COMPUTER MODELLING OF ORE BODY FORMATION BY A MULTI- DISCIPLINARY APPROACH: SOME INITIAL RESULTS PERTAINING TO THE COOLING OF BURIED BODIES OF MOLTEN ROCK (MAGMA CHAMBERS) AND ATTENDANT HYDROTHERMAL CIRCULATION
A. Rice
Professor Rice is in the Departments of Physics and Geology, Rhodes University, Grahamstown, 6140 South Africa
The initial efforts of a computational program at Rhodes University to model the formation of mineral deposits are reported here. The object of the exercise is to determine theoretically the preferential spatial distribution of minerals of economic interest arising from magmatic and hydrothermal processes; for instance, to yield useful constraints such as the evolution of the 350 degrees C isotherm -- important to the deposition of gold -- as heat is pushed out into the country rock and retreats during back cooling. It is apparent from our purely theoretical calculations that, even for simple systems, considerable complexity is to be expected and the modelling has allowed the advance of explanations for mineralisation, whose formation has been enigmatic, such as some tin and molybdenum deposits. If such information saves drilling an exploration hole, then the computational effort has paid for itself Modelling such as this undertaken for geology of interest is relatively inexpensive compared to other assessment techniques and it appears that it will be a valuable tool to add to and complement time-tested procedures.
It is common in the petroleum industry to undertake massive computer modelling of the physics of oil reservoir behaviour to predict the response to extraction and to improve estimates of reserves. Theoretical modelling of the formation of such reservoirs is also undertaken to understand their 'architecture' better; this also assists reserve estimation.
Such modelling involves the computational assessments of the flow of water, gas, oil and other chemistry in rock formations of variable permeability, geometry, and fault and fracture zone distributions. Although much of the petroleum industry's efforts in this area are proprietary, work done by centres such as the Department of Mathematics at the University of Wyoming lies in the public domain. The emplacement of hard rock mineralisation, that is, rocks bearing gold, iron, copper, and other commercially important metals, also entails transport and thermal processes analogous to those that lead to the formation of oil deposits and which govern their commercial exploitation.
Even though the geology and geochemistry of hard rock mineralisation are state-of-the- art bodies of knowledge, the physics of the emplacement of these deposits has not been studied with the intent to assist exploration and exploitation. Rhodes University is attempting to redress this situation with the construction of a modelling package composed of commercial finite element computer codes. The goal of the program is to provide a computer code to which a client may introduce the environment (for instance, geometry, rock permeabilities, temperatures, and orientation of fracture zones) which is believed to have attended the formation of a geologic unit in which they have interest and receive back from the code predicted distributions of mineralisation, some ideally of economic import. These distributions are derived from the finite element solutions of equations describing solidifying and/or porous media flow and chemical transport within
the earth's crust. Our goal includes the training of personnel capable of undertaking these investigations. The effort contributes to a better margin of success for South African industry in exploiting and locating important mineral resources. This in turn affords economic advantages and provides an improved competitive edge in the international arena. The effort is supported by a partnership with industry and various research institutions. The nature of the study is multi-disciplinary and has therefore required the involvement of various academic disciplines (see Box).
The physical models we aim to reproduce theoretically are the distribution of mineralisation in surrounding country rock due to hydrothermal circulation (such as is responsible for hot springs) driven by the heat of solidifying magma chambers and the final distribution of mineralisation in the chambers themselves. By a magma chamber, we mean a body of molten rock emplaced within the crust of the earth. In the two years this effort has been under way, Rhodes University has performed the first 3-D calculations of magma chamber convective cooling. The calculations involve the finite element solution of equations describing fluid flow both in magma and permeable 'country rock', that is, the rock surrounding the magma chamber. This effort is also the first to include all of the following effects together: variable viscosity magma, solidification at the walls, the coupling of hydrothermal circulation in the country rock to the cooling history of the magma chamber and all with wide flexibility regarding the configuration of the geology.
