# Self-Powered Desalination of Geothermal Saline Groundwater: Technical Feasibility

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}at evaporator temperature of 90 °C in desalination of brackish water containing 4000 mg kg

^{−1}NaCl at 70% recovery. A number of exergy studies have been carried out for ORC [13,14] and for RO separately [15,16], but relatively few for ORC coupled to RO [17,18].

## 2. Theory

#### 2.1. Exergy Analysis

_{sys}. Further parameters could be introduced to describe the quality (and not just quantity) of the water output, but these are not considered at the stage of the exergy analysis.

**Figure 1.**Self-powered geothermal desalination plant represented as a control volume that includes geothermal energy conversion and desalination equipment.

_{w}above ambient. The system rejects heat to the surroundings, at ambient temperature T

_{0}, such that the two streams exit at lower temperatures than that of the feed. There is no work input from the surroundings—the only work transfer will be internal to the system. The intention of the exergy analysis is to provide a preliminary and general indication of the theoretical scope for the self-powered separation using analytical expressions. At this initial stage, a highly accurate result is not sought because it is anticipated that the real performance will in any case be much less than the ideal one. Accordingly, the analysis will be simplified by a number of idealised assumptions and approximations as follows:

- The purified water is free of salt i.e., the rejection fraction is 100%. Indeed, most modern desalination technologies typically achieve rejection fractions well above 95%. This assumption is conservative, in that lower rejection fractions will generally require less energy, so the separation will be accomplished more readily.
- The energy consumptions of auxiliary processes (e.g., pre-treatment and post-treatment) are not considered. Due to the varied nature of these processes, however, they are not amenable to a generalised thermodynamic analysis. (In practice, auxiliary processes are important and these will later be discussed in outline in relation to specific case studies).
- Similarly, energy needed to lift the water from the source, and potential or kinetic energy associated with the pressure of the source water, are neglected.
- Assumptions valid for dilute solutions are used: the density and specific heat capacity are considered independent of concentration, and osmotic pressure is considered proportional to the molar concentration of salt. This is justified by the fact that groundwater sources studied here have salt concentrations <10,000 mg/kg.

^{−1}); and $\dot{S}$ the entropy flow (kJ K

^{−1}s

^{−1}). The superscript * refers to the thermal (i.e., restricted) dead state obtained when the water is brought to the ambient temperature T

_{0}and pressure P

_{0}without change in concentration. For a process assumed to have unchanged pressure between inlet and outlet:

_{osm}is assumed to follow the van’t Hoff relation:

_{osm}also takes into account the dissociation of the salts present and experimentally determined values of osmotic coefficient, as detailed in the Appendix.

_{sys}achievable based on the exergy consideration:

_{sys}. Thus, at A = 2.3, r

_{sys}could be as high as 0.9 in principle, which would usually be considered a very good recovery ratio for a desalination process because only 10% of the feedwater is wasted. To give a preliminary practical example, this value of A = 2.3 would be achieved with a feed temperature of just T

_{w}= 57 °C at ambient conditions T

_{0}= 40 °C and saline water with P

_{osm}= 800 kPa, corresponding to NaCl solution of concentration about 10,000 mg kg

^{−1}. The exergy analysis thus reveals plenty of scope for the self-powered desalination process even with low temperature sources.

_{sys}.

#### 2.2. Reverse Osmosis System

**Figure 2.**Essential losses in a simple Reverse Osmosis (RO) system with no Energy Recovery Device (ERD). Allowing for these losses only, a semi-ideal specific energy consumption SEC

_{sideal}is defined for the process.

_{w}is the volume of feed water, the above must be divided by r to get the specific work per volume of purified water i.e., the specific energy consumption:

_{sideal}as it takes only essential losses into account. It is greater than SEC

_{ideal}as given by Equation (5). Differentiation of Equation (11) shows that the minimum SEC

_{sideal}= 2P

_{osm}occurs at r = 0.5. For those cases where multiple stages or ERD have been used, formulae for SEC

_{sideal}given by Qiu and Davies (Table 3 of reference [23]) have been used.

