Grootdraai Catchment Will Soon Experience Severe Water Shortages As Domestic, Industrial and Agricultural Water Use Increases

APPLICATION OF PINCH TECHNOLOGY IN WATER RESOURCE MANAGEMENT TO REDUCE WATER USE AND WASTEWATER GENERATION FOR AN AREA

Report to the Water Research Commission

KJ Strauss

on behalf of

CSIR M&Mtek

WRC Report No. 1241/1/06 ISBN No. 1-77005-488-X

NOVEMBER 2006

DISCLAIMER This report has been reviewed by the Water Research Commission (WRC) and approved for publication. Approval does not signify that the contents necessarily reflect the views and policies of the WRC, nor does mention of trade names or commercial products consitute endorsement or recommendation for use.

EXECUTIVE SUMMARY

BACKGROUND AND MOTIVATION

It has been indicated by DWAF that the Grootdraai catchment will soon experience severe water shortages as domestic, industrial and agricultural water use increases. It is, therefore, important to develop a systematic strategy or plan to reduce the amount of water used in the area, as well as the wastewater generated.

Pinch technology has been successfully applied in improving thermal efficiencies in the chemical and process industries over the last 15 years. This has been through the re- arrangement of heat sources and sinks to optimise the overall thermal efficiency of the process. By taking advantage of certain parallels between the principles of heat and mass transfer, the systematic design procedures of pinch technology have been extended to address the problems of water use and wastewater generation. The overall goal is to reduce the amounts of water used and wastewater generated, with no detrimental effects to the process. The options are the re-use of water in different operations; regeneration and re- use; or regeneration and recycling. Freshwater and wastewater flows are reduced in each case, and in the latter two cases the contaminant load of the wastewater is also reduced.

The application of pinch technology in the reduction of freshwater use and wastewater reduction has already been done on a number of plants and processes internationally as well as in South Africa. Some of these applications have been for industrial complexes where a number of plants were considered and an overall water use optimisation has been conducted.

Therefore the approach of applying pinch technology over a larger area may not necessarily be a novel one, the application of pinch for a multi-sectoral and multi-users application is.

OBJECTIVES

Following the submission of a research proposal to the Water Research Commission in 2000, the project titled “The Application of Pinch Technology in Water Resource Management to reduce water use and wastewater generation for an area” was approved.

The objectives of the project were as follows: Develop an inventory of water users and wastewater generators in the Highveld Ridge area Application of a water pinch technology model that optimises the water use and wastewater generation in the area.

iii

PART I – OVERVIEW

WATER DEMAND MANAGEMENT AND PINCH TECHNOLOGY

Water scarcity has been identified as a driver of implementing new technologies for water use as well as re-use, recycling and regeneration options. However, there are other drivers for initiating water and wastewater saving initiatives. Hall (1997) identified the following water and wastewater reduction drivers: Economics Regulation and compliance Corporate waste reduction goals Regional water shortages/resource limitations Site infrastructure barriers

The increased awareness of dangers to the environment due to over extraction of water, the importance of environmental protection and tougher environmental legislation are further driving forces towards reductions in water consumption and wastewater generation.

The scarcity of good quality industrial water and the stricter discharge regulations have resulted in higher costs for fresh water and the treatment of wastewater respectively. This requires capital expenditure with little or no productive return and there is now considerable economic incentive to reduce both fresh water consumption and wastewater generation. This has impacted all types of industries including chemical processing, paper and pulp, manufacturing, petrochemical and electricity generation industries.

The prime objective of pinch technology is to achieve financial savings in the process industries by optimising the ways in which process utilities, namely energy and water, are applied for a wide variety of purposes. Pinch Technology does this by making an inventory of all producers and consumers of these utilities and then systematically designing an optimal scheme of utility exchange between these producers and consumers.

Pinch Technology provides a method to solve complex multi-stream energy and water integration problems. The technology has provided a rigorous means of analysing processes. It is based on sources and sinks, and the approach of reuse, recycle and regeneration, and combinations of these. The pinch approach not only sets targets but also recommends appropriate network design changes, which maximize the re-use of water/energy.

PART II

WATER PINCH AND CATCHMENT MODELLING

There are numerous activities that affect both the quantity and quality of water in a catchment. The activities meet their water requirements by drawing from the surface bodies and/or groundwater. The effluents generated through these activities are returned to the same system, creating a cycle of use with external inputs and outputs. The major inputs into a catchment are rainfall and inflow from other catchments. Inflow from other catchments can be in the form of surface bodies (e.g. rivers) and groundwater from an upstream catchment, as well as artificial mediums such as canals and pipelines. The major outputs from a catchment are evaporation, transpiration and outflow to other catchments. Outflows to other catchments can be in the form of surface bodies (i.e. rivers and streams) and groundwater to a downstream catchment, as well as artificial mediums such as canals and pipelines.

The increased demand from users and the increased number of users has decreased the availability of water and also the quality of the available water in the Grootdraai catchment. The water in an area has to be managed in such a way that it is not detrimental to the other users, especially downstream users. For a catchment, as mentioned previously, there is a limited supply. The abstraction of water and the release of effluent must be managed in a sustainable way.

The following measures are used to manage the limited water resources available in a catchment: The variation in the quantity of water that enters and leaves a catchment can be controlled with the building of reservoirs. Water use can be regulated by means of permitting, where a user is given the authority to draw a limited amount of water per unit time. These permits can also be applied to the release of effluent, where the volumes and quality of the water released is regulated. Close monitoring of the water quality at selected points.

The water pinch model developed by Mr. C. Brouckaert (referred to as the “model”) from the University of Natal, Durban was used for this study. The decision was taken to use TDS only for the case study, with the focus on whether water pinch can successfully be applied to a catchment situation. It is important that the modelled situation closely resembles the actual situation in the catchment, while at the same time falling within the constraints of the model programmed in the MATLAB computer package.

The model follows a plant set-up, which is made up of different processes and operations, which have specific water requirements. The input requirements for the different users are in the form of a source, processes and sinks.

A comparison between water pinch and a catchment situation highlights the limitations with the application of pinch to a catchment situation. The limitations listed include the following factors: Distance and altitude difference between “processes” Limits and varied supply of the water source Limits posed by the sensitivities of the surrounding ecological environment The effects of groundwater and its movement The effects of evaporation and transpiration

In addition to the limitations listed above, the data available for representation of a catchment situation is limited. Comparing a typical production facility with a catchment under the listed model data requirements shows this: Sources – catchments have numerous sources that are highly variable, data indicating the fate of water that enters the catchment is scarce. Processes – catchments have numerous users with different types of water requirements, uses and releases. Data for water losses in non-industrial users is poorly known. Sinks – include evaporation and transpiration that varies from site to site depending on numerous factors and are poorly known.

To model the catchment, a process of data gathering and identification of gaps in the data needs to be undertaken. The gaps can then be filled through water balances across the various systems in operation in the catchments as well as the catchment itself. The case study on the Grootdraai catchment shows a possible approach.

PART III

CASE STUDY- GROOTDRAAI CATCHMENT

The Grootdraai catchment is located in the Industrial Highveld, which forms part of Mpumalanga Province. The catchment has a surface area of 7924 km2 and forms part of the Upper-Vaal reach. One major river, the Upper Vaal, drains the catchment, with no rivers or streams entering the catchment. All streams within the catchment drain into the Grootdraai dam, which is located at the western boundary.

The major users in the catchment draw their water from the Grootdraai dam. The water available for these uses is therefore dependent on the availability of water in the dam. The Grootdraai dam has a capacity of 364 million m³. The diagram below gives a graphic representation of the water demand from the dam:

DAM OUTLET (SINK)

TRANSFERS TO EXTERNAL DAM INLET GROOTDRAAI USERS (SOURCE) DAM (SINK)

USERS

LOSSES EVAPORATION, TRANSPIRATION, GROUNDWATER, SEEPAGE (SINK)

vii

Information on the users drawing from the dam, with their current demand from the dam and releases back into the system, are provided in the table below:

Overview of water demand and return by the users USER DEMAND RETURN (m3/year) (m3/year) Irrigation 321 500- Tutuka Power Station 47 420 000 - Matla Power Station 53 838 000 - SASOL 91 250 000 4 015 000* Ermelo Municipality 3 600 000 1 982 124 Bethal Municipality 5 420 250 3 011 250 Thuthukane Township 1 427 556 642 400 TOTAL 203 277 306 9 650 774 * Released outside the catchment

The application of the pinch model yielded results that showed that in principle all the waste water of the different users could be re-used, thereby reducing the demand on the dam by the total of the currently released waste waster. The inflow to the dam would also be reduced, as part of the waste water is currently released up-flow from the dam. Due to the limited availability of input information that was required for the model, it was not possible for the model to optimise the allocation of the waste water streams to the users. It appeared that the outcome of the model was effectively a random allocation to the users.

A spread sheet calculation was carried out, which showed that the waste water can indeed be allocated to the different users without infringing on the requirements of the users in terms of maximum allowed inlet TDS. All individual users could take a part or all of the total waste water. Without further constraints e.g. the cost to transport the waste water or additional costs for treatment by the user, there was no preference to allocate the waste water to a specific user. This result confirmed the outcome of the model.