This also includes spatial variation in material properties such as permeability. These input parameters are, for the most part, known. Ours are also the first calculations to attain reasonable Rayleigh numbers for magma chambers (e.g. 1014), and hence represent the first magma convection modelling that is truly turbulent. The Rayleigh number is a function of the degree to which convection enhances heat transfer over that of conduction alone. The higher the Rayleigh number, the more vigorous the circulation within a magma chamber. The modelling effort is performed on commercial codes provided by ANSYS, Inc., an engineering software company based in Pittsburgh. These codes possess extremely robust benchmark histories running over several decades and are supported by a large technical staff. The codes already have a proven history in depicting materials similar to those under consideration here and have seen singular success in application to geological problems such as the basin formation modelling program run by the Geology Department at the Free University of Amsterdam under the direction of Sierd Cloetingh as well as areas elsewhere.[1]
Some results
A general observation in the 3-dimensional computations is that complex structure in temperature distributions and flow patterns will develop even though the initial magma chamber geometry was completely symmetric (for instance, a simple cylinder) as well as the applied initial conditions. That is, if a completely uniform temperature distribution is initially imposed within and around the sides of a geometrically simple chamber (such as a cylinder), this distribution of temperature will eventually take on considerable structure with lobes of hot material intruding cold material. This demonstrates a radical departure from the circulation patterns inferred for 2-D calculations. In the case of highly silicic magmas (such as granites), which are very viscous and flow very slowly, our calculations of 3-D convection indicate the possibility of the development of spirals, much like wisps of smoke from a pipe. Such flow would correspond to that expected for a granitic stock (a
somewhat cylindrical magma chamber with its axis orientated in the vertical). The hot column of rising fluid does not impinge necessarily in the centre of the roof but often goes to the outer edges. The hot plume may also wander about, resting in one position for a while, then moving off to settle on another section of the roof. We find in this behaviour a possible explanation for the formation of mineralised cupolas, the hot plume eroding into the roof of the chamber at one locality, then moving off to erode elsewhere and forming another cupola there. The tortuosity of the flow in the 3-D case tends to leave a twisted, helical column behind, not at all spherical, but quite elongated in the vertical, wherein the last of the warm rock resides. These computationally derived features are similar in form to classic molybdenum/tin porphyries. In particular, the directed flow impinging on the roof may, in some cases, break through. This could provide an explanation for those molybdenum/tin deposits associated with a series of brief eruption events. Even the initial results of this program have therefore provided useful insight into processes of emplacement of ore bodies and have allowed us to propose explanations for field observations that had previously lacked any clear understanding.
Less viscous (that is, more basaltic) magmas in chambers of uncomplicated form show more intense flow which is more cellular in structure. The tendency is not to spiral upward, but simply to rise at the centre and sink at the sides. The temperature distributions are not symmetric in the early cooling histories of these chambers, however, which take on structures that resemble the form of molars (as in teeth), roots and all. In all cases of vigorous flow, the convection of magma is not steady, but displays occasional surging characteristics. Further, particle trace studies in the computations indicate the circulation will actually precess in cases: that is, the flow not only rises to the top to sink at the sides but can also translate in azimuthal directions around the vertical. The lack of symmetry in the response of the country rock is also evident, even though the initial conditions of the problem are completely symmetrical. This reflects in part the complexity of the temperature distribution that eventually develops at the walls due to the vagaries of convection. The implication is that even under rather uncomplicated conditions in the surrounding geology or in the configuration of the magma chamber, 3-D calculations show that the end results have considerable structure which extends well out into the country rock as is also the case for the mobilisation of hydrothermal flow. This 'chaotic' behaviour for which fluids are famous would be in accord with the nonlinearities that attend them. It is clear that even rock possessing uniform permeability throughout (that is, isotropic in nature) will host complex patterns of ground water flow that are not at all symmetric about a heat source that was initially symmetric. The hydrothermal flow seems to prefer, in cases, to depart from one side of a completely symmetric magma chamber, the flow extending outward in the horizontal in a long limb rather than immediately being buoyed upward. There may be analogues to this behaviour in nature.
