joseph f botha p.o. box 339, bloemfontein 9300, south africa · pdf filep.o. box 339,...

Modelling subsurface flow in Karoo aquifers

Joseph F Botha

Institute for Groundwater Studies, University of the Free State,P.O. Box 339, Bloemfontein 9300, South AfricaEMail: jopie @ igs. uovs. ac. za

Abstract

Karoo aquifers are without any doubt one of the primary sources for potable water inSouth Africa. Unfortunately, the aquifers have a very complex and unpredictablebehaviour. The general view is thus that Karoo aquifers are not reliable sources ofwater. However, this investigation has shown that the hydraulic behaviour of theseaquifers is largely controlled by the geometry of the Karoo sediments. The result is thatthe flow pattern, in stressed aquifers, is vertical and linear, and not horizontal and radialas was believed previously. This paper discusses a new three-dimensional numericalmodel, that takes these properties into account, and a few field observations supportingthe development of this model.

Introduction

Sediments of the Karoo Supergroup of formations underlie more than 50 % ofSouth Africa. This Supergroup was formed when an intracratonic, forelandbasin, on Gondwanaland, was filled with sediments during the Carboniferous,Permian, Triassic and Jurassic ages . Since Gondwanaland drifted during thisperiod from polar to tropical latitudes, the sedimentation occurred underdifferent depositional environments. The Supergroup thus consists of a numberof sediments each with its own physical properties.

The Karoo formations occur mainly in the semi-arid and arid central andwestern regions of the country, where there are no major rivers, or other surfacewater sources. The potential thus exists for aquifers in the Supergroup to makea significant contribution to the water budget of the country. Unfortunately,Karoo aquifers have a very complex and unpredictable behaviour. The generalview is thus that Karoo aquifers do not contain large quantities of groundwaterand are unreliable sources of water, in agreement with the name Karoo, which

Transactions on Ecology and the Environment vol 17, © 1998 WIT Press, www.witpress.com, ISSN 1743-3541

380 Computer Methods in Water Resources XII

is the Hottentot word for dry. However, there are boreholes that have providedthe residents of farms and towns with water sustainedly for many years, whilelarge volumes of groundwater are pumped daily from mines and the basementsof buildings in areas underlain by the sediments. A number of studies, of whichthe one by Kirchner et al* was perhaps the most detailed, were thereforeundertaken in the past to try to understand these aquifers better and to use themmore efficiently, but with little success.

A major characteristic of Karoo aquifers is the low permeabilities of thedifferent formations. Boreholes drilled into the Karoo sediments thereforeusually have very low yields (< 3.6 nf fr ). However, it is possible to drillboreholes with yields that vary from 18-72 nf lr\ within the formations atjudicially chosen sites. Unfortunately, these high-yielding boreholes have atendency to dry-up suddenly and permanently. This behaviour would not bestrange, if restricted to periods of droughts, which occur frequently in the areas,but it often occurs under 'normal' conditions. Moreover, it is often possible to

drill a new successful borehole within a couple of metres of the one that dried-up, even during a drought! These observations are so contrary to that commonlydescribed in the literature on groundwater flow, that it was decided to re-investigate these aquifers. Fifteen experimental sites, where various types ofhydraulic tests could be performed under controlled conditions, and whosegeology could be studied in detail, were developed for this purpose.

The major result that emerged from these investigations is that a Karooaquifer is not a single entity, but consists of a number of interacting layeredaquifers, with the vertical as the main flow direction. It will thus be useless toanalyse results from these aquifers with a horizontal groundwater flow model,as was done in previous investigations of these aquifers. The three-dimensionalgroundwater flow model of Verwey and Botha^ was consequently used todevelop a model for the Campus Test Site, and verify the result. The Site, whichis situated on the campus of the University of the Free State, and covers an areaof approximately 180X192 nf.