The following conclusions were reached:

The available information from the users (inlet and outlet quantities of water and requirements for inlet and outlet TDS) were not optimal input information for the model to optimise the allocation of the waste streams to different users and therefore the model output was closer to a random allocation. There are large differences between a catchment and a plant situation for which the model was designed, and in order to use a water pinch type model for a catchment, considerable changes to the current model would likely be required.

viii

The modelling as well as the spreadsheet calculation showed that in terms of TDS inlet requirements all waste water could be re-used by the main water users. The study catchment area may not be representative for other catchments for two reasons. In this particular catchment, only a small percentage of the inlet water is released as waste water, due to the presence of industries that evaporate most water as part of their processes. Also, another aspect of this type of industry is that most of the TDS in the inlet water is not returned to the surface water of the catchment, but becomes part of ash disposal sites.

As good water management is important for South Africa in general and more specifically in catchments such as the Grootdraaidam catchment, where water demand is likely to exceed water supply in the future, it is recommended to investigate the development of a model that can reliably simulate all the important aspects of a catchment and thereby help to reduce water use by optimising the allocation of waste water to different users. This model should be based upon the principles of water pinch, but would probably be substantially different from existing models.

TABLE OF CONTENTS

EXECUTIVE SUMMARY ...... III

LIST OF TABLES AND FIGURES...... XIII

GLOSSARY OF ACRONYMS ...... XIV

1 INTRODUCTION...... 1

1.1 MOTIVATION...... 1 1.2 OBJECTIVES...... 2 1.3 BACKGROUND...... 2 2 LITERATURE SURVEY...... 4

2.1 WATER DEMAND MANAGEMENT ...... 4 2.2 PINCH TECHNOLOGY ...... 5 3 CATCHMENT MANAGEMENT ...... 9

3.1 OVERVIEW ...... 9 3.2 NATURAL ACTIVITIES ...... 10 3.3 MANAGEMENT OF USE ...... 11 4 WATER PINCH AND CATCHMENT MANAGEMENT ...... 12

4.1 WATER PINCH MODEL...... 12 4.2 MODEL REQUIREMENTS ...... 14 4.3 MODEL LIMITATIONS ...... 15 4.4 CATCHMENT DATA LIMITATIONS...... 16 5 GROOTDRAAI CATCHMENT...... 18

6 HYDROLOGY...... 19

6.1 GROOTDRAAI DAM...... 19 6.2 MODEL INPUT...... 20 7 AGRICULTURAL USE...... 28

7.1 MODEL INPUT...... 30 8 INDUSTRIAL USE ...... 32

8.1 ESKOM [17]...... 32 8.2 SASOL [18]...... 33 8.3 MODEL INPUT...... 34

9 MUNICIPALITIES ...... 36

9.1 MODEL INPUT...... 37 10 MODEL APPLICATION...... 39

11 RESULTS AND DISCUSSION...... 42

12 CONCLUSION...... 45

13 RECOMMENDATIONS...... 45

14 ACKNOWLEDGEMENTS ...... 46

REFERENCES ...... 47

APPENDIX: MATHEMATICAL PROGRAMMING APPROACH TO WATER PINCH ANALYSIS ...... 50

xii

LIST OF TABLES AND FIGURES

Page Figure 2.1Typical composite curve ...... 5 Figure 2.2 Pinch design grid ...... 6 Figure 2.3 Concentration/mass flow composite curves...... 6 Figure 3.1 Catchment Graphic...... 10 Figure 4.1 A water using process ...... 12 Figure 4.2 The superstructure for a simple 2-process network...... 12 Table 4.1 Pinch vs. Catchment Management ...... 15 Table 4.2 Comparison between a production facility and a catchment ...... 16 Figure 5.1 Catchment Layout...... 18 Table 6.1 Water quality of Grootdraai dam ...... 19 Figure 6.1 Grootdraai System...... 21 Fig 6.2 Grootdraai dam system...... 22 Fig 6.3 Dam inlet and outlet...... 24 Figure 6.4 Inflow into dam at Goedgeluk measuring station ...... 25 Table 6.2 Grootdraai dam users ...... 25 Figure 6.5: Modelled Grootdraai Dam...... 27 Table 7.1 Extraction volumes of Agriculture...... 28 Table 7.2 Selected SAWQG for Livestock Watering and Irrigation ...... 29 Figure 7.1 Water balance for Agriculture ...... 30 Figure 7.2 Modelled Agriculture ...... 31 Table 8.1 Grootdraai Dam Power Station Water Consumers ...... 32 Table 8.2 ESKOM additional requirements...... 33 Figure 8.1 Modelled Industrial Users ...... 34 Table 9.1: Municipal wastewater releases [1] ...... 36 Table 9.2 Municipal water use ...... 37 Figure 9.1 Modelled municipal users ...... 37 Table 10.1 Model Input ...... 39 Fig 10.1 Intake and outlet volumes ...... 40 Table 11.1 Results for fixed concentration...... 42 Table 11.2 Results for fixed mass loads ...... 43 Table: 11.3 Spreadsheet allocation of waste water to users...... 44

xiii

GLOSSARY OF ACRONYMS

ACRONYMS

CSIR Centre for Scientific and Industrial Research

DWAF Department of Water affairs and Forestry

HENS Heat Exchange Network Synthesis

LP Linear Programming

MEN Mass Exchange Network

MENS Mass Exchange Network Synthesis

MIP Mixed Integer Programming

MILP Mixed Integer Linear Programming

MINLP Mixed Integer Non-linear Programming

MSA Mass Separating Agent

NLP Non-linear Programming

SAWQG South African Water Quality Guidelines

TDS Total Dissolved Solids

WDM Water Demand Management

WRC Water Research Commission

ZLED Zero Liquid Effluent Discharge

xiv

PART I – OVERVIEW

1 INTRODUCTION

The CSIR has been commissioned by the Water Research Commission to conduct a Pinch Technology study in water resource management. The aim of the study is to reduce water use and wastewater generation for the Grootdraai catchment area. There is a large number of multiple sector users e.g. petrochemical industry, electricity generation, mining, farming and increasing domestic water use in this area.

1.1 MOTIVATION

It has been indicated that the proposed area of study will soon experience severe water shortages as domestic, industrial and agricultural water use increases [1]. It is therefore important to develop a systematic strategy or plan to reduce the amount of water used in the area, as well as the wastewater generated.

Pinch technology has been successfully applied in improving thermal efficiencies in the chemical and process industries over the last 15 years. This has been through the re-arrangement of heat sources and sinks to optimise the overall thermal efficiency of the process. By taking advantage of certain parallels between the principles of heat and mass transfer, the systematic design procedures of pinch technology have been extended to address the problems of water use and wastewater generation [2]. The overall goal is to reduce the amounts of water used and wastewater generated, with no detrimental effects to the process. The options are the re-use of water in different operations; regeneration and re-use; or regeneration and recycling. Freshwater and wastewater flows are reduced in each case, and in the latter two cases the contaminant load of the wastewater is also reduced.

The application of pinch technology in the reduction of freshwater use and wastewater reduction has already been done on a number of plants and processes internationally [3] as well as in South Africa [4]. Some of these applications have been for industrial complexes where a number of plants were considered and an overall water use optimisation has been conducted.

Therefore the approach of applying pinch technology over a larger area may not necessarily be a novel one, the application of pinch for a multi-sectoral and multi- users application is.

1.2 OBJECTIVES

1.3 BACKGROUND

One of the greatest challenges to be faced in the 21st century is developing an innovative strategy to avert serious local and regional water scarcities, and to meet the rapidly growing demand for water. This includes addressing the issues of quality, equity and incentives for both water managers and users. Because water is a key life-supporting resource, its scarcity can have far reaching implications.

South Africa is characterized by erratic and unevenly distributed rainfall. As regional populations continue to grow, so does the demand for water by all sectors. A regional (Southern Africa) study on water demand management (WDM) was undertaken by the IUCN [5] in recognition of the importance of water to the region and the fact that supply-side approaches alone are inadequate to address the region’s water challenges. One of the critical outcomes of the study was that WDM is not yet an intrinsic part of water resource planning and management in Southern Africa.

The motivation for the study was the view that if water resource management is to be sustainable and socially efficient it needs to move away from a historical emphasis on simply developing new supplies to meet projected water needs. The emphasis on supply solutions has led to inefficient use of water resources, over- capitalisation in infrastructure, and environmental damage, and yet has still not provided water security to the region.

The study identified the following factors driving WDM in the region: Growing divergence between demand and supply – demand is increasing due to increasing population and income growth, but supply is fixed by natural constraints and limited by financial ones. Increasing supply costs as countries are forced to look further a field for new water sources;

Increasing fiscal restraint resulting from externally structural adjustment programmes i.e. sharper focus on the financial sustainability of public utilities, on the removal of subsidies, and on cost recovery from consumers. Increased potential for WDM – through access to technology and economics of scale in urban areas Regional water security and risk aversion – WDM offers an alternative to moving further a field to source water and avoids exposure to risk and potential regional conflict.

The study also went on to identify a range of measures that have been used to modify the demand for water. These are: Economic measures (e.g. use of pricing policies – block tariff systems), Regulations (e.g. use of permits for water use), Education and awareness raising (e.g. public awareness strategies), Technology improvements (e.g. efficient water use equipment, improved irrigation systems), Water loss control (i.e. control of unaccounted-for water), and Water re-use and recycling (e.g. re-use of mining water, recycling of municipal wastewater).

It is therefore proposed that pinch technology be used as a means of assessing the potential for water re-use, recycling and regeneration in a water stressed area (catchment). If the application of pinch technology for water use management proves to be successful, then we have another tool for WDM.