_{sys}to be used instead of Equation (11):

_{sys}< r (Figure 3a). This situation occurs when no ERD is used and the value of A is low (A < 2) such that not enough work is available to operate the RO at optimal r = 0.5 while treating the whole feed stream. With the bypass arrangement, the water output is constrained by the work available with the RO system working at r = 0.5 and:

**Figure 3.**Self-powered desalination system comprising a heat engine coupled to a RO system: (

**a**) without energy recovery device with optional bypass of feed water around the RO stage to allow it to work at optimum recovery r = 0.5 for cases where work output from the heat engine is limiting; (

**b**) with energy recovery device (ERD) in which case no such bypass is used.

_{sys}even though the stage is then operating sub-optimally at r > 0.5. In this case, Equation (12) applies.

_{sys}, are given in Table 1 for 1- and 2-stage systems with and without energy recovery and these relations are also illustrated in Figure 4 for comparison with the ideal case of Equation (8). Even for the worst case of a stage with no ERD, the prediction is still very promising: A = 2.3 now gives r

_{sys}= 0.57. Note however that the heat engine is still assumed to be thermodynamically ideal and non-essential losses of the RO system have not yet been taken into account.

**Table 1.**Expressions for upper limit to system recovery ratio r

_{sys}according to RO configuration, as a function of dimensionless parameter A defined by Equation (9), based on semi-ideal theoretical SEC

_{sideal}taking into account only essential losses. With a batch system, (or infinitely many stages) the ideal case Equation (8) is reached. In all cases, the system is assumed driven by a reversible heat engine with work output given by Equation (3).

Configuration | Without Energy Recovery Device | With Energy Recovery Device |
---|---|---|

1-stage | When A < 2 (bypass): | ${r}_{sys}=\frac{A}{1+A}$ |

${r}_{sys}=\frac{A}{4}$ | ||

When A ≥ 2 (no bypass): | ||

${r}_{sys}=1-\frac{1}{A}$ | ||

2-stage | When A < 2 (bypass): | ${r}_{sys}=1-\frac{4}{{(2+A)}^{2}}$ |

r_{sys} = 0.278 A | ||

When A ≥ 2 (no bypass): | ||

${r}_{sys}=1-\frac{4}{{(1+A)}^{2}}$ | ||

Ideal (batch system, or infinite number of stages with ERD). | r_{sys} = 1 − e^{−A} |

**Figure 4.**Maximum possible values of system recovery ratio r

_{sys}using a reversible geothermal heat engine to drive the desalination process, based on Table 1. Exergy limit is for an ideal reversible RO system (Equation (8)). Lower curves are for theoretical 1- and 2-stage RO systems with and without energy recovery device (ERD), with only essential losses taken into account. Parameter A is defined by Equation (9) (or by Equation (15) once real losses are taken into account).

_{RO}which can be used to estimate SEC in proposed systems:

_{RO}in the range 0.07–0.14 (Table 2). In this study, a value of ε

_{RO}= 0.1 is adopted, based on the work of Li and Noh [25], as this is considered a thorough and recent experimental study of a large operational plant. This value, which also concurs with that from the large element study [26], is considered representative of current design and operational practice. Incorporation of this ratio in Equation (14), and use of a similar factor for the ORC system leads to a new expression for the real value of A taking into account all losses.

_{ORC}is the exergy efficiency of the ORC to be discussed next. The value of A

_{real}thus calculated is then used in place of A in the equations of Table 1 to work out realistic values of achievable r

_{sys}.