Properties of Karoo aquifers

The Karoo sedimentation ended with the outpour of the Drakensberg lavaswhich can be associated with the second phase of the break-up of Gondwana-land (Fitch and Miller ). This event was not only responsible for the wide-scaleintrusion of dolerite in the sediments, in the form of ring and linear dykes, butalso buried them completely to depths of 2 500-3 000 m . The increase inpressure and temperature, caused by this overburden, compacted and lithifiedthe layers of sand, and even metamorphosized the deeper sediments slightly.The sediments consequently lost a large part of their primary porosity andelasticity, already at this stage.


Computer Methods in Water Resources XII 381

Indications are that the Karoo sediments have not been disturbed signifi-cantly after the end of the Jurassic Period (141 Ma). This gave groundwater the

opportunity to deposit secondary minerals containing carbonates and silica into

the open voids, thereby reducing the porosity of the sediments even further.

Boreholes, drilled into the Karoo sediments, therefore, do not have high yields.Hydrogeologists have known for a long time that high-yielding boreholes

in Karoo aquifers always intersect at least one fracture. However, they alsoassumed that the water is stored within the fractures, and that the fractures arevertically or subvertically orientated. The reason for this believe probablyemanates from the observation that the intruding magma has baked andfractured the surrounding Karoo formations considerably in the vertical direc-tion. Boreholes in Karoo aquifers are, consequently, usually sited next todolerite dykes. However, the present investigation showed that these fracturescan affect the yields of the boreholes adversely, and that they usually do notoccur next to ring dykes, which seemed to have more metamorphosized theformations than baked them.

The idea of vertical and sub vertical fractures was so imbedded in the mindsof hydrogeologists in South Africa that they were completely surprised whenthe present investigation revealed that the yields of Karoo boreholes arecontrolled by horizontally orientated bedding-parallel fractures. Although, it isnot possible to explain the existence of these fractures at the moment, indica-tions are that they formed in weak zones created by the intrusion of the ringdykes in the form of laccoliths Botha et al*.

The apertures (~ 1 mm) and densities (~ 1 per 20 m) of the bedding-parallelfractures in Karoo aquifers are not very large, but individual fractures may covera considerable area (typically from 5 000-100 000 nf, and even more). Thefracture, therefore, can only store a limited volume of water; certainly not

enough to supply a high-yielding borehole continuously with water. Thisobservation suggested that the formations themselves, and not the bedding-parallel fractures, are the major storage units of water in Karoo aquifers. Thisconcept, was confirmed by drilling 11 core-boreholes on the experimental sitesand analysing hundreds of hydraulic tests, performed on these aquifers.

One consequence of the previous interpretation of is that the flow in Karooaquifers must be mainly vertical. Flow in these aquifers should, therefore, bemodelled with a full three-dimensional model, which takes the internal geom-etry of the aquifer into account.

The concept that the behaviour of an aquifer is largely determined by itsinternal geometry may be well-known, but is, nevertheless, usually neglectedBlack . One reason for this is that the methods, commonly applied, are all basedon porous formations, whose geometry is very simple. However, as Blackpoints out this geometry is of vital importance in the analysis and interpretationof aquifer tests in any secondary aquifer. Indeed, there is little doubt that the



neglect of their internal geometry is the main reason why so many difficultieswere experienced with Karoo aquifers in the past (Botha et al*).

Approximations used in the Model

Geometry of the Geology on the Campus Test Site

A first impulse would be to regard Karoo aquifers as fractured aquifers, andapply one of the modern fracture flow models to them. However, cores from theexperimental sites showed that there are very few water-bearing fractures inKaroo aquifers. Moreover, the flow is not restricted to the fracture itself, but alsooccur through a small washed-out domain in the formation adjacent to thefracture. The model for the Campus Test Site was consequently based on theconventional porous flow theory, with the assumption that the rock matrix hasa limited hydraulic conductivity, but high specific storati vity, while the fracturehas a low specific storati vity, but high hydraulic conductivity.

The aquifer on the Campus Test Site actually consists of three layeredaquifers, as illustrated in Figure 1, with the one on top a phreatic aquifer.However, it was assumed in the model that the aquifers were all confined.

