The feed water quality associated with mine water treatment is typically characterised by a dynamic variability resulting from the fact that the final feed water to the water treatment plant (WTP) can be an amalgamation of water streams emanating from a number of sources. Consequently, the ability to deal with the dynamic nature of the feed water quality towards successful and sustainable mine water treatment goes beyond a proactive approach and requires a systemic, predictive approach. This paper discusses the development of an unsteady state mass balance model on a surface dam located on a coal mine towards predicting the dynamic fluctuations in total dam volume and its total dissolved solids (TDS) concentration in the feed water to a NuWater 20 MLD mobile WTP, comprising chemical conditioning, ultrafiltration and reverse osmosis (RO). The unsteady state mass balance, incorporated water entering the dam via the opencast pits, underground compartments, seasonal rainfall and the RO brine return. Water leaving the dam comprised the feed water to the WTP, partial brine treatment, surface evaporation and seepage. Validation of the model using actual data over an 8-month period showed excellent results. The model showed that without water treatment, the dam would overflow in 218 days. Although the dam's volume could be sustained at the ideal volume by treating 14.2 MLD, its TDS would exceed the maximum environmental limit in 197 days. Consequently, the combination of a 13.2 MLD WTP with a 1 MLD brine treatment plant provided the optimal water treatment strategy to sustainably maintain the dam's TDS concentration and volume within acceptable limits over the 5-year investigation period. This paper demonstrates the importance of using a predictive methodology for forecasting feed water characteristics and as an early warning system for most water treatment systems that are subjected to dynamic conditions.

INTRODUCTION

The design of a water treatment system is fundamentally centred on the quality (characteristics) of the feed water and the corresponding required product water quality. Amongst other criteria, the capital and operating costs, the availability of chemicals and energy demand and supply etc. are also taken into consideration.

Often a single feed water analysis together with temporal and spatial variability in the feed water characteristics accounted for by utilising the 75th percentile or 95th percentile data, containing information such as the dissolved cationic and anionic species, the suspended solids concentration, biological descriptors and stream parameters such as pH and temperature are used to design and build a water treatment plant (WTP). Ideally, it is expected that any variability in the quality of the feed water during the operational lifespan of the WTP will be within the design limitations of the plant.

The feed water quality associated with mine water treatment is typically characterised by a dynamic variability in the concentration of dissolved ionic species, suspended particles, the presence of heavy metals, organics and biological species. This variability results from the fact that the final feed water to the WTP can be a complex amalgamation of water streams emanating from a number of sources such as surface water, pit water, mine drainage water etc. Seasonal climatic variability with regards to rainfall, evaporation and feed water temperature also impact on the final feed water quality.

Consequently, the ability to cope with this dynamic nature of the feed water quality towards preparing and executing a successful, sustainable mine water treatment operational strategy goes beyond a proactive approach and requires a systemic, predictive approach.

To this end, the unsteady state mass balance approach was adopted to model and predict the temporal variability in the characteristics of the feed water abstracted from a surface dam to a NuWater 20 mega litre per day (MLD) (20,000 m3/day) mobile and modular WTP that is located on a coal mine in South Africa's Gauteng Province.

The WTP's key unit operations are chemical conditioning, which consists mainly of pH adjustment, ultrafiltration (UF) for the removal of suspended solids and desalination by reverse osmosis (RO). Owing to the fact that the brine generated from the RO process is returned to the dam, there is a continuous year-on-year increase in salinity in the dam, not withstanding the local minima and maxima observed during the year, which are attributed to the dilutive influence of the rainy season and conversely the opposite effect during the dry season. Consequently, there is a necessity for partial RO brine treatment to maintain the dam's salinity within an acceptable level.

A key driver for this study was to investigate the temporal implications of a range of scenarios covering various combinations of WTP capacities and brine treatment plant (BTP) capacities on key dam descriptors that have a direct influence on specific constraints of the overall water treatment system. This was subsequently used to forecast the required plant operating strategy and to highlight the interventions necessary for ensuring sustainable water treatment. The results were also used to forecast if and when the feed water quality would deteriorate to a point that would fall outside of the plant's design limitations.