2 LITERATURE SURVEY

2.1 WATER DEMAND MANAGEMENT

Water scarcity has been identified as a driver of implementing new technologies for water use as well as re-use, recycling and regeneration options. However there are other drivers for initiating water and wastewater saving initiatives. Hall [6] identified the following water and wastewater reduction drivers: Economics – Hall referred to a study conducted by the US Centre for Waste Reduction Technologies where it was found that 75% of respondents cited economics as the reason for implementing a water/effluent minimization programme. It was proposed that increasing fresh water and effluent discharge costs are prompting companies to look for means to save on water use and effluent discharge thereby saving costs. Regulation and compliance – regulations can stipulate the quantity and sometimes quality of wastewater discharged by a company. Companies have to ensure that their releases comply with regulatory requirements. Corporate waste reduction goals – some companies set tough goals for wastewater reduction which go beyond discharge consent limits, as there is still the possibility of environmental impact from their wastewater. Regional water shortages/resource limitations – this is generally manifested in terms of charges, legislation and compliance. There may not be enough capacity in the piping and distribution system, or local treatment works may limit effluent loading. Regional natural based water shortages have been previously discussed. Site infrastructure barrier – Plant water systems are generally already complex due to years of plant modifications. There may be opportunities to make better use of the existing equipment and even improve the water quality.

The increased awareness of dangers to the environment due to over extraction of water (P Castro et al) [4], the importance of environmental protection (VR Dhole et al) [7] and tougher environmental legislation (Schaareman et al., P Tripathi, R Hamilton, Cripps) [8; 9; 10; 11] are further driving forces towards reductions in water consumption and wastewater generation.

Another important driver towards water demand management as mentioned above are the economic aspects. The scarcity of good quality industrial water and the stricter discharge regulations has resulted in higher costs for fresh water and the treatment of wastewater respectively (Alva-Argaez et al) [12]. This requires capital expenditure with little or no productive return and there is now considerable economic incentive to reduce both fresh water consumption and wastewater generation (R Smith, E Petela) [13]. This has impacted all types of industries

including chemical processing, paper and pulp, manufacturing, petrochemical and electricity generation industries.

2.2 PINCH TECHNOLOGY

The prime objective of pinch technology is to achieve financial savings in the process industries by optimising the ways in which process utilities, namely: energy and water are applied for a wide variety of purposes. Pinch Technology does this by making an inventory of all producers and consumers of these utilities and then systematically designing an optimal scheme of utility exchange between these producers and consumers.

Pinch Technology is a systematic method of process analysis and design, which maximizes use of inherent thermodynamic potential. Thermal (energy) pinch was developed 20 years ago. The basic premise that heat flows from high to low temperature led to temperature/energy composition curves, the grid design method and other key concepts (see Figure 2.1 and 2.2). More recent water/wastewater pinch and related techniques are based on analogous concepts of contaminated mass flow vs concentration profiles (see Figure 2.3).

Figure 2.1 Typical composite curve

Figure 2.2 Pinch design grid

Figure 2.3 Concentration/mass flow composite curves

El-Halwagi and Manousiouthakis (1989) [14] first applied pinch technology to mass exchange network synthesis (MENS). They introduced the use of a minimum composition difference, ε, which is analogous to the minimum approach temperature in heat exchanger network synthesis (HENS). They showed how specifying the value of ε locates the mass transfer pinch, which is a thermodynamic bottleneck for mass transfer between streams. This allows a target for the minimum flow rate of external mass separating agent (MSA) required by a network to be determined. This target is analogous to the energy target in HENS. Avoiding the transfer of mass across the pinch ensures that the MSA target is met in design.

The implementation of pinch principles to mass exchanging processes was announced by El-Halwagi and Manousiouthakis (1990) [15] and later extended by Wang and Smith (1994) [16]. The analysis uses the water concentration profiles of individual water consuming processes (washing, steam stripping, extraction, etc.). Individual concentration profiles are combined in so-called Concentration Composition Curves, which are analogous to the traditional thermal Pinch Composition Curves. Here the temperature/enthalpy curve is replaced by the concentration-mass of contaminant composite profile. This composite curve is matched to a straight line through the origin, which represents a minimum water supply line. This minimum water supply line touches the composite curve at a minimum of two points i.e. the origin and one another. The points other than the origin are known as the Pinch points. Wang and Smith then presented two methods to achieve minimum flow rate design. The first is referred to as the maximum driving force method, which uses concentration differences between the various streams to target the minimum flow rate. The second method is referred to as the minimum number of water sources method and uses load intervals. In each interval only enough water is used to maintain network feasibility, the remainder is by passed and used later. They considered also a case where more that one contaminant is present and extended their methodology to cover this situation. They also considered the implications of regeneration of wastewater.

With the application of pinch technology, savings can be achieved in both capital investment and operating cost. Emissions can be minimised and throughput maximized.

2.2.1 SINGLE CONTAMINANT, GRAPHICAL APPROACHES TO PINCH ANALYSIS Analogies between heat and mass transfer have been used to extend the concept of pinch analysis to encompass waste minimisation and pollution prevention. Techniques have been developed in order to design optimal mass exchanger networks (MEN). These minimum flow rate networks minimise the amount of fresh water consumed and waste water produced. El-Halwagi et al. (1989-1997) presented several methodologies for the design of MENS, pioneering the extension of the pinch analysis from thermal to mass integration. Wang and Smith (1994a) developed an approach, which involves the generation of a single composite curve, which is used to set minimum flow rate targets. The methods developed allow the designer to identify alternative structures for the same problem. Wang and Smith also considered the possibility of regenerating wastewater and presented a conceptually based approach, which distinguishes between regeneration re-use and regeneration recycling. They later extended this idea to situations where flow rates are constrained (Wang and Smith, 1995a). 7

2.2.2 MATHEMATICAL PROGRAMMING APPROACH TO WATER PINCH ANALYSIS The graphical approaches considered so far provide many valuable insights to the water optimisation problems, but become increasingly difficult to apply when multiple contaminants or special process constraints are involved. They also cannot deal with optimisation in terms of objective functions, which include factors other than water use, in particular, economic factors. Previous investigators have used mathematical programming for mass-transfer networks, (e.g. Takama et al., 1980; Rossiter and Nath, 1995); the formulation, which corresponds to the water pinch approach, was set out by Doyle and Smith (1997) and extended by Alva- Argaez et al (1998). A detailed description of their approach is provided in Appendix A. The Water Pinch software developed by Dr Chris Brouckaert is largely based on this approach.

PART II WATER PINCH AND CATCHMENT MODELLING

3 CATCHMENT MANAGEMENT

3.1 OVERVIEW

There are numerous activities that affect both the quantity and quality of water in a catchment. The activities meet their water requirements by drawing from the surface bodies and/or groundwater. The effluents generated through these activities are returned to the same system, creating a cycle of use with external inputs and outputs. The major inputs into a catchment are rainfall and inflow from other catchments. Inflow from other catchments can be in the form of surface bodies (e.g., rivers) and groundwater from an upstream catchment, as well as artificial mediums such as canals and pipelines. The major outputs from a catchment are evaporation, transpiration and outflow to other catchments. Outflows to other catchments can be in the form of surface bodies (i.e. rivers and streams) and groundwater to a downstream catchment, as well as artificial mediums such as canals and pipelines.

The users within the catchment influence both the volume and quality of water within the system. Processes that lead to evaporation, transpiration and seepage, decrease the volume of water in the catchment. Processes that lead to the addition of pollutant loads to the water, affect the water quality.

Users can be separated into those that directly affect the quality and quantity of water in the system and those that affect the system indirectly. Users that directly affect the quality and quantity of water are those that release their effluents in the form of pipelines that discharge into surface bodies (point source pollution). Users that indirectly affect the quality and quantity of water are those that release their pollutants with the aid of runoff and seepage (non-point source pollution).

The diagram below (Figure 3.1) graphically demonstrates the different processes that take place in a catchment.

EVAPORATION Non-point Source RAIN Pollution

Seepage Runoff

Point Source

Pollution

GROUNDWATER GROUNDWATER

Figure 3.1 Catchment Graphic

3.2 NATURAL ACTIVITIES

As previously mentioned, one of the major sources of water for a catchment is rainfall. In catchments where there are no rivers flowing into the catchment, rainfall can be the only source of water. The quantity and quality of water that ends up in the surface bodies, from rainfall, is dependent on runoff, evaporation and seepage. Runoff and seepage are interdependent occurrences, and in turn, are dependent on the following factors: Initial moisture content of the soil during a rainfall event Soil with a low initial moisture content will absorb more water before the onset of runoff occurs Soil cover and/or soil type The type of cover will determine how much water the soil is able to absorb before the onset of runoff occurs. The soil type determines the permeability of the soil and therefore the amount of water that can seep through. It also determines the speed of release of water from groundwater storage into surface bodies. Slope of ground Determines the speed at which water flows which also affects the amount of water the soil is able to absorb.

Intensity of the rainfall 10

Rainfall with a high intensity allows less time for the soil to absorb water as compared to rainfall with a low intensity.

Upon reaching the major rivers and streams, the characteristics of the water do not remain constant. Physical, biological and chemical factors such as settling, bacterial activity and chemical reactions respectively, significantly change the characteristics of the water. Added to this, users located along these water bodies may remove water, as well as, return their effluent, which is a lower quality, affecting both the quality and quantity of water along these streams.

3.3 MANAGEMENT OF USE

The increased demand from users and the increased number of users has decreased the availability of water and also the quality of the available water. The water in an area has to be managed in such a way that it is not detrimental to the other users, especially downstream users. For a catchment, as mentioned previously, there is a limited supply. The abstraction of water and the release of effluent must be managed in a sustainable way.