Approximation of a Borehole

A borehole is conventionally approximated in horizontal two-dimensional flowmodels as a point source (Huyakorn and Finder ). However, the method cannotbe applied to three-dimensional problems, except to represent the borehole asa series of point sources spread out vertically along the borehole. Since themethod yields a logarithmic singularity at the position of the source, the methodcannot yield an accurate solution for a three-dimensional problem near aborehole (Botha and Bakkes ).

A method that does not suffer from this limitation, is the Dirichlet boundarymethod, introduced by Huang®. In this method, the borehole is considered as aboundary of the aquifer, but instead of prescribing a Neumann boundarycondition, one prescribes an arbitrary Dirichlet boundary condition along theborehole's surface, and adjust that to the discharge rate. Huang's Dirichletboundary condition was consequently added to the Program SATS of Verweyand Botha ) which was then used to model for the Campus Test Site.

Numerical Model of the Campus Test Site

The exact extent of the aquifer on the Campus Test Site is not known precisely.However, the water levels in boreholes on its boundary did not respond to



i ttezometnc Level Aquiier L

-30

-35

-40

Aquifer 3

I MucLstone • Shale Carbonaceous I I Sandstone Mudstones

Figure 1 Illustration of the aquifers on the Campus Test Site and the singlebedding-parallel fracture that intersects all high-yielding boreholes.

pumping in the other boreholes, while packer tests have shown that themudstone layers are highly impermeable below depths of 40 m. The arealextend of the aquifer was therefore taken as 344X380 m and its thickness as40 m, in the model. The cores indicated that the active domain of flowsurrounding the fracture is approximately 0.01 m thick. The fracture was,therefore, represented by two pencil elements, each 0.005 m thick, in the finiteelement mesh of the model. The hydraulic parameters required by the modelwere derived from various hydraulic tests performed at the Site, and assignedto the nodes in the finite element mesh.

The model was applied with excellent results to a number of situations oftenencountered in Karoo aquifers (Botha et al*). The present discussion will,however, be restricted to the simulation of an hour long constant rate hydraulictest, performed on one of the boreholes at the Campus Test Site. In this test thehigh-yielding borehole, UP16, was pumped at a rate of 3,6 nf h'l

An interesting feature that emerges from the simulation is the relationshipbetween the simulated piezometric heads and the water level in the open



u

10

/— N

5 20&Q>Q

30

/in

• H •

g g |Is 1

4Q •

» a •

i i , , i ,^i pi i , , - , i

*

•

# D

Water Level(Observed)

— Initial

0,5 h

_. 1 h

i , , , , , ,

G •

D •

•

Piezometric Level(Computed)

• Initial

Q 0,5 ho 1 h

, i i , i , , ,

1397 1399 1401 1403Water Levels and Piezometric Heads (mamsl)

1405

Figure 2 Comparison of the observed water levels and simulated piezometricheads, in borehole UP16 after pumping the borehole for 0.5 and 1 h.

borehole UP16, shown in Figure 2. This result suggests that the water level inan open borehole does not represent the piezometric level in any of the aquifers,but an average of the piezometric levels of all aquifers weighted in favour of thepiezometric level in the fracture. Hydraulic parameters derived from waterlevels measured in open boreholes will, therefore, not be representative ofKaroo aquifers.

A very interesting result of the model, illustrated by Figure 3, is thebehaviour of the piezometric head in the sandstone compared to that of thefracture. The shape of the dewatering cone of the fracture remains the same,although the actual values decrease with time. The cone of the piezometric headin the sandstone, on the other hand, widens with time, and ultimately approachesthat of the fracture. This indicates that the flow velocity in the fracture willremain constant, as long as the pumping rate does not exceed the rate at whichthe surrounding formations can supply water to the fracture. Boreholes in Karooaquifers thus have an optimal pumping rate, which will be difficult to determinewith conventional methods. One important consequence of this optimal pump-ing rate is that the fracture may be completely dewatered near a pumpingborehole, if the pumping rate is too high, and then collapse. This behaviour isprobably responsible for the 'dried-up' boreholes so frequently observed inKaroo aquifers.