DEFINING THE SYSTEM BOUNDARY

Figure 1 below shows a flow diagram of the system with its input and output streams.
Figure 1

System flow diagram showing various input and output streams.

Figure 1

System flow diagram showing various input and output streams.

The system for which the unsteady state mass balance model was developed incorporated water entering the dam via the opencast pits, underground compartments, seasonal rainfall and the return of the RO brine back into the dam. The water leaving the dam comprised the feed water to the WTP, surface evaporation and seepage.

MODEL DEVELOPMENT

The unsteady state mass balance model was developed primarily to predict the temporal variability in:

  • 1. The total dissolved solids (TDS) concentration in the feed water for the purposes of assessing the proximity of the TDS to the maximum acceptable levels based on the mine's environmental guidelines, as well as the proximity to the hydraulic pumping design limitations of the RO plant due to the increase in the feed water's osmotic pressure at a higher TDS

  • 2. The overall volume of water remaining in the dam for the purposes of assessing the proximity of the water volume (level) to a maximum level beyond which the dam would overflow. Or conversely, the minimum volume below which, as a result of the proximity of the submersible intake suction pumps to the dam floor, the increased total suspended solids (TSS) concentration in the feed water abstracted from the dam would be higher than the maximum UF feed water design limit of 50 mg/L.

Model equations

The surface dam is a transient system and requires an unsteady state mass balance approach. The general unsteady mass balance equation for a chemical process is (Felder and Rousseau 2000): 
formula
1
Using the differential form of Equation (1) and recognizing that there are no generation and consumption terms for the surface dam system results in the following: 
formula
2
where M represents the mass of the system and represents the mass flowrate of a process stream.
Two independent mass balances are required to determine the TDS and dam volume as a function of time. Applying Equation (2), an overall mass balance on the dam yields: 
formula
3
Assuming that the water in the dam and all the process streams have a specific gravity of approximately one, Equation (3) can be written as: 
formula
4
where V represents the volume and represents the volumetric flowrate of a process stream. and can be related to the RO product water flowrate, as follows: 
formula
5
 
formula
6
where RO recovery represents the feed water recovery of the WTP and BT fraction represents the fraction of the total RO brine (stream 8) that is sent to the BTP.
The second mass balance developed is a balance on the TDS. Applying Equation (2) again: 
formula
7
where represents the mass flowrate of the TDS in a process stream.
The mass or mass flowrate of TDS can be written as a function of the volume or volumetric flowrate and the TDS: 
formula
8
Assuming that the TDS in the WTP feed water (stream 4) and seepage (stream 6) is the same as the TDS in the dam at any time: 
formula
9
Applying the product rule (Stewart 2001) to the left hand side of Equation (9) and rearranging: 
formula
10
The TDS of RO brine return (stream 5) can be related to the TDS of the dam by knowing the RO recovery, the RO rejection of the WTP and the BT fraction: 
formula
11

Equations (4) and (10) are the two independent unsteady state mass balances and together with the relationships (5), (6) and (11) represent the unsteady state model for the surface dam system. Various input parameters are required before the model can be used to solve for the dam TDS and overall dam volume as a function of time.

Setting up of the basis and specification of the input parameters

A description of the various streams, stream flowrates, TDS levels and the assumptions made in setting up the basis of the model to investigate different scenarios is presented below.

Pit water

The pit water inflow into the dam consisted of an amalgamation of streams emanating from four active pits on the opencast strip mine. The TDS concentration in the combined pit water blend into the dam was 2,500 mg/L based on information supplied by the mine. An average daily pit water volumetric inflow was used for all scenarios investigated and was calculated based on actual daily measured flows over the period 21 June 2013 to 20 February 2014 and found to be 18.87 MLD.