For sustainability, the following requirements have to be met, in this order: 1. Ecological requirements 2. Human requirements 3. Agricultural and Industrial requirements

The following measures are used to manage the limited water resources available in a catchment: The variation of the quantity of water that enters and leaves a catchment can be controlled with the building of reservoirs. Water use can be regulated by means of permitting, where a user is given the authority to draw a limited amount of water per unit time. These permits can also be applied to the release of effluent, where the volumes and quality of the water released is regulated. Close monitoring of the water quality at selected points

4 WATER PINCH AND CATCHMENT MANAGEMENT

4.1 WATER PINCH MODEL

The water pinch model developed by Dr. C. Brouckaert (referred to as the “model”) from the University of Natal, Durban was used for this study. What follows is a brief description of the pinch model.

The basic model of a water-using operation, similar to Wang and Smith’s fixed load model (Figure 4.1) is used, except for the following: 1. An alternative option is considered, where the mass load is allowed to vary in order to fix the outlet concentration of a contaminant; 2. A water gain or loss is allowed, to model operations such as cooling towers or evaporators.

Contaminant δjn Wj Water

Water in Water out Process j cjn

Figure 4.1 A water using process

The basic concepts of limiting flows and concentrations, and the relationship between them via the mass balances, are exactly the same as in Wang and Smith. To automate the procedure for finding the optimal set of connections between units, a superstructure for the network is considered (Figure 4.2). This allows, in principle, all possible connections.

Fresh Waste 1 2 water water

Figure 4.2 The superstructure for a simple 2-process network

The balance over process i can be expressed as

Flow balance: ∑Fij ∑Fjw (∑Fji ∑Fjk W j ) 0 (1) i wik

Balance for component n: ∑Fji cin ∑Fjk ckn G jn (∑Fji ∑Fjk W j )c jn (2) ik ik

Where

Fji is the flow of reused water from outlet of process i to process j

Fjw is the flow of used water from outlet of process I to sink w

Fjk is the flow of fresh water from source k to inlet of process j

Cin is the concentration of ion n in outlet stream from process I

δin is the mass gain of contaminant n over process I

Wi is the water gain over process i

To complete the formulation, an objective function must be defined to provide the basis for optimisation. A general form for the objective function was proposed, representing fixed and variable costs associated with each stream, to be minimised:

c : ∑[aij bij (Fij ) ] (3) i, j

This formulation of the problem has non-linearities in the objective function (Equation 3) and in the component balances (Equation 2). It should usually be possible to use a linearised objective function as an approximation, but, in the case of fixed contaminant loads, the component balances are intrinsically non- linear. The terms are products of flow rate and concentration, since both are variables in the same problem. In the case of fixed outlet concentrations, however, Equation 2 is linear in the flow rates, since the concentrations are then known constants. Thus, if all processes in the system are of the fixed-outlet- concentrations type, the problem could be formulated to a linear programming (LP) optimisation. Although this is an unlikely scenario, it is reasonable to suppose that, in an optimised system, the concentrations will approach their limiting values. This means that the LP solution could be taken as a good starting estimate for a non- linear programming (NLP) optimisation. Providing a good starting estimate is the most important means of achieving satisfactory convergence in non-linear programming. This rationale forms the basis of the linear/non-linear approach.

4.2 MODEL REQUIREMENTS

For the purposes of this study it has been decided to use the constraint of Total Dissolved Solids (TDS) only, with the focus on whether Water Pinch can be used successfully on a catchment situation. It is important that the modelled situation closely resembles the actual situation in the catchment, while at the same time falling within the constraints of the model programmed in the MATLAB computer package.

The model can also incorporate cost aspects of the different options, but this function was not used as very little cost information was available. What follows is a brief description of these requirements.

As mentioned previously, the model follows a plant set-up. A plant set-up is made up of different processes and operations, which have specific water requirements. The input requirements for the different users are in the form of a source, processes and sinks.

Source The required input for a source is limited to its cost and quality, excluding the quantity available. The reason the model only places a limitation on the quality and not quantity is because of the intended use of the model, for a plant situation. The focus in a general plant situation is that the only limitation is the cost. The model does allow for more than one source, and includes cost indicators for each.

Process The required input for a process is: 1. The maximum allowed inlet concentration 2. The maximum allowed outlet concentration 3. The flow through the process1 4. The water gains or losses in the process

Sinks The required input for the sinks are similar to that of a process, where the distinction occurs in what is referred to as the “connectivity” matrix. This matrix is used to manipulate flows to and from specific processes. It allows the user to allow or prevent the flow from one process to another. In the case of a sink, the user would set the connectivity matrix so that no flow is allowed from the sink.

1 The model only allows for one flow as an input 14

4.3 MODEL LIMITATIONS

A comparison between water pinch and a catchment situation highlights the limitations with the application of pinch to a catchment situation. The limitations listed include the following factors:

Distance and altitude difference between “processes”

Limits and varied supply of the water source

Limits posed by the sensitivities of the surrounding ecological environment

The effects of groundwater and its movement

The effects of evaporation and transpiration

The limitations of the pinch model presented are now discussed by outlining the differences between the offerings of the model as compared to the situation in a catchment (Table 4.1).

Table 4.1 Pinch vs. Catchment Management Pinch Catchments Water can be routed in any direction Limited by distance and altitude Infinite supply Limited and varied supply Dispose of all effluent Limited by ecological requirements and downstream users Load doesn’t change with flows Load changes with change in flows

4.4 CATCHMENT DATA LIMITATIONS

Table 4.2 Comparison between a production facility and a catchment Typical Production Facility Catchment Source: Sources: Municipal (or other) via Rainfall, dispersed over the catchment – highly pipeline – largely dictated variable from year to year and season to by facility demand season Inflow from upstream catchment – highly variable, unless controlled (buffered) by a dam Water transfers Users: Dynamic users: Machinery with well known Agriculture (and controlled) intake seasonal volumes and outlet non-point release of effluent volumes and quality (e.g. pollutant load added through runoff, poorly TDS) known water balance poorly known, site specific (dependent on soil, climate, water table, crop, etc) Municipal seasonal to a small degree water losses through piping consumptive use (e.g.) gardening poorly known outlet quality variable Industrial (see “Typical Production Facility”) Sinks: Sinks: Single pipeline from Evaporation (poorly known) combined outlets Transpiration (poorly known) Outflow (well known and sometimes controlled) Seepage (poorly known) Transfers (well known and controlled)

To model the catchment a process of data gathering and identification of gaps needs to be undertaken. The gaps can then be filled through water balances across the various systems in operation in the catchments as well as the catchment itself. The case study on the Grootdraai catchment shows a possible approach.

PART III CASE STUDY – GROOTDRAAI CATCHMENT

5 GROOTDRAAI CATCHMENT

Matla Power Station

Bethal Municipality SASOL (Secunda) Ermelo Municipality

Tutuka Power Station

Direction of flow Thuthukane Municipality

Grootdraai Dam

Figure 5.1 Catchment Layout

6 HYDROLOGY

On an annual basis rainfall, by its nature, varies considerably over the catchment. There are no streams or rivers leading into the catchment, thus the water available in the catchment has its only source as rainfall. With its only source as rainfall, it follows that the available water varies considerably too (Figure 6.3) with some moderation. The major users, such as industrial and the municipalities in catchment, require a steady supply of water throughout the year. This has led to the construction of the Grootdraai dam. By controlling the flow of water that leaves the catchment through storage, the dam is able to provide a constant, but limited supply, throughout the year.

6.1 GROOTDRAAI DAM

The historical firm yield for the catchment is estimated by DWAF to be 124 million cubic meters per year [1], where the historical firm yield is the smallest amount of water that was available in the recorded history of the catchment. The rivers and streams within the catchment require a minimum flow to meet the needs of their aquatic environment. This minimum flow is known as the Ecological Reserve. The estimated Ecological Reserve for the catchment is 27 million cubic meters per year [1].

6.1.1 WATER QUALITY Water quality measurements are taken for monitoring purposes by DWAF at eight stations throughout the catchment. As mentioned previously, the majority of water extractions, by the major users, occur at the dam. Given that the majority are supplied from the dam, the water quality measurements taken at the dam wall will be taken as representative of the quality received by users (Table 6.1). The details of the station are as follows:

Station number: C1R002Q01 Station name: Grootdraai dam on Vaal River: Near dam wall Data collection: 738 samples collected from November 1982 to September 1999

Table 6.1 Water quality of Grootdraai dam TDS STATISTIC (mg/P) Maximum 251 Mean 164 Minimum 8 Standard Deviation 24.9

The data above shows a large variation from minimum to maximum. This can be due to high rainfall, which will have a dilution effect on the TDS within the rivers and streams. For the purposes of the study, the number for the will mean water quality within the dam will be used for the modelling.

6.2 MODEL INPUT

A schematic diagram is used to describe how the various components of the catchment and its users have been divided into sources, processes and sinks to allow application of the pinch model. The key below describes the different symbols and arrows used in the sections that follow: A flow that will not be included in the model, but is required in the balance of the system is listed as a “Constant Flow”. A flow that will be included in the model is listed as a “Modelled Flow” KEY to diagrams:

XYZ Process XYZ

Constant flow

Modelled flow

To represent the catchment as a whole, it is necessary to include all activities, grouped into their categories. The only input to the catchment as a whole (rainfall) is listed as a source. The outputs are listed as sinks. As discussed previously, the water reaching the dam from rainfall is influenced by activities in the catchment, both man-made and natural, ending up in the dam for use by the major users.

