A suite of mathematical models to simulate the water and salt circulation in the Vaal River water supply system
Date
2015-08-03
Authors
Herold, C E
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Abstract
The Pretoria-Witwatersrand-Vereeniging (PW) complex relies for
water supply on the resources of the Vaal basin# supplemented
by Importation from the Tugela river. Most of the water
supplied to the region is abstracted from the Vaal Barrage#
which is also the sink for much of the water-borne pollution
generated in the southern portion of the PWV complex. This
feature of the system has led to an ever-increasing build-up of
total dissolved solids (TDS) in the water supplies# resulting
in substantial economic loss to consumers. Increasing
mineralization is ascribable mainly to return of effluents to
the Vaal Barrage where the concentrated salts are re-introduced
to the Rand Water Board distribution system. The problem is
exacerbated by the washoff, during the wet season#
of enormous diffuse-source salt loads# leading to intolerably
high peak TDS concentrations.
A suite of deterministic mathematical models has been developed,
and successfully tested, with the aim of predicting the
anticipated severity of mineralization problems of the future
and of facilitating objective comparison of the merits of
various ameliorative measures.
The first of the suite is the daily washoff model, designed to
simulate daily catchment runoffs and associated daily diffusesource
salt washoff. Basic input is daily meteorological data.
In the model account is taken of both surface and sub-surface
flow processes. Calibration of the model parameters for each
of the twelve sub-catchments comprising the southern PWV region
was effected with records of discharge and water quality at key
monitoring points. A relationship was established between
industrial water consumption and diffuse-source salt generation
rates by means of which pollution levels likely to arise in the
future could be predicted.
Daily fluctuations of discharge and salt concentration at any
point in the tributaries of the southern PWV region and in the
Vaal Barrage, as well as water and salt storages in the major
impoundments of the Vaal basin are simulated by means of the
daily feed-back model. A feed-back element is incorporated
which accounts for the mixing of water distributed to each of
27 sub-regions of the southern PWV catchment, the addition of
salts through usage and the routing of effluents, together with
diffuse-source washoff generated by the first model, through
the tributary system back into the Barrage. The transmission
of pollutants through the Barrage is simulated by means of a
one-dimensional, cell-type level-pool model. This model was
used to check the reliability of calibrated parameter values
used in the daily washoff model by comparing simulated daily
salt concentrations in the Vaal Barrage with those observed at
the Rand Water Board Barrage intakes.
The third model, a simplified version of the daily feed-back
model designed to operate at a monthly computational time step,
was developed to facilitate preliminary comparisons of the
various options. This coarse tlme-etep model is relatively
cheaper to run and makes pos-lble the testing of each option
with several different hydrological sequences. Economic
factors relating salt concentration in water supply to costs to
consumers have also been incorporated.
The two feed-back models were designed in such a way that a
wide variety of planning and management options could be
modelled with the minimum of programming changes.
Procedures for comparing, with the aid of the models, the
merits of various planning and management options to improve
water quality have been evolved and are illustrated by way of
example.
Description
A thesis submitted to the Faculty of Engineering
University of the Witwatersrand Johannesburg
' for the degree of Doctor of Philosophy
September 1981