Cases in point are mesothermal gold deposits, which extend laterally away from intrusive bodies for some distance such as occurs at Pilgrim's Rest in Mpumalanga. It is also clear that the ground water flow and magma chamber cooling are truly coupled phenomena:
one influences the other. Figure 2 displays graphically the computer calculations of ground water velocity magnitude (not direction!), showing preferential distribution of flow to one side of the spherical magma chamber even though the initial temperature distribution in the surrounding country rock was uniform, as was the temperature in the
magma (albeit higher). This is an important result as the role of the movement of ground water in the formation of ore bodies cannot be over-emphasised. Heating the water enhances its capacity to dissolve chemicals, which it carries in solution elsewhere due to convection through permeable zones in the crust of the earth. As a result of either cooling or encountering different chemistry in the earth, or both, these solutes are eventually deposited away from their source.
Viscosities of magmas are strongly temperature dependent and can increase by 10 orders of magnitude during the cooling history of the magma chamber. This effect indicates the convection of magma in protrusions of the chamber into country rock will quickly choke and come to a halt. This is due to the enhanced cooling of the magma at edges, wedges, and other peripheral features.
High Rayleigh number convection, which implies relatively vigorous flow, which would attend mafic (basalt-like) melts because of their small viscosities, indicates even further complexity in the temperature and velocity distribution of the magma while cooling. The number of convection cells rises with increasing Rayleigh number and these cells develop, disappear and redevelop. This imposes attendant changes in the boundary layers wherein it has been postulated that most of the important mineralisation aggregates, in particular, the platinum group elements (PGEs).[2] Boundary layer thicknesses will vary, then, across the chamber and hence so will their ore grade if 'convective scavenging'[2]
takes place. Convective scavenging is a process by which the first material freezing from the magma tends to concentrate in regions of high shear such as boundary layers. Figure 1 displays a still shot of travelling waves that occur in basalt-like magmas.
There have been other surprising outcomes that have important implications for the Bushveld Complex of South Africa. This region of geologic renown is located north of Pretoria and contains about 80% of the world's known platinum reserves. There are researchers who hold that the Bushveld was emplaced in a series of pulses. This opinion, however, is not free of difficulties, one being manifestations of contamination by surrounding country rock and another being the question of understanding the mechanism that so meticulously metres out pulses of input.
Magma is a multi-component melt. Some of its constituents have higher melting points than others. As the magma cools, the first material to be precipitated into the melt as solid particles (referred to as crystals) is that of the highest melting point. It has been demonstrated that suspended loads of these crystals are carried by magmas and their influence must be included in ascertaining the 'effective' density of the melt (as water content must be included to determine the full force exerted by the winds of a hurricane).[3] The inclusion of this effect on density in computational models of convection in magma chambers apparently serves to split the chamber into a series of horizontal convecting layers. This is caused by the buildup of crystal content in the magma as the magma cools against the cold roof and walls of the chamber. The crystal- laden portion of the melt eventually slumps to the bottom of the chamber, where it continues to convect as a new layer of magma at the bottom.[4] This slumping process will repeat itself several times to yield from a single input features often accorded to multiple inputs.
Verification of the splitting process was found in the literature of other disciplines,[5,6]
such as mechanical engineering (for instance, transport of slurries, fluidised beds), limnology and the mechanics of sedimentation in stream beds. Further, these other disciplines have quantified these processes independently of our own computer-generated observations and provide the thicknesses of the splits. The splits are expected to remain relatively constant throughout the life of the chamber.
Figure 3 depicts the implications. A build-up of a suspended load of crystals in the melt with heat loss from the magma raising the temperature of the roof leads to turbidity currents (see Fig. 3a) that carry the suspended load to the bottom of the chamber to form a new layer there. It can be shown that the suspended load in the new, bottom layer is yet far from settling. This new layer, suspended load and all, continues to convect. The new, lower layer displaces the hotter remaining magma to the roof of the chamber. This sustains high temperatures at the heated roof, and secures significant assimilation of roof rock into the magma: at least of the first low-melting point components of the roof rock (see Fig. 3b). The new layer now adjacent to the roof eventually cools to repeat the process as before: a second turbidity current laden with a suspended load of crystals descends downward (see Fig. 3c) to rest atop the first, which has continued to cool to retain a higher density, preventing its displacement by the descent of the second turbidity current. Again, remaining magma is forced to the roof (see Fig. 3d) but, since the chamber has seen continued cooling, temperatures have dropped and the convection is less vigorous, hence the assimilation of roof rock abates as predominantly high-melting point components are left to erode away. The final distribution of contamination from the roof rock is then: little in the bottom layer, most in the middle layer, and an intermediate amount in the top layer (see Fig. 3e). Although the magma is assumed to be of uniform composition when it was emplaced, these splitting processes serve to alter it. This introduces both temperature and compositional gradients in the vertical, which brings into play double diffusive convection mechanisms. This causes the initial stratifications to break up into many layers as depicted in Fig. 3f. If the vertical distribution of strontium ratios (87Sr/S6Sr) in the final frozen magma chamber is determined by the degree of roof rock contamination, then the Sr ratio distribution by the mechanism put forth here follows that often reported for the Bushveld Complex (see Figs 3g and 3h).