Rainfall and evaporation

The average monthly rainfall used in the model was based on actual historical rainfall data over a 22-year period spanning January 1989 to December 2011. The average monthly rainfall data in millimetres was converted to equivalent daily volumes (MLD) of rainfall into the dam by using the surface area of the dam as shown in Table 1. Furthermore, it was assumed that rainwater runoff into the dam was negligible and that the TDS concentration in the rainwater was 0 mg/L.

Table 1

Average monthly rainfall into the dam (January 1989 – December 2011)

Month Rainfall [mm] Rainfall into dam [MLD] 
January 125.85 8.24 
February 109.56 7.18 
March 88.92 5.82 
April 40.71 2.67 
May 21.96 1.44 
June 8.97 0.59 
July 0.10 0.01 
August 9.89 0.65 
September 17.72 1.16 
October 74.09 4.85 
November 95.62 6.26 
December 119.77 7.85 
Month Rainfall [mm] Rainfall into dam [MLD] 
January 125.85 8.24 
February 109.56 7.18 
March 88.92 5.82 
April 40.71 2.67 
May 21.96 1.44 
June 8.97 0.59 
July 0.10 0.01 
August 9.89 0.65 
September 17.72 1.16 
October 74.09 4.85 
November 95.62 6.26 
December 119.77 7.85 

A daily evaporation rate of 3 MLD was used based on information supplied by the mine. It was assumed that the TDS concentration of the evaporated water was also 0 mg/L.

Seepage

Both saturated and unsaturated seepage modelling typically takes into account various conditions such as variability in the soil type, seepage rates based on the differential head between the dam level and the water table, variability in the water table level etc. For the purposes of this study however, a fixed daily seepage rate of 5.5 MLD was used based on information supplied by the mine. Furthermore, it was assumed that the TDS concentration in the seepage was always equivalent to the prevailing dam TDS concentration.

WTP feed water

The feed water to the WTP was calculated as a function of the specified RO product water required for each of the scenarios and the current WTP RO recovery of 70%.

RO brine return

The RO brine return was calculated as a function of the specified RO product water required for each of the scenarios, the current WTP RO recovery of 70%, the WTP RO rejection and the BT fraction. An RO rejection of 98% was assumed for the purposes of this study. The BT fraction was dependent on the specific scenario being modelled.

RO product water

The required RO product water volume was a key input parameter in the model and was dependent on the specific scenario being modelled.

BTP product water and salt product

The BTP water recovery was assumed to be 100% with the BTP product water having a TDS concentration of 0 mg/L and consequently all of the dissolved species reporting to the BTP salt product.

Key dam volume specifications

  • 1. Maximum dam water holding capacity: The maximum water holding capacity of the dam was 8,290 ML, as stipulated by the mine based on detailed surveying. This maximum dam volume corresponds to a dam water elevation level of 1,426.2 m.

  • 2. Minimum dam water volume for effective water treatment: The minimum effective dam volume was 4,237 ML (elevation of 1,423 m) and was operationally determined as the dam elevation below which the increase in the uptake of suspended solids from the floor of the dam causes the TSS concentration to exceed the maximum UF feed water design TSS limit of 50 mg/L.

  • 3. Ideal dam water volume for sustained water treatment: The ideal dam water level was determined based on two key factors, namely (a) ensuring that in the event of the WTP being offline for a period of 6 months, there is sufficient spare water holding capacity in the dam to contain the total rainfall that could accumulate in the dam as a result of a one hundred year flood incident and (b) operating at dam elevation that maintains the WTP feed water TSS at an optimal concentration. Consequently, the ideal dam water volume for sustained water treatment was operationally determined to be 5,952 MLD (1,424.5 m).

