they form fractures
that act as conduits for fluids. Higher temperatures both speed diffusion
and make rocks more likely to flow than fracture. Where fractures cannot
form, fluid flow is more likely to be controlled by rock texture. This makes
textural equilibrium a more important control on fluid flow in warmer rocks
– rocks deep in the crust, unusually hot rocks at shallow depths, such as
those near large bodies of molten rock that have pushed their way up into
the crust, and rocks within the Earth’s mantle (the Earth below the crust
and above the core, between about 70 and 3000 kilometres down), for example.

The main advances so far have come for the deep Earth. How fast does
magma escape when rock melts? How much of the mantle, which can flow as
a fluid, is liquid? How uniform is its chemistry? How do its physical characteristics,
such as the rheology (stiffness), electrical conductivity, and the velocity
of seismic waves vary? One problem in particular has been clarified: what
happens between a rock melting and magma flowing to the surface? Melting
rock is not like melting wax; different minerals fuse under different conditions
of temperature and pressure, so varied compositions of molten rock form
at different times. This process is called partial melting; the molten rock
rarely has the same composition as the rock that melted, nor is the rock
left behind identical to the original rock. The various compositions change
depending on how much rock has melted, as well as the temperature and pressure
of melting.

Geologists reasoned that the molten rock either accumulates somewhere
deep in the Earth, or somehow spreads away from the melting rock. All this
happens at temperatures and pressures too high for fractures to form, so
textural equilibrium applies to the fluid movement. Because the physical
properties of rocks in the Earth’s mantle depend on the amount of melt present,
geologists have experimented with partial melting to find out the dihedral
angles for molten rock in a variety of rock compositions. So far, the dihedral
angles of all compositions of molten rock examined are less than 60 degrees.
This is a significant result, for it means that small volumes of magma can
always seep towards the surface along channels at the edges of grains when
a rock is partially molten.

But textural equilibrium has further implications for igneous petrologists
in general. The processes of melting and melt extraction that we see happening
today at volcanoes such as Mount St Helens, the Hawaiian chain and the string
of volcanoes forming the mid-ocean ridges are a necessary component of understanding
the geochemical evolution of the Earth as a whole. No one can look directly
into the Earth, so geologists have to rely on the magma that erupts at the
surface to provide a window into the mantle. To understand the processes
that produce magma we try to reproduce its chemistry by laboratory experiments
in which mantle material is taken to high pressures and temperatures, or
by numerical calculations. The composition of a lava or a magma, the end
result of melting mantle rock, depends in particular on the rate at which
the melt moves away from its parent rock. If the melt stays in contact with
its source until melting has stopped (a process termed batch melting) the
end result will be very different from the rock formed if the melt escapes
as soon as it forms (known as fractional melting). Calculations by Dan McKenzie
of the University of Cambridge have shown that the melting of the mantle
is more like fractional melting than batch melting; the combination of the
low dihedral angle of melts and mantle rocks and the pressure resulting
from the weight of rock above, squeezes the melt from the rock almost instantaneously.
This process is not exactly like simple fractional melting because once
the magma has left its source rock, its composition tends to alter as it
interacts with the minerals as it travels along the tiny channels at the
edges of grains.

McKenzie was the first to apply textural equilibrium to show how magma
finds its way out of the mantle. He calculated that rocks in the mantle
cannot contain more than about 0.1 per cent of their own volume of fluid
before the pressure of the surrounding and overlying rocks squeezes it out,
compacting the remaining solid rock. Unfortunately most experiments to date
have used batch melting models to examine the composition of magmas produced
by melting the mantle. Their results cannot accurately reflect the melting
process for the mantle. Attempts to do this using fractional melting and
taking into account the likely pathways for the melt, in order to understand
the chemical interaction between molten rock and surrounding rocks, are
clearly a high priority for geologists.

McKenzie has also shown that the rate of seepage depends critically
on the viscosity of the magma. Melts rich in carbon dioxide and elements
such as potassium, uranium, and thorium – unusual magmas such as carbonatites
– are not very viscous and move rapidly though the mantle. But they are
very rare as lavas, precisely because of their low viscosity.