The methods commonly used to analyse hydraulic test data from Karooaquifers, in the past, are all based on the assumption that the flow in theseaquifers is radial. This implies that the drawdown in the aquifers should be a



1 400,0

1399,5

1 399,0

1 398,5

1 398,0

TFracture plane (0,25 h) Plane 1 m above Fracture 0,25 h)

Fracture plane (1 h) Plane 1 m above Fracture (1 h)

_L JL _L _L _L-200 -150 -100 -50 0 50 100 150 200

Distance (m)

Figure 3 Piezometric heads in the fracture plane and a plane l(m) above thefracture in the sandstone layer.

e 1402

(9

"3

^ 1 3982I-oea•oJ * 394u"C*v

IZ 1390 J_ _L J_

0 1 2 3 4 5 6 7 8Vt (t in min)

Figure 6 Comparison of the simulated piezometric heads, at the centre of thefracture, and the water levels in Borehole UP16.

function of the logarithm of time, instead of the square root of time, which is

characteristicoflinearflow(Milne-Home ).Itisthereforeimportanttonotethatboth the simulated piezometric heads of the fracture and the observed waterlevels of borehole UP 16, in Figure 4, are functions of the square root of time.



Flow in these aquifers is therefore linear and not radial. It will therefore be futileto try to analyse data from Karoo aquifers with a model that does not take thisproperty of the flow into account

It is well-known that the value of the solution of a partial differentialequation, at any point in space and time, is determined by the boundaryconditions, while the constitutive parameters and thus the geometry of thedomain determines the shape of the solution. What the simulated piezometricheads in Figure 4 therefore suggest is that one cannot expect to develop arealistic groundwater flow model for a Karoo aquifer, without taking thegeometry of the various formations and fractures into account.Ackowledgement: The author would link to thank the Water Research Commis-sion and the University of the Free State for their financial support.

References

[1] Kirchner, J. O. G., Van Tonder, G. J. and Lukas, E. Exploitation Potentialof Karoo Aquifers. WRC Report No 170/1/91. Water Research Commis-sion, P.O. Box 824, Pretoria 0001,1991.

[2] Verwey, J. P. and Botha, J. F. A Comparative Study of Two- and Tlwee-dimensional Groundwater Models. WRC Report No 271/1/92. WaterResearch Commission, P.O. Box 824, Pretoria 0001, 1992

[3] Fitch, F. J. and Miller, J. A. Dating Karoo igneous rocks by the conventionalK-Ar and 40Ar/39Ar age spectrum methods. Special Publication of theGeological Society of South Africa. 13, pp 247-266, 1984.

[4] Botha, J. F., Verwey, J. P., Van der Voort, I., Vivier, J. J. P., Colliston, W.P. andLoock, J. C. Karoo Aquifers. Their Geology, Geometry and PhysicalBehaviour. Report to the Water Research Commission. Institute forGroundwater Studies, University of the Free State, P.O. Box 339,Bloemfontein 9300, 1997.

[5] Black, J. H. Hydrogeology of fractured rocks—a question of uncertaintyabout geometry. In: Proc. of the Conf. Hydrogeology of Hard Rocks. S.Banks and D. Banks (eds.). Vol 2, pp. 783-796. IAHS, 1993.

[6] Huyakorn, P. S. and Pinder, G. F. Computational Methods in SubsurfaceFlow. Academic Press, Inc., New York, N.Y., 1983.

[7] Botha, J. F. and Bakkes, G. N. Galerkin finite element method and thegroundwater flow equation: 1. Convergence of the method. Advances inWater Resources. 5,pp 121-126, 1982.

[8] Huang, Y. H. Unsteady Flow toward an Artesian Well. Water ResourcesResearch. 9 (2), pp 426-433, 1973.

[9] Milne-Home, W. A. Interpretation of aquifer tests in fractured aquifers:from theory to routine field analysis. In: Proc. of the IV Canadian/AmericanConference on Hydrology in Fractured Rocks, pp. 177-184, 1988.


joseph f botha p.o. box 339, bloemfontein 9300, south africa · pdf filep.o. box 339,...

Documents