DAM OUTLET (SINK)

LOSSESA TRANSFERS TO EVAPORATION, GROOTDRAAI EXTERNAL GROUNDWATER DAM USERS SEEPAGE (SINK) (SINK)

CATCHMENT RAINFALL (SOURCE)

USERS

LOSSESB EVAPORATION, TRANSPIRATION, GROUNDWATER, SEEPAGE (SINK)

Figure 6.1 Grootdraai System

Balance for the system:

Sc - Sc-1 = Gi - Go + R - E- Od - Uod + Uid (4) Where,

Sc = Storage in catchment for current year

Sc-1 = Storage in catchment carried over from previous year

Od = Surface water outflow from catchment for current year

Gi = Groundwater inflow into catchment for current year

Go = Groundwater outflow from catchment for current year R = Rainfall on catchment for current year E = Evaporation (incl. Transpiration) from catchment for current year

Uod = Extraction for use

Uid = Return from users

The major users in the catchment draw their water from the Grootdraai dam. The water available for these users is therefore dependent on the availability of water in the dam. The Grootdraai dam has a capacity of 364 million cubic meters. It should be noted that this does not translate into a water availability of 364 million cubic meters. Instead, the availability of water for a specific year depends on storage from previous years including inflow to the dam, minus all losses. The diagram below (Figure 6.2) gives a graphic description:

DAM OUTLET (SINK)

TRANSFERS TO EXTERNAL DAM INLET GROOTDRAAI USERS (SOURCE) DAM (SINK)

USERS

LOSSESB EVAPORATION, TRANSPIRATION, GROUNDWATER, SEEPAGE (SINK)

Fig 6.2 Grootdraai dam system

The balance across the dam is as follows

Sj - Sj-1 = Id - Od + Gid - God + Rd - Ed - Uod + Uid (5) Where,

Sj = Storage in dam for current year, i.e. available water for current year

Sj-1 = Storage in dam carried over from previous year

Id = Inflow for current year

Od = Outflow for current year

Gid = Groundwater inflow to dam for current year

God = Groundwater outflow from dam for current year

Rd = Rainfall on dam for current year

Ed = Evaporation from dam for current year

The balance can be simplified by grouping terms:

Rd - Ed = net loss due to rainfall and evaporation = Lc

Gid - God = net loss due to groundwater seepage = Lg

Equation (5) becomes:

Sj - Sj-1 = Id - Od + Lg + Lc - Uod + Uid (6)

6.2.1 STORAGE The pinch model is a steady state model. To overcome the annual changes that occur in the catchment, the available data is averaged over the 20 years that it has been collected. In doing this, storage becomes insignificant in terms of the water balance. The general water balance for a system is as follows:

Sx = Sx-1 + gainsx – lossesx (for system x)

But, Sx-1 = Sx-2 + gainsx-1 – lossesx-1

Therefore, Sx = Sx-2 + gainsx-1 – lossesx-1 + gainsx – lossesx x

(S x S xn ) ∑(Gainsx Lossesx ) xn

For n-large and/or Sj+1 ≈ Sj, x x

∑(Gainsx Lossesx ) (S x S xn ) ⇒ ∑(Gainsx Lossesx ) xn xn

Following this, equations 4 and 5, over 20 years, can be simplified to the following:

- Od + Gi - Go + R – E - Uod + Uid ≈ 0 (4a)

Id - Od + Gid - God + Rd - Ed - Uod + Uid ≈ 0 (5a)

The dam is a system that is located within the catchment system. It is located at the downstream end of a catchment and receives the surface water that flows from the catchment.

Catchment Dam System System

Id, Uid, Od, Uod, R, Gi E, Go Rd, Gid Ed, God

Fig 6.3 Dam inlet and outlet.

The dam outlet is an output for both the catchment and the dam itself. The two systems are compared by using this commonality and making the dam, Od, the subject of the formula for both systems:

Od = (Gi - Go) + (R – E) + (Uid - Uod) (4b)

Od = (Gid - God) + (Rd - Ed) + Id + (Uid - Uod) (5b)

The inputs and outputs to the catchment that take place outside the dam can be found by taking the difference between the two systems: Equation 4b – Equation 5b:

0 = (Gi - Go)+ (R – E) – Id – (Gid - God) – (Rd - Ed)

0 = (R – Rd) – (E - Ed) + (Gi – Gid) – (Go - God) – Id

In words, 0 = Rainfall (excl dam) – Evaporation (excl dam) + Groundwater inflow (excl dam) – Groundwater outflow (excl dam) – Inflow to dam

Rearranging this, Inflow to dam = Rainfall (excl dam) – Evaporation (excl dam) + Groundwater inflow (excl dam) – Groundwater outflow (excl dam)

Therefore, the inflow to the dam equals the activities that take place outside the dam. Since the dam receives its surface water from these activities, it is further concluded that the inflow to the dam is a result of, and accounts for, all losses and gains in the catchment, excluding those that occur in the dam itself.

6.2.2 DAM INFLOW The details of the measuring point upstream of the dam is as follows:

Station No. C1H007 Station name: Vaal River at Goedgeluk

1200

1000

800

600

Flow [m3/a] 400

200

0 1980 1985 1990 1995 2000

Figure 6.4 Inflow into dam at Goedgeluk measuring station

The average dam inflow from the above graph is 299 million cubic meters. The current demand from the dam and releases back into system is provided in the table below:

Table 6.2 Grootdraai dam users USER DEMAND RETURN REFERENCE Irrigation 321 500 - Section 7 Tutuka Power Station 47 420 000 - Section 8 Matla Power Station 53 838 000 - Section 8 SASOL 91 250 000 4 015 000 Section 8 Ermelo Municipality 3 600 000 1 982 124 Section 9 (water from upstream dam) Bethal Municipality 5 420 250 3 011 250 Section 9 Thuthukane 1 427 556 642 400 Section 9 Township TOTAL 203 277 306 9 650 774

Therefore, 3 Uod = Demand = 203 277 306 m /a 3 Uid = Return = 9 650 774 m /a

Substituting into equation 5a, using the average inflow (299 million m3) and the permitted use of water from the dam:

299.0 = Od + Lg + Lc – 203.3 + 9.7

105.4 = Od + Lg + Lc (6a) The numbers are in million m3 /year

Therefore the sum of dam outflow, the net loss of evaporation and rainfall, and the net loss due to ground water seepage is on average 105.4 million m3/year after taking the use into account.

6.2.3 WATER QUALITY The quality measured in the dam is also dependent on point releases from industry and municipalities (see Figure 6.2). The assumption is made that the mass load contribution, for TDS, from the grouped non-point-sources is much greater than the mass load from the point sources. To justify this assumption, an indication of the contribution of the non-point-sources is determined by taking the difference between the average mass load measured, in TDS, at the inlet to the dam and the total mass load, in TDS, from the point sources to the surface water bodies. Excluded from the calculation, are the users that release their wastewater outside the catchment and users that do not release wastewater.

Mass Loads: Average TDS at dam = 164 mg/l Average annual flow into dam = 299 x 106 m3 Total Mass Load = 164 (x 10-3 kg/m3) x 299 x 106 m3 = 49.04 x 106 kg

Average TDS and volumes released by users: Ermelo = 2 x 106 m3 at 633 mg/P = 1.27 x 106 kg Bethal = 3 x 106 m3 at 547 mg/P = 1.64 x 106 kg Thuthukane = 642 x 103 at 390 mg/P = 0.25 x 106 kg Total mass of point loads = 3.16 x 106 kg = 6.4% of Total Mass Load

Based on the previous discussions and assumptions, the modelled situation for the dam is as follows:

DAM INLET

LOSSES DAM DAM OUTFLOW

USERS

Figure 6.5: Modelled Grootdraai Dam

Using the above configuration the following data were used for the model 1. Dam Inlet to Dam Volume = Average over 20 years of 299 million m3 TDS = 8 – 251mg/P, with an average of 164 mg/P

2. Dam outflow + Losses from Dam Volume = Average over 20 years of 105.4 million m3 TDS = 8 – 251mg/P, with an average of 164 mg/P

3. Dam to Users Volume = Modelled, with a maximum intake of 203.3 million m3 TDS = 8 – 251mg/P, with an average of 164 mg/P

7 AGRICULTURAL USE

The volumes extracted by the agricultural sector are recorded by DWAF in the form of permits. Farmers provide information to DWAF on their water requirements for specific farming activities, which are collated for catchment management, and charging purposes. The data on extractions in the Grootdraai catchment are provided in the table below.

Table 7.1 Extraction volumes of Agriculture USER SOURCE PERMIT (m3/a) Irrigation Borehole 2 202 690 Dams* 7 598 115 Rivers/Streams 33 131 898 Other 373 297 Livestock Watering Borehole 990 920 Dams 5 600 Rivers/Streams 596 271 Other 113 209 *Grootdraai dam = 321 500 m3/a

The agricultural users have three main sources of water, namely, rainfall, surface water (dams, rivers and streams) and groundwater. The water extracted from the surface and groundwater sources are used to supplement the water obtained from rainfall. The water extracted is therefore dependent on the amount or lack of rainfall and varies considerably. The release of water is, as mentioned previously, treated as a non-point source, i.e. evapotranspiration and seepage. The volume released annually as evapotranspiration, is dependent on numerous factors, which vary from site to site: Type of crop Humidity Soil moisture content and the height of the water table Wind speed Temperature

The quality demanded by the two subcategories, namely livestock watering and irrigation, was derived from the South African Water Quality Guidelines (SAWQG)2. The SAWQG serve as the primary source of information for determining the water quality requirements of different water users and for the protection and maintenance of the health of aquatic ecosystems.