If melts move in very small amounts, in other words if they have such
low viscosity that they are quickly squeezed out of their source rock by
compaction, then each small quantity will cool rapidly and soon solidify.
If a magma is going to erupt at the surface then, obviously, the melt must
not solidify on the way. Very low viscosity melts, such as those produced
deep within the mantle, start to move and leave their source rocks when
only 0.001 per cent of the rock volume has melted. These melts, including
carbonatites, will tend to solidify before they can reach the surface. In
contrast, some much more common products of melting, such as granites, are
very sticky and can move only slowly. Although this high viscosity tends
to produce large volumes of melt, they tend to pond and solidify at depth
within the crust, because they move slowly.

Another fruitful area is the flow of fluids through metamorphic rocks.
Textural criteria may help geologists understand the movement of fluids,
such as supercritical water and carbon dioxide, at shallower levels within
the crust. The source of these fluids may be crystallising magmas, rocks
which are being heated enough to drive off volatile fluids, or even rain
and sea water that has percolated down from the surface along deep cracks
and fractures. The passage of these fluids may transport heat or trace elements
and can influence the mineral reactions that take place during metamorphism.
Evidence that fluids have passed through a rock includes differences in
the amounts of minerals, and mineral veins and variations in isotope ratios
of elements such as oxygen and carbon. The ratio of the stable isotopes
of oxygen will vary according to the temperature of the sediment when it
formed and will be very different to the ratio in igneous rocks, which solidify
at much higher temperatures. Water which has come from an igneous rock will
therefore have a different isotopic signature to sedimentary water, and
the passage of such igneous water will tend to alter the isotope ratio of
the sediment by ion exchange. Because large volumes of fluid may be involved,
perhaps even many times the volume of the rock, it is evidently an important
phenomenon which must be understood. So work has begun in several laboratories
to ascertain values of dihedral angles for common rock-forming minerals
with simple fluids like water and carbon dioxide. We also need to discover
under what conditions textural equilibrium will apply and when fluid will
simply flow along fractures.

As a rock heats up during metamorphism, hydrous minerals such as micas
react to lose their water and form minerals that do not contain water within
their structure. Such fluid, produced within the rock itself, escapes along
grain edge channels if the dihedral angle is less than the critical value
of 60 degrees. If the rock and the fluid have a higher dihedral angle, then
the volatile fluids will accumulate in the isolated corner pores. This may
sound as if the rock is impermeable, but as the metamorphic reactions proceed,
they produce more fluid, and the pressure in the pores grows. Rocks cannot
withstand more than a few hundred bars of pressure, so eventually the pore
bursts, forming a crack a few tenths of a millimetre long, which releases
the fluid pressure. These microfractures commonly leave traces in metamorphic
rocks. Because they tend to heal up almost as soon as they form, they are
marked by tiny fluid-filled bubbles that outline where the crack once was.

So the volatile component can always escape from a metamorphic rock,
no matter what the dihedral angle. What this angle does signify is how the
fluid loss happens. For angles greater than 60 degrees, the water will flow
away along microfractures; if the angle is less, the fluid will flow between
grains.

But for another class of metamorphic fluids, those that pass through
a particular body of rock but have been produced elsewhere, the dihedral
angle has a far greater influence on the effects of the fluid. For example,
the chemistry of a fluid and the host rock, which determine the dihedral
angle, can control where and how ores form.

Many sequences of sedimentary rock are made up of units of varying composition,
such as sandstones and mudstones. This layering gives some outcrops a striped
appearance; it can be caused by variations in the source of sediment or
the rate at which it is deposited, for example. In a lake or shallow sea,
mud may accumulate continuously, but layers of sand are washed in only occasionally
when a nearby river floods. If only one of the two rock types in a sequence
has a dihedral angle less than 60 degrees for a particular fluid, only this
lithology can hold the fluid stable in its grain edge pores. Fluid will
concentrate in that rock type, so that it acts as a metamorphic ‘aquifer’,
carrying fluid through the rocks. The division of rocks into aquifers and
impermeable layers may also happen at shallow depths in the crust or in
regions which are in the process of being deformed, when mountains are built,
for example. In these cases, textural equilibrium will not control the permeability
of the rocks. If one rock type is more brittle than another, fluid flow
will be concentrated within the brittle layer, because this will contain
more fractures.

Evidence for this partitioning comes from the distribution of types
of carbon and oxygen atoms through the rocks. When a fluid passes through
a rock, atoms within the fluid interact with the minerals that form the
grains. If the fluid flooding through the rock has ratios of isotopes that
are very different from those normally found in the rock, the fluid will
alter the isotope ratios of the rocks. Such changes brought about by the
passage of fluid will mark only the aquifer rocks.