Solution procedure

Equations (4) and (9) represent a set of coupled linear first order ordinary differential equations. The differential equations, equations (5), (6) and (11), and the various input parameters were implemented into a Matlab (version 7.11, R20102b) code. The differential equations were solved using the ode45 function with initial conditions of dam TDS and dam volume being specified. The initial conditions for all the scenarios investigated corresponded to the dam TDS (4,190 mg/L) and dam volume (5,638 ML) measured on 20 February 2014. The ode45 function is a non-stiff differential equation solver based on an explicit Runga-Kutta (4,5) formula (Hahn 2002).

SCENARIOS INVESTIGATED

Three key scenarios were investigated as summarised in Table 2. All scenarios were investigated starting from 1 March 2013 over a window period of 5 years, which was determined to sufficiently cover the mine's short-medium mining plan during which fixed parameters such as the pit water inflow and the required overall water treatment were expected to remain relatively constant.

Table 2

Description of different scenarios investigated

Scenario Description RO product water [MLD] BT fraction BTP product water [MLD] 
1 No water treatment – – – 
No brine treatment 
2 Fixed water treatment 14.2 – – 
No brine treatment 
3 Fixed water treatment 13.2 0.19 
Fixed brine treatment 
Scenario Description RO product water [MLD] BT fraction BTP product water [MLD] 
1 No water treatment – – – 
No brine treatment 
2 Fixed water treatment 14.2 – – 
No brine treatment 
3 Fixed water treatment 13.2 0.19 
Fixed brine treatment 

RESULTS AND DISCUSSION

Model validation

The model was firstly validated by comparing the model output data with the historical TDS and dam volume data (calculated from the elevation) over a period of 8 months from 21 June 2013 to 20 February 2014. The input data used in the model for the validation comprised of actual pit water inflows, WTP product water volumes and RO brine return volumes during the validation period. Figures 2 and 3 respectively show comparisons of the model-calculated dam volumes and TDS concentrations in comparison to the actual measured values for these parameters.
Figure 2

Comparison between the actual and simulated dam volume from June 2013 to February 2014.

Figure 2

Comparison between the actual and simulated dam volume from June 2013 to February 2014.

Figure 3

Comparison between the actual and simulated dam TDS concentrations from June 2013 to February 2014.

Figure 3

Comparison between the actual and simulated dam TDS concentrations from June 2013 to February 2014.

As can be seen from the validation results shown in Figures 2 and 3, the temporal variability of the model-simulated dam volume and TDS concentrations compare satisfactorily with the actual observed data over the validation period. In accordance with the validation testing procedure described by Sterman (2000), the model demonstrates good dimensional consistency and behavior reproduction.

Scenario 1: temporal variability in dam volume and TDS concentration with no water treatment and no brine treatment

Scenario 1 investigated the effect that an immediate cessation in the operation of the WTP would have on the temporal variability in the dam volume and TDS concentration. The results of this scenario are shown in Figures 4 and 5.
Figure 4

Temporal variability in dam volume with no water or brine treatment.

Figure 4

Temporal variability in dam volume with no water or brine treatment.

Figure 5

Temporal variability in dam's TDS concentration with no water or brine treatment.

Figure 5

Temporal variability in dam's TDS concentration with no water or brine treatment.

The results of the temporal variability in dam volume for Scenario 1 show that with an immediate cessation in water treatment, the net positive inflow of water into the dam would cause the level to rise to a point where it would reach the maximum dam volume of 8,290 ML within 218 days (5 October 2014), after which the dam would overflow. This confirms the central importance of the WTP in the overall mining operation.

The results of the temporal variability in dam's TDS concentration for Scenario 1 shows that with an immediate cessation in water treatment, the TDS concentration would start to decrease due to the dilutive effect of the net positive inflow of the lower salinity water i.e. rainfall and pit water at a TDS concentration of 2,500 mg/L, as well as the absence of salts re-entering the dam with the RO brine return stream. At the point in time when the dam would overflow (218 days), the TDS concentration of the dam water would be 3,541 mg/L, which is significantly higher than the environmentally acceptable limit for discharge into a natural river system.