**Table 2.**Comparison of theoretical and real specific energy consumptions of some reported brackish water RO systems.

Location | Configuration * | Feedwater Concentration | Osmotic Pressure P_{osm} | Recovery r | Reported SEC_{real} | Semi-Ideal SEC_{sideal} | Loss Ratio ε_{RO} | Capacity | Year Reported | Reference |
---|---|---|---|---|---|---|---|---|---|---|

mg kg^{−1} | kPa | kWh m^{−3} | kWh m^{−3} | m^{3}/day | ||||||

Kerkennah, Tunisia | 1-stage no ERD | 3,700 | 293 ** | 0.75 | 1.1 | 0.150 | 0.14 | 4,700 | 2003 | [28] |

Chino, California (train A) | 1-stage no ERD | 950 | 62 | 0.809 | 0.490 | 0.0353 | 0.07 | 8,300 | 2011 | [29] |

Chino, California (train A—optimised) | 1-stage no ERD | 950 | 62 | 0.9 | 0.441 | 0.044 | 0.10 | 8,300 | 2012 | [25] |

Large Element Study § | 1-stage no ERD | 2,200 | 175 | 0.75 | 0.88 | 0.090 | 0.10 | 189,000 | 2004 | [26,30] |

******based on assumed NaCl composition; § a detailed design study carried out by consortium of US companies.

#### 2.3. Organic Rankine Cycle

_{ORC}is defined by:

_{p}= T

_{p}− T

_{5}

_{p}= 0 when the temperature profile of the geothermal source intercepts the organic working fluid temperature profile on the saturation curve at the pinch point (5). The energy efficiency of the heat exchanger (evaporator) transferring the geothermal heat to the Rankine cycle working fluid is given by:

_{w}and T

_{w}

_{′}refer to the geothermal water temperature entering and leaving the heat exchanger. Similarly, the condenser efficiency can be defined as follows:

_{0}refers to the terminal temperature difference of the condenser defined as the difference between the saturation temperature of the refrigerant and the exit temperature of the coolant.

- -
- Dry expansion to avoid wet vapour and erosion in the turbine;
- -
- Non-corrosive, non-flammable and non-toxic fluid;
- -
- High molecular weight to reduce the turbine nozzle velocity;
- -
- Low ozone depletion potential (ODP) and global warming potential (GWP).

Fluid | ASHRAE Designation | Mol. Weight (kg/kmol) | Critical Temperature T_{c} (°C) | Critical Pressure P_{c} (MPa) | Latent Heat (at 25 °C) (kJ/kg) | ODP | GWP |
---|---|---|---|---|---|---|---|

[33] | [34] | [34] | [34] | [34] | [35] | [35] | |

1,1,1-trifluoroethane | R143a | 84.04 | 72.7 | 3.76 | 159.3 | 0 | 4470 |

difluoromethane | R32 | 52.02 | 78.1 | 5.78 | 270.9 | 0 | 500 |

propane | R290 | 44.10 | 96.7 | 4.25 | 335.3 | 0 | 3.3 |

1,1,1,2-tetrafluoroethane | R134a | 102.03 | 101.0 | 4.06 | 177.8 | 0 | 1430 |

Ammonia | R717 | 17.03 | 132.3 | 11.33 | 1166 | 0 | 0 |

_{0}= 2 °C, pinch temperature difference ΔT

_{p}= 2 °C. T

_{3}(refrigerant temperature at the expander inlet) = T

_{win}− 2ΔT

_{p}.

_{ORC}. The basic equations for the cycle are well known and can be found in many sources e.g., [36]. They were obtained using steady state energy and mass balances for each component of the system as well as for the whole ORC unit. An optimisation method based on the quadratic approximation one was applied to maximise ψ

_{ORC}by changing the evaporation pressure and the condensation pressure subsequently. The objective function to maximise here was the exergy efficiency ψ

_{ORC}.

## 3. Case Studies

#### 3.1. Case Study 1: Tuwa, Gujarat

^{−1}(Figure 7).

^{−1}(Tuwa 5) was the most representative. Therefore this spring is used as the basis for the case study. The composition of electrolytes in Tuwa 5 is predominantly sodium chloride, with calcium and sulphate ions also present (Figure 8a). Tuwa 5 water also contains a high level of silica (122 mg kg

^{−1}). This relative composition is also representative of the other springs at Tuwa.