Fluid will infiltrate the second, impermeable lithology only if the
hydraulic gradient is high enough to force fluid through it, forming fractures
that we later see as veins. If one of these impermeable layers cracks to
form a few large fractures, considerable volumes of fluid can pass along
each conduit. This is how many ore deposits originate. Materials such as
ore minerals dissolved in the fluid can build up large deposits in these
cracks. Understanding how the fluids move through different types of rock
helps researchers to predict where valuable minerals may be found.

But there is a problem with applying the ideas of textural equilibrium
to metamorphic rocks; we know only a little about the conditions in which
textural equilibrium will control fluid flow, and even less about the values
of dihedral angles between rock-forming minerals and geological fluids.
In general, research has concentrated on the characteristics of simple fluids
with either calcite or quartz. This data applies to fluid flow in rocks
composed of quartz or calcite, such as sandstones, limestones, quartzites
and marbles.

Some general points have come from the experiments. Adding common salt
(sodium chloride) to water lowers its dihedral angle with quartz and calcite.
The stronger the brine, the more likely it is that the rock will be permeable
to it. Adding carbon dioxide to water increases its dihedral angle for quartz,
but against calcite the angle depends on the proportion of carbon dioxide
to water; roughly half and half gives the lowest dihedral angle, higher
concentrations of either water or carbon dioxide increase the angle. At
less than about 5 kilometres depth, quartzites are permeable to strong brines
only, but calcite is permeable to intermediate mixtures of water and carbon
dioxide and strong brines. At 10 kilobars pressure, equivalent to a burial
depth of about 30 kilometres, quartzites become permeable to pure water
as well as brines. No high pressure data are available for calcite so far.

Because the existing experimental data are so limited, it is impossible
to completely characterise fluid flow through crustal rocks. Much more work
is necessary to erect a large data set for all the common rock-forming minerals
and complex natural fluids containing compounds such as methane. Another
gap in our understanding is the effect of pressure and temperature on the
dihedral angle and the rates at which rocks reach equilibrium. But the relatively
new field of texture dynamics has already come a long way from beer froth
and soap bubbles. Armed with the new data that is coming from laboratories
around the world, geologists may soon know far more about the flow of fluids
throughout the depths of the Earth.

Marian Holness is al research fellow at the University of Edinburgh.

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THREE INTO ONE MIGHT GO

The flow of more than one fluid is especially interesting to geologists
working in the oil industry. Oil reservoirs commonly contain three fluids;
oil, gas and sea water. These three do not mix (they are known as immiscible
liquids) and have very different physical characteristics. They tend to
behave independently of each other and have different flow paths. The distribution
of just one fluid in a reservoir is a relatively simple problem. Water,
for example, would saturate the pores of a sandstone, and could flow through
the rock relatively easily. But this is not the usual case. Much effort
has gone into working out how the three components of a reservoir fluid
interact and move within their sandstone reservoirs.

If one component, say the oil, is much rarer than the other, the water,
for example, the oil will be in the form of isolated globules. These may
be suspended within the water, as in a salad dressing or sticking to the
surfaces of the pores, depending on the relative sizes of the interfacial
energies of water, oil and the mineral that makes the reservoir rock, often
quartz in a sandstone reservoir rock.

The oil will be isolated within the water, the dominant fluid in the
pores, so the reservoir is effectively impermeable to oil – provided the
interconnections of the pores are not much larger than individual globules.
If the oil forms droplets in the water, the droplets will be held back by
constrictions in the pore network at the same time as the water flows around
them.

Immiscible fluids are also a feature of metamorphic rocks. Water and
carbon dioxide do not mix at low pressures and temperatures, they separate
out – think of the bubbles in a can of fizzy drink. This unmixing also happens
at much higher pressures and temperatures if the water contains some salt.

Unfortunately the enormous body of work which has been done by the oil
geologists is not entirely relevant to metamorphic rocks. Fluid flow in
oil and gas reservoirs all happens at low temperatures (below about 250
°C) where textural equilibrium is not in general relevant.

No one knows exactly how two fluids move within a pore network when
the controlling factor is the balance of inter-facial energies between them
and the surrounding rock. Understanding this is the next big challenge facing
the theory of textural equilibrium.