Scenario 2: temporal variability in dam volume and TDS concentration with fixed volume water treatment but no brine treatment

Scenario 2 was set up to determine the required volume of treated water that needs to removed from the dam in the form of RO product water to achieve a water level that fluctuates within a narrow band just below the ideal dam volume of 5,952 ML (elevation of 1,424.5 m). An iterative process, whereby the RO product water was varied until the dam level remained stable, established that the required RO product volume was 14.2 MLD. The model-predicted temporal variability in the dam volume and TDS for Scenario 2 are shown in Figures 6 and 7.
Figure 6

Temporal variability in dam volume with a fixed of RO product water production rate of 14.2 MLD and no brine treatment.

Figure 6

Temporal variability in dam volume with a fixed of RO product water production rate of 14.2 MLD and no brine treatment.

Figure 7

Temporal variability in dam TDS concentration with a fixed of RO product water production rate of 14.2 MLD and no brine treatment.

Figure 7

Temporal variability in dam TDS concentration with a fixed of RO product water production rate of 14.2 MLD and no brine treatment.

Figure 7 shows that, despite the fact that the dam volume remains at the ideal level, the temporal variability in the dam's TDS concentration increases rapidly to the point where after 197 days (14 September 2014), the TDS exceeds the mine's environmental maximum level set point of 5,250 mg/L. Moreover, within 856 days (4 July 2016), the TDS concentration reaches a level of 6,500 mg/L, which marks the TDS beyond which the RO system's hydraulic pumping limitation is reached as a result of the increased osmotic pressure and that would result in a decline in the WTP's overall water recovery.

Consequently, the modeling results for Scenario 2 clearly demonstrate the necessity for, at the very least, some degree of brine treatment in order to ensure that the dam TDS remains within acceptable limits.

Scenario 3: temporal variability in dam volume and TDS concentration with fixed volume water treatment and fixed volume brine treatment

Scenario 3 investigated the effect that an immediate (i.e. implementation on 1 March 2014) addition of a BTP to the WTP would have on the temporal variability in the dam volume and TDS concentration. Given that the addition of a thermal BTP would result in an immediate and substantial increase the cost per cubic meter of water treated, irrespective of whether the selected brine treatment process was a thermal evaporation process, a freeze/eutectic freeze crystallization process or a hybrid of the two, the obvious strategy was to select the smallest capacity BTP that would meet the dam's 5,250 mg/L TDS concentration limitation. To this end, the brine treatment fraction and by extension the required capacity of the BTP was determined iteratively by incrementally raising the BTP capacity up to the point where the dam's TDS concentration remained below the 5,250 mg/L limit over the 5-year scenario window. This minimum capacity of brine treatment required was determined to be 1 MLD. The results of this scenario are shown in Figures 8 and 9.
Figure 8

Temporal variability in dam volume with a fixed of RO product water production rate of 13.2 MLD and a BTP production rate of 1 MLD.

Figure 8

Temporal variability in dam volume with a fixed of RO product water production rate of 13.2 MLD and a BTP production rate of 1 MLD.

Figure 9

Temporal variability in dam's TDS concentration with a fixed RO product water production rate of 13.2 MLD and a BTP production rate of 1 MLD.

Figure 9

Temporal variability in dam's TDS concentration with a fixed RO product water production rate of 13.2 MLD and a BTP production rate of 1 MLD.

The Scenario 3 results show that by addition of a 1 MLD BTP, the dam's TDS concentration can be maintained below the critical level of 5,250 mg/L over the 5-year scenario window period.

A summary of the model-predicted critical dates for when the dam overflows or the TDS concentrations exceeds the maximum levels for the three scenarios is presented in Figure 10.
Figure 10

Summary of the critical dates for the three scenarios.

Figure 10

Summary of the critical dates for the three scenarios.