The Bushveld was emplaced in the vicinity of an older geologic unit, the Pretoria Shales, which seem to be the most likely candidate for the source of the contamination. It has been suggested elsewhere[2] that dispersive pressure along with shear aggregation will cause those crystals first out of the melt -- hence those rich in PGEs -- to populate preferentially the boundary layers separating different stratifications of layers of suspended load. As double diffusion processes lead to a multiplicity of boundary layers about the original ones, these new layers will also accumulate crystal content but to lesser and lesser degrees as indicated in Fig. 3h. Depending on initial viscosities, depth of chamber and other factors, there are variations on the basic mechanism outlined above:
there may be more or fewer layers, and they may have different thicknesses.
Quantitative estimates may be made of their number and thicknesses. One important aspect stands out in making these estimations: the thicknesses of the layers carrying suspended load are critically dependent on the thickness of the remaining magma from
which they are formed[.[1,5] and show an exponential-like increase with the thickness of the melt from which they are derived. This means that if a magma 10 km deep yields an initial layer 1 km deep at the bottom, then given the same conditions (of temperature, composition, crystal load), a magma chamber initially 7 km deep will yield an initial layer some 590 m in thickness. Similarly, a magma 3 km deep will yield a layer 160 m thick and a chamber 500 m deep will yield a layer 11 m thick. The implications of this behaviour are depicted in Fig. 3i, which shows the variation of PGE enrichment (to be expected from the suspended load) versus initial depth of the magma chamber in green.
Further, the shallower the chamber, the less efficacious the scavenging process and the longer it takes to scavenge the PGEs into concentrations that are economically interesting. This is because velocities and shear rates are less in the shallower fluids. That is, not only are there less PGEs to scavenge in the shallower layers (hence a lower 'R factor',[7] which is the ratio of magma to sulphides, the partition coefficients between sulphides and the PGEs being sufficiently great to ensure that although the PGE content of magmas is not great, a large amount of magma ensures a large deposit), but it is even less likely that they will be concentrated. The red bars in Fig. 3i depict the combined effect of both the R factor and the efficacy of scavenging in terms of magma chamber size. The combination of both the R factor and scavenging efficacy provides a rationale for the observation that only the thick-layered intrusives yield PGE deposits that are economically worthwhile.
Conclusions
Although the methodology employed in addressing the above issues has been well benchmarked elsewhere and on simple geologic systems that have been amenable to calculation by other means, this latest effort has pushed off into a completely unexplored area. We have been encouraged, however, by the fashion in which the computations have yielded for the appropriate environment, characteristics that have been seen in the field.
We do seem to be replicating the geology. And we have discovered potential explanations for observations that until now have not been understood. Some of the processes we have inadvertently uncovered are rather surprising and simple but carry with them quantification and replicate the complexities seen in nature. We need to do more benchmarking against real geology and have assembled a database to do so. This year's forthcoming effort will attempt to incorporate the transport of chemical species as well. At a minimum, the project has opened up an area of research which must be pursued before the emplacement of ore bodies is completely understood: the physics.
That is, the hydrodynamics of the convective processes attending solidifying magma chambers and the associated ground water circulation and their mutual role in transporting important chemistry through the rock. The program further provides the mining community with an additional, valuable, yet relatively inexpensive tool with which to complement classical exploration procedures.