_{0}for this case study was chosen as the average daily maximum of 41 °C for the hottest month of May, as the greatest water demand is likely to occur at the hottest time of year. Based on the Van’t Hoff law and using the osmotic coefficients as in the Appendix, the osmotic pressure of the solution was calculated to be 245 kPa for Tuwa 5 at this temperature.

**Figure 7.**Temperatures and salinities of the thermal springs in the Tuwa area of Gujarat [39].

#### 3.2. Case Study 2: Salbukh, Najd Plateau, Saudi Arabia

^{−3}[41]. This gives a strong incentive to make use of inland water sources but such use requires desalination at high recovery to avoid problems of pollution by the concentrate.

^{−1}. The samples were rich in sodium, calcium, magnesium, chloride and sulphate, as shown by the example composition of Figure 8b. Many groundwater sources show geothermal activity. In the Riyadh area, the wells at Salbukh and Albobb are reported to emerge at 70 °C. Salbukh is taken as the case for use in this study. The well water has salinity of 1800 mg kg

^{−1}which, based on the same relative composition as in Figure 8b, gives an osmotic pressure of 117 kPa.

#### 3.3. Case Study 3: Kebili Geothermal Field, Tunisia

^{2}extending into Tunisia, Algeria and Libya [42]. This large aquifer is already exploited in Tunisia for the heating of greenhouses, bathing, and for irrigation of crops. However, the water is reported to have salinities in the range 2500–5000 mg kg

^{−1}and this makes the water unsuitable for human consumption and only marginally suitable for agriculture [43]. Typically the water emerges at 70 °C and it is sometimes passed through cooling towers to dissipate the heat prior to utilization [44].

^{−1}. Based on these a median value of 2440 mg kg

^{−1}(well number 7) was selected; its chemical analysis shows high sodium, calcium, magnesium, chloride and sulphate (Figure 8c below). The average daily maximum temperature in Kebili is 38 °C in July–August and this was taken as the value of T

_{0}.

#### 3.4. Case Study 4: Eynal Spring, Simav Geothermal Field, Turkey

^{−1}. The composition of the Eynal Spring consists mainly of sodium sulphate and sodium bicarbonate and as shown in Figure 8d below. These result in an osmotic pressure of 97 kPa at ambient temperature of 31 °C. The water also contains a significant level of silica (54 mg kg

^{−1}).

## 4. Results

_{sys}> 0.99 (Table 4). Whereas this very high value is not presented as a practically achievable level of system recovery (e.g., because it would lead to problems of membrane scaling) it does indicate the sound theoretical feasibility of achieving self-powered geothermal desalination at good recovery even for very low enthalpy sources at temperatures below 70 °C. Semi-ideal assumptions, with only essential RO losses taken into account, also predict high values of r

_{sys}≥ 0.89 in all cases—even using single stage RO systems with no ERD.

**Table 4.**Calculated values of system recovery r

_{sys}using the organic Rankine cycle and reverse osmosis under ideal, semi-ideal and real assumptions.