2 A water quality guideline is a set of information provided for a specific water quality constituent. 28

The upper boundaries of the No Effects3 water quality range of the SAWQG were used for TDS. The limits relevant to this study were as follows:

Table 7.2 Selected SAWQG for Livestock Watering and Irrigation Agriculture Type TDS (mg/P) Livestock Watering 1000 Irrigation 267

The Grootdraai dam has an average TDS of 164mg/P, which is of a higher quality than is required by the agricultural sector.

3 For each water quality constituent there is a No Effects Range. This is the range of concentrations or levels at which the presence of that constituent would have no known or anticipated adverse effects on the suitability of water for a particular use. These ranges were determined by assuming long-term continuous use and incorporation of a margin of safety. 29

7.1 MODEL INPUT

There are numerous users located throughout the catchment. Extraction methods utilised include both surface and groundwater sources. The effluents generated by agricultural users are non-point releases through seepage into ground water and runoff into rivers. The use of water in the agricultural sector can be described as follows:

GROUNDWATER WATER FLOW OUT OF CATCHMENT RAINFALL

SYSTEM BOUNDARY

SEEPAGE

GROUNDWATER

AGRICULTURE EVAPORATION, TRANSPIRATION

SURFACE WATER

RUNOFF

SURFACE FLOW SUPPLY FROM INTO DAM GROOTDRAAI DAM

Figure 7.1 Water balance for Agriculture

Irrigation serves as a supplement to the shortages from rainfall. For a water balance across the system, the focus is on the inputs and outputs:

RA + U0A = EA + G0A + IA

Where,

RA = Rainfall onto agricultural land

U0A = Water demand from dam

EA = Evaporation and transpiration from agricultural land

G0A = Portion of groundwater flow out of catchment, originating from agriculture

IA = Portion of dam inflow from agriculture

But,

RA is an element/portion of R (total rainfall)

EA is an element/portion of E (total evaporation)

IA is an element/portion of I (total inflow into dam)

GOA is an element/portion of G (total groundwater flow from catchment)

Since these elements have been accounted for in the overall balance (Section 6.2), they do not have to be considered further. Therefore, the only variable not accounted for thus far is water demand from the dam for agricultural purposes. Of all the numerous agricultural users, only one irrigation user actually draws from the Grootdraai dam. Following this argument, the model should only include this user and exclude the rest of the agricultural users that do not draw from the dam.

Based on the above arguments, the modelled situation for agriculture is therefore as follows:

AGRICULTURE

Figure 7.2 Modelled Agriculture

X to Agriculture Volume = Permitted amount of 321 500 m3 TDS = Maximum of 267 mg/P

8 INDUSTRIAL USE

The industrial sector consists of users located inside and outside the catchment. The major users are ESKOM and SASOL. A description of these users follows in the subsections below.

8.1 ESKOM [17]

8.1.1 WATER REQUIREMENTS Eskom has two power stations that draw water from the Grootdraai dam, namely, Tutuka and Matla. The required volumes are presented in Table 3.

Table 8.1 Grootdraai Dam Power Station Water Consumers Power Station Permit (m3/year) Tutuka 47 420 000 Matla 53 838 000

The quality requirements of power stations are such that they can be operated on water of poor quality provided sufficient water treatment is undertaken. With the added desalination, increased brine disposal is required, where brine is the by- product of water treatment. The disposal of brine has been specifically highlighted by ESKOM as a major problem.

To limit the brine disposal and its associated problems, ESKOM has set the following TDS requirements for the Vaal River system: Ideal TDS concentration of less than 120 mg/P Tolerable TDS concentration of: 120 – 240 mg/P Unacceptable TDS concentration of greater than 240 mg/P

In addition to the TDS requirements listed above, ESKOM also have the following water quality objectives for their power stations operating on a raw water supply from the Vaal River system:

Table 8.2 ESKOM additional requirements Parameter Units Ideal AcceptableNot Acceptable Conductivity uScm-1 < 160 160 to 320 > 320 Total Organic Carbon mgkg-1 as C < 2 2 to 5 > 5 Sodium mgkg-1 as Na < 10 10 to 25 > 25 Chloride mgkg-1 as Cl < 5 5 to 15 > 15 Sulphate mgkg-1 as < 15 15 to 40 > 40 SO4 Permanent hardness mgkg-1as Nil < 8 > 8 (T Hardness – M CaCO3 Alkalinity) M Alkalinity mgkg-1 as < 60 60 to 120 > 120 CaCO3 Total hardness mgkg-1 as < 60 60 to 120 > 120 CaCO3 Barium ugkg-1 as Ba < 30 30 to 60 > 60 Strontium ugkg-1 as Sr <80 80 to 120 >120

8.1.2 WASTEWATER Both power stations must conform to the Zero Liquid Effluent Discharge (ZLED) policy. The two power stations therefore release zero effluent into the system. The effluent is used instead to transport the coal-ash to the ash disposal site. Thuthukane Township, which forms part of Tutuka power station, has a maximum allowable (permitted) discharge of 1760 m3 per day and TDS of 390 mg/P.

8.2 SASOL [18]

8.2.1 WATER REQUIREMENTS SASOL extracts 91 250 000 m3 per year of its water requirements from the Grootdraai Dam. This is used for boiler feed water and cooling water. The raw water, obtained from the dam, is treated by a water treatment plant to meet their water quality requirements. The volume of water required increases with an increase in TDS, e.g. an additional 10 950 000 m3 per year is extracted when TDS increases from 200 to 300 mg/P. This increases the volume of water required to 102 200 000 m3/a for a TDS of 300 mg/P.

8.2.2 WASTEWATER Most wastewater, that is high in TDS, is used to transport coal ash to the ash disposal site. Therefore the ash disposal site functions also as a sink for a large part of the TDS. Approximately 4 015 000 m3 per year at a TDS of 900 mg/P is released into the Waterval river, located in the Waterval catchment.

8.3 MODEL INPUT

Industrial plants are treated as processes. The pinch program is not equipped to handle differences between inlet and outlet volumes; therefore to overcome this, the plants with a difference between inlet and outlet volumes are divided into two processes. For the first of the two processes the process volume and the inlet concentration are the characteristics of the water that enters the process. The outlet concentration in the model is the actual outlet concentration of the plant, but does not have the associated volume that the plant releases. The second of the processes is used to account for the change in volume. The inlet and outlet concentration is equalled to the outlet of the first process, while the process volume is set to the actual outlet volume of the plant.

Based on the above arguments, the modelled situation for industrial users is therefore as follows:

INDUSTRIAL (IN) LOSSES

INDUSTRIAL (OUT)

Figure 8.1 Modelled Industrial Users

1a) X to Tutuka (in) Volume = Permitted amount of 47 420 000 m3 TDS = Maximum of 240 mg/P 1b) Tutuka (in) to Tutuka (out) Volume = 0 TDS = 0

2a) X to Matla (in) Volume = Permitted amount of 53 838 000 m3 TDS = Maximum of 240 mg/P 2b) Matla (in) to Matla (out) Volume = 0 TDS = 0

3a) X to SASOL (in) Volume = 91 250 000 m3 (TDS = Maximum of 200 mg/P) Volume = 102 200 000 m3 (TDS = Maximum of 300 mg/P) 3b) SASOL (in) to SASOL (out) Volume = 4 015 000 m3 TDS = 900 mg/P

9 MUNICIPALITIES

Municipalities either source their input water from the Grootdraaidam or from an upstream dam or tributary. For the modelling it was assumed that all water was extracted from the dam. No specific information on TDS content for the upstream dams or tributaries was available and therefore the TDS content of the Grootdraaidam was used for the model.

The municipalities and their wastewater releases are listed in Table 9.1. Amersfoort and Morgenzon municipalities’ wastewater is used for irrigation. Given the end use and the small volumes, these two municipalities have not been included in the modelling. To prevent municipalities from receiving the wastewater of other municipalities and users, due to the sensitivity of their requirements outside that of TDS, the inlet water quality was limited to that of the dam. The data from the DWAF report, the Augmentation of the Eastern Sub-system of the Vaal River system [17], is described in the table below:

Table 9.1: Municipal wastewater releases [1] Flow TDS Point Sources (m3/day) (mg/P) Recipient Ermelo Municipality (2 treatment Klein Kafferspruit works combined) 5683 633 Bethal Municipality Tributary 8250 547 (Blesbokspruit) Armersfoort Municipality 170 - Irrigation Morgenzon Municipality Irrigation / Diluting 400 - medium (nightsoil) Thuthukane Township 1760 [17] 390 Leeuspruit

An estimate of the water losses were made by using Ermelo municipality as a base. The inlet volume for Ermelo raw water treatment plant is 3 600 000 m3 per year [19]. The outlet for Ermelo wastewater treatment plants is 1 982 124 m3 per year. This is a total loss across the system of 45%. Using a loss of 45% for the remaining 2 municipalities the inlet and outlet volumes for the municipalities are as follows:

Table 9.2 Municipal water use Ermelo (in) 3 600 000 Ermelo (out) 1 982 124 Bethal 5 420 250 Bethal (out) 3 011 250 Thuthukane (in) 1 427 556 - Sourced from Tutuka Power Station Thuthukane (out) 642 400

9.1 MODEL INPUT

The same situation as far as difference in inlet and outlet volumes occurs in Municipalities as with Industrial users. The same approach of splitting the user into two processes is therefore taken.