This study demonstrates the value of utilizing a predictive model such as the one described in this paper towards ascertaining the temporal variation in the feed water's TDS concentration and the fluctuations in total dam volume as a function of the rate of product water produced by the WTP and the partial brine treatment process. Furthermore, the information gained was used to forecast the required plant operating strategy in terms of selecting the appropriate volumes of water treatment and interventions such as brine treatment necessary for ensuring sustainable water treatment. The results were also used to forecast if and when the feed water quality would deteriorate to a point that exceeded the plant's design limitations.

It is important to highlight that the model is by no means limited to the three types of scenarios presented in this study. Given that one of the input parameters is the pit water inflow, the model will be a valuable tool for guiding the operating strategy for variability in the pit water inflow. This would include specifying the required changes to the WTP feed water and RO brine return volumes. Moreover, any variability of input parameters, such as changes in rainfall patterns and seepage can easily be investigated. The model can also be used to determine the required variability in terms of the required treatment capacities of the WTP and BTP in order to maintain a constant TDS and dam volume, even though this may not be a practical operating strategy.

Further applications of the model could be to use the predicted temporal variations in the dam TDS concentration to calculate the osmotic pressure and subsequently to determine the pumping power and energy demand of an RO system. In addition to this, by using the trend of the TDS concentration as an indicator of the variation in the dominant scaling species, the expected RO recoveries, antiscalant demand, etc. can be approximated.

Finally, this paper highlights the potency of developing and using smart process monitoring systems or sensors that can provide real-time data that can continuously be used to update predictive models for forecasting feed water characteristics not only for mine water treatment but most water treatment systems that are subjected to dynamic conditions.

CONCLUSIONS

  • 1. The development of an unsteady state model to predict temporal variability in the overall dam volume and dam TDS is a very useful tool for forecasting required interventions and future plant operating strategies. The model can be used as an early warning system to identify critical points in time when key plant or system operating limitations or constraints will be reached.

  • 2. The validation of the model with actual data over a 8 month period showed excellent results both with regards to the temporal variation in the predicted dam volume and the TDS concentration.

  • 3. The ramifications of an immediate cessation of water treatment are that the dam will reach its holding capacity in 218 days before overflowing. Furthermore, the TDS of the dam water at this point would be 3,541 mg/L, which is significantly higher than the environmentally acceptable discharge limit into a natural river system.

  • 4. For a scenario with a WTP but no BTP, the required volume of treated water that needs to removed be from the dam in the form of RO product water to achieve a water level that fluctuates within a narrow band just below the ideal dam volume was found to be 14.2 MLD. However, whilst the dam volume was maintained at an ideal level, the TDS concentration increased continuously to the extent that it firstly exceeded the maximum environmental limit within (197 days) and secondly the plant's RO system hydraulic pumping limitation within (856 days)

  • 5. The immediate (i.e. implementation on 1 March 2014) addition of a 1 MLD BTP to the WTP maintains the dam volume close to the ideal dam volume and the dam TDS concentration below the critical level of 5,250 mg/L over the 5-year modeling window period investigated.

  • 6. The unsteady state model can be used extensively to study the effect that a dynamic variation in input parameters such as the pit water inflow and TDS would have on the overall water treatment system. This information could subsequently be used to develop operational strategies that optimise plant performance and operational life.

  • 7. The development of smart process monitoring systems or sensors that can provide real-time data to continuously update predictive models can be used towards forecasting feed water characteristics not only for mine water treatment but most water treatment systems that are subjected to dynamic conditions.

REFERENCES

REFERENCES
Felder
R. M.
Rousseau
R. W.
2000
Elementary Principles of Chemical Processes
.
John Wiley & Sons, Inc.
,
NJ
, pp.
554
555
.
Hahn
B. H.
2002
Essential MATLAB for Scientists and Engineers
.
Pearson Education South Africa
,
Cape Town
,
South Africa
, pp.
287
296
.
Sterman
J. D.
2000
Business Dynamics: Systems Thinking and Modeling for a Complex World
.
McGraw-Hill
,
NY
.
Stewart
J.
2001
Calculus Concepts and Contexts
.
Wadsworth Group
,
CA
, pp.
199
201
.