Case Study | ||||
---|---|---|---|---|

1. Tuwa—Gujarat (India) | 2. Salbukh—(Saudi Arabia) | 3. Kebili—(Tunisia) | 4. Eynal—(Turkey) | |

Total salt concentration (mg/kg) | 3350 | 1800 | 2440 | 1830 |

Osmotic Pressure (kPa) | 245 | 117 | 119 | 97.5 |

Source temperature T_{1} | 60 | 70 | 70 | 96 |

Ambient temperature T_{0} | 41 | 44 | 38 | 31 |

Parameter A | 9.4 | 36.1 | 54.1 | 261.2 |

ψ_{ORC} (R290) | 0.3085 | 0.3271 | 0.373 | 0.4503 |

ε_{RO} | 0.10 | 0.10 | 0.10 | 0.10 |

A_{real} | 0.29 | 1.18 | 2.02 | 11.76 |

Maximum r_{sys} | ||||

Ideal exergetic limit * | >0.99 | >0.99 | >0.99 | >0.99 |

Semi-ideal **: | ||||

1-stage RO (no ERD) | 0.894 | 0.972 | 0.982 | >0.99 |

2-stage RO (no ERD) | 0.963 | >0.99 | >0.99 | >0.99 |

1-stage RO (with ERD) | 0.904 | 0.973 | 0.982 | >0.99 |

2-stage RO (with ERD) | 0.969 | >0.99 | >0.99 | >0.99 |

Real §: | ||||

1-stage RO (no ERD) | 0.073 | 0.295 | 0.505 | 0.915 |

2-stage RO (no ERD) | 0.081 | 0.328 | 0.561 | 0.975 |

1-stage RO (with ERD) | 0.225 | 0.542 | 0.669 | 0.922 |

2-stage RO (with ERD) | 0.238 | 0.605 | 0.752 | 0.979 |

_{ORC}in the range 0.286–0.450 (Table 5). Of the two refrigerants investigated, propane (R290) gives slightly better performance than R143a for the lower temperature applications, and worse for the higher temperature ones. Because the differences are not large, propane is preferred because of its better environmental properties with respect to global warming and ozone depletion (Table 3).

**Table 5.**Results for exergy efficiency ψ

_{ORC}as a function of the source and ambient temperatures for two working fluids (R143a and R290).

Case Study | |||||
---|---|---|---|---|---|

1. Tuwa—Gujarat (India) | 2. Salbukh—(Saudi Arabia) | 3. Kebili—(Tunisia) | 4. Eynal—(Turkey) | ||

Source temperature T_{w} | 60 | 70 | 70 | 96 | |

Ambient temperature T_{0} | 41 | 44 | 38 | 31 | |

R143a | ψ_{ORC} | 0.286 | 0.359 | 0.366 | 0.563 |

(P_{evap}, P_{cond}) | (2390,2000) | (2756,2115) | (2756,1850) | (3700,1550) | |

R290 (propane) | ψ_{ORC} | 0.3085 | 0.3271 | 0.373 | 0.4503 |

(P_{evap}, P_{cond}) | (1754,1468) | (1899,1570) | (1899,1370) | (2408,1165) |

_{ORC}for propane, together with the practically observed values of ε

_{RO}for real RO plant, give values of r

_{sys}in the range 0.073−0.979. These are much lower than the values based on ideal and semi-ideal assumptions. The difference is most significant for Tuwa (case study 1, geothermal water supplied at only 60 °C) where using single-stage RO without ERD, only r

_{sys}= 0.073 is predicted which would be unsatisfactory as effectively 93% of the source water would be wasted. Use of ERD improves this significantly to r

_{sys}= 0.225. On the other hand, for the Eynal Spring emerging at 96 °C (case study 4), r

_{sys}has a high value of 0.915 even for a single-stage system without ERD.

_{RO}= 0.1. This occurs because brackish water RO plants typically operate at well above the osmotic pressure [29]. In comparison, seawater desalination plants have lower values of ε

_{RO}; for example, at 3.5 kWh/m

^{3}ε

_{RO}= 0.2. Using this value of ε

_{RO}in the current calculations would give, for case study 1, a value of r

_{sys}increased from 0.225 to 0.368 (single-stage, with ERD).

## 5. Discussion

#### 5.1. Pre- and Post-Treatment

Case Study | Scaling Issue | Pre-Treatment |
---|---|---|

1: Tuwa, Gujarat | Calcium sulphate precipitation would limit recovery to about 0.3High silica level | Use anti-scalants e.g., phosphonates (or work at lower recovery) |

2: Salbukh, Saudi Arabia | Calcium sulphate already near saturation | Anti-scalant or water softening by cation-exchange resin |

3: Kebili, Tunisia | ||

4: Eynal Spring, Turkey | Calcium sulphate precipitation would limit recovery to about 0.5Significant silica level | Use anti-scalants e.g., phosphonates (or work at lower recovery) |

#### 5.2. Equipment Design for Performance and Low Cost

## 6. Conclusions

_{sys}.

_{sys}> 0.99). Under semi-ideal assumptions, whereby only essential losses in a RO system are taken into account, achievable recovery remains very high (r

_{sys}> 0.89) even for single-stage RO without ERD which is the least efficient arrangement.