Based on the above arguments, the modelled situation for municipalities is therefore as follows:

MUNICIPALITY LOSSES (IN)

MUNICIPALITY (OUT)

Figure 9.1 Modelled municipal users

1a) Dam to Ermelo (in) Volume = 3 600 000 m3 TDS = 8 – 251mg/P, with an average of 164 mg/P 1b) Ermelo (in) to Ermelo (out) Volume = 1 982 124 m3 TDS = Average of 633 mg/P

2a) Dam to Bethal (in) Volume = 5 420 250 m3 TDS = 8 – 251mg/P, with an average of 164 mg/P 2b) Bethal (in) to Bethal (out) Volume = 3 011 250 m3 TDS = Average of 547 mg/P

3a) Dam to Thuthukane (in) Volume = 1 427 556 m3 TDS = 8 – 251mg/P, with an average of 164 mg/P 3b) Thuthukane (in) to Thuthukane (out) Volume = 642 400 m3 TDS = Average of 390 mg/P

10 MODEL APPLICATION

Based on the data and its manipulation in the previous sections, the water pinch model developed by Chris Brouckaert was applied to the following data, used as representation for the Grootdraai catchment. The part of the model that takes costs into consideration was excluded from the modelling as this was not part of the scope. The differences between the two parts of the table are explained on page 52. Table 10.1 Model Input

Mass balance for individual water users

Maxim Maximum TDS Outlet Outlet Process Inlet Inlet vol TDS(ton) Vol loss (Tons) Outlet vol Concn (Tons) Irrigation 0.267 321500 85.84 321500 85.84 0 0.00 Tutuka 0.24 47420000 11380.804742000 11380.8 0 0.00 Matla 0.24 53838000 12921.125383800 12921.1 0 0.00 Sasol 0.3 102200000 30660.009818500 27046.5 4015000 0.903613.50 Ermelo 0.164 3600000 590.401617876 -664.28 1982124 0.63 1254.68 Bethal 0.164 5420250 888.922409000 -758.23 3011250 0.55 1647.15 Thutukane 0.164 1427556 234.12 785156 -16.42 642400 0.39 250.54 Total 214227316 9650774 Best TDS Outlet Outlet Process Inlet Inlet vol TDS(ton) Vol loss (Tons) Outlet vol Concn (Tons)

Irrigation 0.164 321500 52.73 321500 52.73 0 0.00 Tutuka 0.164 47420000 7776.884742000 7776.88 0 0.00 Matla 0.164 53838000 8829.435383800 8829.43 0 0.00 Sasol 0.164 102200000 16760.809818500 13147.3 4015000 0.903613.50 Ermelo 0.164 3600000 590.401617876 -664.28 1982124 0.63 1254.68 Bethal 0.164 5420250 888.922409000 -758.23 3011250 0.55 1647.15 Thutukane 0.164 1427556 234.12 785156 -16.42 642400 0.39 250.54 Total 214227316 9650774

In the above table the input information is summarized in the form of a mass balance, taking volume and TDS into account. The table shows that the total amount of available waste water is 9650774 m3. However the municipalities release waste water back into the catchment and therefore if this water is re-used it does not reduce the overall amount of water used in the catchment. In the following diagram the intake volumes and the outlet volumes are represented graphically showing that the total outlet volumes are 4.5% of the intake volumes.

WATER DEMANDWATER USAGE WATER RELEASE

Tutuka Power Station

Matla Power Station

SASOL discharge to Waterval River SASOL

Ermelo Municipality

Bethal Municipality

Thuthukane Township Irrigation Fig 10.1 Intake and outlet volumes

Two scenarios are represented.

The first scenario is based upon the maximum inlet concentrations that the users accept as explained in the previous sections. From these maximum inlet concentrations and the actual intake volumes the maximum TDS was calculated. The same procedure was followed for the output streams, therefore the concentrations in table 10.1 are the maximum outlet concentrations for each user. In the previous sections it was discussed that irrigation and the power stations have no outlet stream and therefore also no outlet TDS. The loss of both volume and TDS is 100%. Therefore the modelling parameters are set so that no waste water from these users is available for others. The other users have an outlet stream and therefore also an outlet TDS, but there are losses which can be either positive or negative. For example SASOL has a volume loss of 96% and a TDS loss of 88%. The reason is that most of Sasol’s intake water is evaporated as cooling water and brine stream is used to transport coal ash to the ash dump. The municipalities reported a water loss of 45%, but a TDS increase (negative loss). 40

The reason for the volume reduction is that part of the intake water is not returned to the sewage system as it is used for e.g. watering gardens. The reason for the increase in overall TDS is that the sewage water has a much higher TDS than the intake water.

In the second scenario it is assumed that all users use the best input quality water e.g. water from the dam. It is further assumed that the outlet volumes and concentrations are the same as in the first scenario. Therefore all volumes in the second scenario are the same as in the first scenario, but for the industrial users the TDS loss is smaller than in the first scenario. In a real plant situation the volume of the intake water would have been reduced for the second scenario as was discussed in the previous section, but no information about this reduction was available and therefore it was not taken into account.

During the modelling a comparison was made between the first scenario and the second one during each modelling run, showing how much water could be saved, if all waste water would be re-used.

11 RESULTS AND DISCUSSION

The model was applied in two ways, namely fixed concentration and fixed mass load.

With fixed concentration, the concentration of TDS was fixed for the outlet water stream. No matter what is done to the flow rate to/from that plant or process or what happens to the inlet concentration, the outlet concentration will remain the same. The program will adjust the mass load over the process in such a way as to satisfy the fixed concentration condition. The fixed concentration mode is typically used in a plant situation where there is something precipitating or dissolving in contact with a solid phase, so that the outlet concentration is fixed by equilibrium considerations. It can also be used in a situation where there is a treatment process with some kind of feedback control to maintain a specified outlet concentration.

The result was as follows: Table 11.1 Results for fixed concentration

Flows (ML) To Irrigati Tutuka Matla Sasol Ermelo Bethal Thutukane Total from on dam

From Irrigation 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Tutuka 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Matla 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Sasol 30.4 1992.2 1992.2 0.0 0.0 0.0 0.0 Ermelo 6.3 984.2 984.2 7.5 0.0 0.0 0.0 Bethal 7.1 1501.4 1501.4 1.3 0.0 0.0 0.0 Thutukane 0.0 321.1 321.1 0.0 0.0 0.0 0.0 Dam 277.7 42621.1 49038. 102191. 3600.0 5420.3 1427.6 20457.5 7 2 Conc Inlet 0.2513 0.2184 0.2119 0.164 0.164 0.164 0.164 (kg/m3) Outlet 0.901 0.633 0.547 0.390 Flows if all users are supplied only from dam (ML) Dam 321.5 47420 53838 102200 3600 5420.3 1427.6 214227.3 Difference 9650.8

With Fixed Mass Load, the mass load change over a plant/process was fixed. In this way a constant amount of TDS is added to the stream no matter what is done to the flow rate to/from the plant or process or what happens to the inlet concentration. The program will adjust the outlet concentration of the stream in order to satisfy this condition. The fixed mass load approach is the standard model of a water-using process. The philosophy is that the function of the water is to remove contaminants from the process stream and as the pinch analysis will not

affect the operation of the process, the load of TDS will be fixed. The results are shown below:

Table 11.2 Results for fixed mass loads

Flows To (ML) Irrigation Tutuka Matla Sasol Ermelo Bethal Thutukane Total from dam From Irrigation 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Tutuka 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Matla 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Sasol 0.0 1.0 1.0 4012.0 0.0 0.0 0.0 Ermelo 0.0 0.0 0.0 1982.0 0.0 0.0 0.0 Bethal 0.0 0.0 0.0 3011.0 0.0 0.0 0.0 Thutukane 0.0 0.0 0.0 642.0 0.0 0.0 0.0 Dam 321.0 47419.0 53837.0 92552. 3600.0 5420.3 1427.6 20457.5 0 Conc Inlet 0.2513 0.2184 0.2119 0.164 0.164 0.164 0.164 (kg/m3) Outlet 0.901 0.633 0.547 0.390 Flows if all users are supplied only from dam (ML) Dam 321.5 47420 53838 102200 3600 5420.3 1427.6 214227.3 Difference 9650.8

The output of the model for both fixed concentration and fixed mass load shows that all waste water can be re-used in principle. However the fixed concentration model allocates nearly all waste water to the two power stations and the fixed mass load model allocates nearly all waste water to SASOL. Upon trying to understand this difference in allocation it appeared that the number of parameters to be optimised was small and that the model could satisfy its requirements in many ways depending on chance starting conditions. It is therefore concluded that the model cannot indicate the optimum solution, as more than one optimum solution exist. The differences between the two results above are in fact not nearly as significant as the output would suggest.

In order to increase the understanding of the possible allocations for the different waste water streams to the potential users, a spreadsheet was compiled showing the different users and how effluent water can in principle be allocated depending on the maximum TDS levels that the user can tolerate. It must be emphasized that this study is considering only TDS as a parameter, and that if allocations would be done in the real world that all contaminants for which a user has set a maximum must be taken into account.

Table: 11.3 Spreadsheet allocation of waste water to users Supplier User Vol. Irrigation Tutuka Matla Sasol Ermelo Bethal Thutuka Irrigation 321500 0 0 0 44993 71061 86461 146524 Tutuka 4742000 0 0 0 4015000 1982124 3011250 642400 Matla 5383800 0 0 0 4015000 1982124 3011250 642400 Sasol 1022000 0 0 0 4015000 1982124 3011250 642400 Ermelo 3600000 0 0 0 0 0 0 0 Bethal 5420250 0 0 0 0 0 0 0 Thutukane 1427556 0 0 0 0 0 0 0

NB Tutuka can take all Sasol’s waste water and Thutukane’s and Ermelo’s or another combination without exceeding its TDS limit. Matla can take all Sasol’s waste water and Thutukane’s and Ermelo’s or another combination without exceeding its TDS limit. Sasol can take all waste water including its own without exceeding its TDS limit.