1. Rice A., Betha A., Harrison K., Moore J., Clayton R, Panagon S. and Watkins K.
(1997). 3-Dimensional calculations of transport processes associated with convection in freezing magma chambers and attendant hydrothermal circulation in country rock. Proc. South African Geophysical Association Fifth Technical Meeting, Swakopmund, pp. 77-80.
2. Rice A. and von Gruenewaldt G. (1994). Convective scavenging and cascade enrichment in Bushveld melts: a possible mechanism for the concentration of PGEs and chromite in mineralized layers. Trans. Inst. Min. Metall., 103, B31- B38.
3. Rice A.R. and Eales H.V. (1995). The densities of Bushveld melts: textural and hydrodynamic criteria. Mineral. Petrol. 54, 45-53.
4. Van den Berg A. and Rice A.R. (1993). Low and then intermediate Rayleigh number numerical models of magma chambers: on the trail to the Bushveld. Proc.
Symposium on Layering in Igneous Complexes, Wager and Brown 25th Anniversary Commemorative Meeting, University of the Witwatersrand, Johannesburg, 8-10 Sept., pp. 102-103.
5. Rice A. (in press). PGE enrichment due to the splitting of freezing magma chambers by suspended crystal loads. Explor. Mining Geol.
6. Xuequan E. and Hopfinger E.J. (1990). Stratification by solid particle suspension.
In Stratified Flows, eds E.J. List and G.H. Jirka. American Society of Civil Engineers, New York.
7. Campbell I.H. and Naldrett A.J. (1979). The influence of silicate sulfide ratios on the geochemistry of magmatic sulfides. Econ. Geol. 74, 1503-1505.
Fig. 2. A schematic illustration of computed ground water velocity magnitudes (not direction!) in country rock driven by the heat of a spherical magma chamber. The lighter the colour, the greater is the magnitude of the ground water velocity. The chamber is embedded in a cube of country rock 5 km to a side. Although the country rock was assigned uniform permeability, there is a preferential distribution of flow to one side of the spherical magma chamber as indicated by the orange-yellow blobs signifying enhanced ground water flow in this region. This occurred even though the initial temperature distribution in the surrounding country rock was uniform (at 100 degrees C) as was the temperature in the magma (albeit higher, at 1100 degrees C). Although the outline of the chamber is discernible, there is no ground water flow in it at this stage as there is still enough heat from the chamber to maintain a hydraulic gradient (due to thermal expansion) which forces ground water away from it.
S: Fig. 3. A series of figures showing the evolution of a thick but single input magma chamber and the effect of chamber thickness on potential ore grade for platinum group elements. The text discusses each inset in detail. Note, however, that the nomenclature la- le in the diagrams designates the history (a-e) of the initial pulse of magma I as part of it splits into new layers of magma II and III.
MAKING IT HAPPEN
The team members of this cooperative effort are as follows: From the South African research programmes, the cooperative funding agency THRIP, which is managed by the Foundation for Research Development, is involved. The South African Council for Geoscience also participates. Industry representatives Include: Anglo American Corporation of South Africa; Gencor/Billiton; RTZ Mining and Exploration; Gold
Fields/Goldco of South Africa, and BHP Minerals. The industrial partners also provide scientific input. From the university side the effort comprises a team of five departments at Rhodes: Geology, Physics, the Institute for Water Research, Information Systems, and Computer Sciences and enjoys collaboration with several South African universities and others abroad. There is direct involvement with the University of Fort Hare and contributions from colleagues at the University of Natal, Durban, the University of the Witwatersrand, the University of Pretoria and the University of Cape Town. Overseas collaborators are at, in the UK, the Camborne School of Mines of the University of Exeter and at the University of Manchester, as well as at the University of Toulouse in France. In the main, other universities provide field input with which to benchmark the calculational effort as does the Geology Department at Rhodes. The Information Systems Department has created a data bank to facilitate the benchmarking. The Physics and Computer Sciences departments contribute to the calculational and graphics side, and the Institute for Water Research in particular contributes expertise in ground water flow. A number of students are doing postgraduate degrees and honours students are or have been involved in the programme.