_{w}= 60 °C) r

_{sys}is in the range 0.073−0.238; while for the Eynal Spring, Turkey (T

_{w}= 96 °C) r

_{sys}= 0.915–0.979. These results give considerable incentive to develop, optimise and apply geothermal desalination as a dependable source of fresh water for a number of arid areas. The framework presented here should be developed further to incorporate more detailed engineering and economic data such that these systems can be practically realized.

## Nomenclature

A | dimensionless parameter defined by Equation (9) |

ṁ | mass flow (kg s ^{−1}) |

n | moles of solute (kmol) |

P | pressure (kPa) |

r | recovery ratio |

R | gas constant ( = 8.314 kJ·kmol ^{−1}·K^{−1}) |

T | temperature (K or °C) |

V | volume (m ^{3}) |

$\dot{V}$ | volumetric flow (m ^{3}·s^{−1}) |

W | mechanical work (kJ) |

Ẇ | rate of mechanical work (kW) |

SEC | specific energy consumption (kJ m ^{−3} or kWh m^{−3}) |

## Greek letters

ε | loss ratio |

η | energy efficiency |

ψ | exergy efficiency |

## Subscripts

_{c} | concentrate |

_{cond} | condenser |

_{evap} | evaporator |

_{ideal} | ideal |

_{p} | purified water (permeate), or pinch point |

_{ORC} | organic Rankine cycle |

_{osm} | osmotic |

_{real} | real |

_{RO} | reverse osmosis |

_{s} | relating to work of desalination |

_{sideal} | semi-ideal |

_{sys} | system |

_{t} | relating to conversion of thermal energy to work |

_{w} | feedwater at system inlet |

_{w’} | feedwater at outlet to heat exchanger |

_{0} | ambient |

_{0’} | at condenser outlet |

_{1} | at pump inlet |

_{2} | at pump outlet |

_{3} | at evaporator outlet |

_{4} | at expander outlet |

_{5} | pinch point |

## Abbreviations

ERD | Energy Recovery Device |

GWP | Global Warming Potential |

MSF | Multi-stage Flash Unit |

ODP | Ozone Depleting Potential |

ORC | Organic Rankine Cycle |

RO | Reverse Osmosis |

## Acknowledgments

## Author Contributions

## Appendix: Calculation of Osmotic Pressures

_{i}/V is the molar concentration (kmol/m

^{3}) of each species present; v

_{i}the number of ions available by complete dissociation each species (e.g., 2 for NaCl, 3 for CaCl

_{2}); and a

_{i}is the osmotic coefficient for each species, which is generally close to unity. Table A1 gives the osmotic coefficients used in this study for dilute solutions of the main salts occurring in the sources considered. Based on the data in [49], this approach was found to give good representation of osmotic pressure up to concentrations of 0.4 kmol m

^{−3}, which is an order of magnitude higher than encountered in this study. It was also found to predict the osmotic pressure of diluted seawater (concentration 18,039 mg/kg) with less than 1% error [50]. Therefore Equation (A1) is considered to be of good accuracy and is preferred over more complex methods of calculating the osmotic pressure, because it is a linear equation which greatly simplifies the analysis.

## Conflicts of Interest

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**MDPI and ACS Style**

Davies, P.A.; Orfi, J.
Self-Powered Desalination of Geothermal Saline Groundwater: Technical Feasibility. *Water* **2014**, *6*, 3409-3432.
https://doi.org/10.3390/w6113409

**AMA Style**

Davies PA, Orfi J.
Self-Powered Desalination of Geothermal Saline Groundwater: Technical Feasibility. *Water*. 2014; 6(11):3409-3432.
https://doi.org/10.3390/w6113409

**Chicago/Turabian Style**

Davies, Philip A., and Jamel Orfi.
2014. "Self-Powered Desalination of Geothermal Saline Groundwater: Technical Feasibility" *Water* 6, no. 11: 3409-3432.
https://doi.org/10.3390/w6113409