Table 11.3 shows options for the users. For example, irrigation as a user can take 44993 m3 from Sasol or 71061 m3 from Ermelo or 86461 m3 from Bethal or 146524 m3 from Thutukane. A similar situation exists for the other users. From the table it is clear that there is more than enough capacity to re-use all the waste water streams without exceeding the inlet requirements on TDS for the individual users. It shows that the larger users can take the total waste water stream of a supplier or even a number of suppliers. The table also shows that there are many potential allocations and as long as no additional criteria are set e.g. the cost of transporting the waste from the generator to the user or criteria for other contaminants, all these allocations are equivalent confirming the observation that the model chooses, more or less at random, a solution.

The overall reduction on the demand from the dam would be equal to the total amount of re-used waste water, which is 9.6 million m3/year (4.5% of the current demand on the dam). However a large part of the waste water that is currently returned upstream from the dam in the rivers of the catchment is flowing into the dam. If this waste water would be allocated to other users the inflow to the dam would be reduced by this amount which is 5.6 million m3 /year. (2.6% of the current demand on the dam.

12 CONCLUSION

The following conclusions were drawn from the study:

There are large differences between a catchment and a plant situation for which the model was designed and in order to use a water pinch type model for a catchment, considerable changes to the current model would likely be required.

The modelling as well as the spreadsheet calculation showed that in terms of TDS inlet requirements all waste water could be re-used by the main water users.

The study catchment area may not be representative for other catchments for two reasons. In this particular catchment, only a small percentage of the inlet water is released as waste water, due to the presence of industries that evaporate most water as part of their processes. Also another aspect of this type of industry is that most of the TDS in the inlet water is not returned to the surface water of the catchment, but becomes part of the ash disposal sites.

13 RECOMMENDATIONS

As good water management is important for South Africa in general and, more specific, in catchments such as the Grootdraaidam catchment, where water demand is likely to exceed water supply in the future, it is recommended to investigate the development of a model that can reliably simulate all the important aspects of a catchment and thereby help to reduce water use by optimising the allocation of waste water to different users. This model should be based upon the principles of water pinch, but would be substantially different from existing models.

14 ACKNOWLEDGEMENTS

The authors wish to acknowledge the Water Research Commission for financially supporting this project.

The authors wish to acknowledge Greg Steenveld for his technical advice during the execution of the project, Chris Brouckaert for making the water pinch programme available and the valuable contributions that he made in the application of water pinch modelling. The authors also wish to acknowledge the other members from the steering committee for making their time available for the meetings and their inputs in the report.

REFERENCES

[1] DWAF, BKS, 1998 Augmentation of the Eastern Sub-system of the Vaal River System: Desktop Study

[2] Rossiter A P, 1995 Waste Minimisation Through Process Design, Chapter 5, Pinch Analysis in Pollution Protection

[3] Eastwood A R, Tainsh R A, Fien G J, 1998 Minimising Wastewater Emissions using Water Pinch TM Analysis: A Technical White Paper

[4] Brouckaert C J, et al, 1999 Optimal location of a membrane treatment plant in a Power Station. Paper presented at IAWQ International Specialised Conference on Membrane Technology in Environmental Management, Tokyo

[5] IUCN, Goldblatt, N. et al., 2000 Water demand management: Towards developing effective strategies for Southern Africa [6] Hall SG, 1997 Water and effluent minimisation, Institution of Chemical Engineers, North Western Branch Papers, No. 4

[7] Dhole VR, Ramchandani N, Tainsh RA, 1996 Make your process water pay for itself, Chemical Engineering, Vol. 103, Issue 1, pp 100-103

[8] Schaareman M, Verstraeten E, Blaak R, Hooimeijer A, Chester I, 2000 Energy and water pinch study at the Parenco Paper Mill, Paper Technology, Vol. 41, Part 1, pp 47-52

[9] Tripathi P, 1996 Pinch technology reduces wastewater, Chemical Engineering, Vol. 103, Issue 11, pp 87-89

[10] Hamilton R, Dowson D, 1994 Pinch cleans up, Chemical Engineer, Part 566, pp 42-44

[11] Cripps, H, 2000 Pinch technology for waste minimisation, Paper Technology, Vol. 41, Part 1, pp 33-38

[12] Alva-Argaez A, Kokossis AC, Smith R, 1998 Wastewater minimisation of industrial systems using an integrated approach, Computers and Chemical Engineering, Vol. 22 - supplement, pp s741-744

[13] Smith R, Petela R, 1994 Wastewater minimisation and the design of effluent treatment systems using pinch analysis, Environmental Protection Bulletin, Part 030, pp 5-10

[14] El-Halwagi, Manousiouthakis V, 1989 Synthesis of mass exchange networks, AIChE Journal, Vol. 35, No. 8, pp 1233-1244

[15] El-Halwagi, Manousiouthakis V, 1990 Simultaneous synthesis of mass-exchange and regeneration networks, AIChE Journal, Vol. 36, No. 8, pp 1209-1219

[16] Wang YP, Smith R, 1994 Wastewater minimisation, Chemical Engineering Science, Vol. 49, No. 7, pp 981-1006

[17] Discussion with Dirk Hanekom, ESKOM

[18] Discussion with Mario Augoustinos, Roux du Toit, SASOL

[19] Discussion with Ermelo Municipality

APPENDIX: MATHEMATICAL PROGRAMMING APPROACH TO WATER PINCH ANALYSIS

DOYLE AND SMITH (1997) Doyle and Smith considered that a water-using network is not simply a special case of a mass-exchange network, because operations such as cooling towers, steam systems and hosing operations cannot be considered as mass-exchangers. They pointed out that non-linear mathematical programming techniques suffered from difficulties in ensuring that they found the global optimum to a problem, rather than a local optimum, particular for problems involving many variables. Linear programming techniques, on the other hand, can handle very large problems, and global convergence is readily obtained. They therefore presented linear and non- linear formulations of the problem, and proposed a combined linear/non-linear approach to overcome the previously encountered difficulties. The basic model of a water-using operation (Figure A1) is similar to Wang and Smith’s fixed-load model, except that: i) an alternate option is considered, where the mass load is allowed to vary in order to fix the outlet concentration of contaminant ii) a water gain or loss is allowed, to model operations such as cooling towers or evaporators.

Figure A1 A water using process

The basic concepts of limiting flows and concentrations, and the relationship between them via the mass balances, are exactly the same as in Wang and Smith (1994a). To automate the procedure for finding the optimal set of connections between units, a superstructure for the network is considered (Figure A2). This allows, in principle, all possible connections.

Figure A2 The superstructure for a simple 2-process network

In the original paper, several different versions of the balance equations were given, which made the treatment difficult to follow. Here a somewhat different formulation is used, for compactness and clarity. The balance over process i can be expressed as Flow balance:

(7) Balance for component n.

(8) Where

Fji is the flow of (re-used) water from outlet of process i to inlet of process j

Fjw is tile flow of (used) water from outlet of process i to waste sink w

Fjk is the flow of (fresh) water from source i to inlet of process j

Cin is the concentration of ion n in outlet stream from process i

δin is the mass gain of contaminant n over process i

Wi is the water gain over process i

Balances of this form exist for each of the P processes and k contaminants in the system, and can be viewed as the basic set of process constraints. Specific limits on flows and concentrations, for a particular system, will form additional constraints. To complete the formulation, an objective function must be defined to provide the basis for optimisation. A rather general form for the objective function was proposed, representing fixed and variable costs associated with each stream in the system, to be minimised:

(9) (In fact, this form fails to address an important practical issue, namely where the cost associated with a particular stream is dependent on the contaminant load,

rather than just the flow rate, however there is no particular problem in including terms to represent this.) This formulation of the problem has non-linearities in the objective function (Equation 9) and in the component balances (Equation 8). It should usually be possible to use a linearised objective function as an approximation, but, in the case of fixed contaminant loads, the component balances are intrinsically non- linear because the terms which are products of flow rate and concentration, since both are variables in the problem. In the case of fixed outlet concentrations, however, Equation 8 is linear in the flow rates, since the concentrations are then known constants. Thus, if all processes in the system are of the fixed-outlet- concentration type, the problem could be formulated to a linear programming (LP) optimisation. Although this is a most unlikely scenario, it is reasonable to suppose that, in an optimised system, the concentrations will approach their limiting values. This means that the LP solution could be taken as a good starting estimate for a non-linear programming (NLP) optimisation. Providing a good starting estimate is the most important means of achieving satisfactory convergence in non-linear programming. This rationale forms the basis of the linear/non-linear approach.

ALVA-ARGAEZ, KOKKOSIS AND SMITH (1998) The extension to the Doyle and Smith treatment consisted of noting that once a set of flow rates had been obtained from the linear-programming solution, which assumes that the outlet concentrations are at their limiting values, one can calculate the corresponding set of concentrations, and determine where the assumptions are in error. If the calculated concentrations are below the limits, the errors are of no consequence. For concentrations which exceed the limits the errors can be added into the objective function to be minimised, so that running the LP algorithm again will tend to drive the errors to zero. This provides the basis for a method which uses a series of LP optimisations which converge to the NLP solution, taking advantage of the particular mathematical structure of water pinch problems. A further refinement introduced binary variables corresponding to each possible connection in the network. For these, a value of 1 indicates that the connection exists, and a value of 0 that it does not. This formulation allows automatic control of features such as the elimination of streams that fall below a specified flow rate, or the maximum number of connections allowed in the network, to avoid excessive complexity. These variables move the optimisations into the class of Mixed Integer (MI) programming - once again MILP is very much more tractable than MINLP.