*2.1. CT Water E*ffi*ciency*

Recirculating cooling towers operate in a feed and bleed mode. Circulating water is evaporated to reject heat while fresh feed water is continuously added, and a fraction of the circulating water is discharged as blowdown. The water regime of a cooling tower is conventionally expressed in terms of cycles of concentration (COC). *COC* measures the degree to which the solid impurities in the makeup water are concentrated in the recirculating water of an evaporative system due to evaporation of water. *COC* is defined (Equation (1)) as the ratio between chloride concentration (chemical *COC*) in the circulation water and make-up water or in terms of flowrate (physical *COC*) of make-up ( *Qmakeup*) and evaporate ( *Qevap*).

$$\text{COC} = \frac{[\text{Cl}^-]\_{\text{circular}}}{[\text{Cl}^-]\_{\text{makup}}} \text{\"\textdegree} \frac{\text{Q}\_{\text{makup}}}{\text{Q}\_{\text{makup}} - \text{Q}\_{\text{cvup}}} = \frac{1}{1 - \text{Q}\_{\text{cvup}} / \text{Q}\_{\text{makup}}} \tag{1}$$

A more conventional parameter for a system's water use is water use e fficiency or utilization ( *U*), defined as the ratio of e ffectively used (evaporated) water flow over feed water flow (Equation (2)).

$$
\mathcal{U} = \frac{Q\_{crap}}{Q\_{in}} \tag{2}
$$

*COC* is the reciprocal of (1 − U) and therefore a non-linear and less appropriate measure of CT water consumption (Equation (1)). For the coupled MCDI-CT system (Figure 1) it is therefore preferred to use *U* as a measure for water consumption (Equation (2)).

**Figure 1.** Process scheme for membrane capacitive deionization (MCDI) pretreatment of cooling tower including mass balance components flow ( *Q*), [NaCl] and hardness (*TH*) for MCDI feed (*in*), product (*out*) and waste ( *w*) and cooling tower evaporate (*evap*) and blowdown (*BD*).

For the MCDI-CT system, *U* is found as the ratio (Equation (2)) of evaporate flow and MCDI intake water flow ( *Q*in). The maximal achievable utilization ( *U*max), i.e., the maximal fraction of intake water flow that can be used for evaporation, is of specific interest when comparing the e fficiency of MCDI-CT under various settings and feed water types. *U*max is limited by both MCDI water recovery and the maximal CaCO3 concentration that can be achieved in the cooling tower not causing scaling (Equation (3)). For practical use, this can also be expressed in terms of MCDI process characteristics.

$$\mathcal{U}\_{\text{max}} = \frac{Q\_{\text{evap},\text{max}}}{Q\_{\text{in}}} = \,\,\mathcal{W}R\left(1 - \frac{T H\_{\text{out}}}{T H\_{\text{BD,\,max}}}\right) \tag{3}$$

where *Umax* is determined by maximal achievable evaporation flow ( *Qevap,max*), MCDI intake flow (*Qin*), MCDI water recovery (*WR*), hardness of the MCDI treated water (*THout*) and maximal allowable hardness in the CT (*THBD,max*) limited by the maximal solubility of CaCO3. Scaling (by CaCO3) is applied here as single limiting concentration factor for CTs. Several alternative limiting conditions for CT water usage can obviously be envisaged including discharge limitations, material technical limitations (e.g., corrosion) and non CaCO3 related scaling/fouling. These additional limitations could be implemented however following a similar approach.

#### *2.2. MCDI Lab Tests: Setup*

The lab-scale setup consists of an Enpar Inc. (Guelph, ON, Canada) lab-scale MCDI cell (0.7 m<sup>2</sup> electrode surface) coupled to a Voltea MCDI circulation loop (Sassenheim, the Netherlands). The system is equipped with a DC power supply, pump, conductivity probe, valves, flow meter and a laptop with LabView-based control and data logging software. During operation, the MCDI system passes through cycles of purification and regeneration. During the purification step, charge builds up in the electrodes as ions are adsorbed from the water. Regeneration is achieved by reversing the polarity over the MCDI cell. All experiments are carried out under fixed flow rate, adsorption current and adsorption time. At the start of each experiment, the MCDI-module is shorted and rinsed with feed water for at least 30 min (at adsorption flowrate) until outlet conductivity equals feed conductivity. In each experiment at least 10 cycles (adsorption-desorption) are completed in flow-through mode (no recycle). Desorption is performed at constant voltage (−1.2 V) or at maximal desorption current (110 A) if −1.2 V is not reached; desorption flow rate is equal to adsorption flow rate and constant; maximal current is applied during desorption; the required desorption time is derived from the charge balance. Feed water is filtered (Pall profile II filter cartridge, 5 μm) prior to testing. During experiments pH, *EC* (μS cm<sup>−</sup>1), Δ *V* (V), *Q* (mL min−1) and *I* (A) are continuously monitored. Samples are taken from the influent, purified and waste streams during the last 3 cycles and analyzed for Cl (discrete analysis system and spectrophotometric detection), Na and Ca (ICP-OES).

#### *2.3. MCDI Lab Tests: Experimental Design*

MCDI parameter screening is performed on synthetic cooling water following a design of experiments (DOE) approach. Synthetic cooling water is prepared from demineralized water, pro analysis grade NaCl (Merck, Darmstadt, Germany) and CaCl2 (≥94% Merck). The chosen experimental design [24] is a half fractional central composite design (CCD) with 5 factors at 2 levels, i.e., a 2(5−1) design, and star points (α = 1.719, 30 runs, 3 center points). This type of design consists of a fractional factorial design with center points and is augmented with a group of 'star points' to allow estimation of curvature. The star points are at distance alpha ( α) from the center and represent extremes for the low and high settings for all factors. The design is of resolution V, indicating no main e ffect or two-factor interaction is aliased with any other main e ffect or two-factor interaction, but two-factor interactions are aliased with three-factor interactions. α is computed for orthogonality using Dell Inc. (2015) Statistica software (data analysis software system, version 12). The design contains 5 factors of which three are MCDI operational factors (adsorption phase time (*tads*), adsorption current (*Iads*), adsorption phase flowrate ( *Qads*)) and 2 factors are related to feed water composition *([NaCl]in*, feed water hardness (*THin*)). Factor ranges are selected based on previous experience and real cooling tower feed water qualities (Table 1).

Primary (directly measured) response variables are product water composition *([NaCl]out*, *THout*) and MCDI water recovery (*WR*). Secondary (calculated) response variables are specific energy use (*E*, kWh m<sup>−</sup>3in), estimated cost (*Cost*, € m<sup>−</sup>3in) both expressed relative to the feed water flow and selectivity (*S*, -). Cost estimation is based on the experimental data and standard cost data (unit cell cost: 150 € m<sup>−</sup><sup>2</sup> electrode, E-cost: 0.1 € kWh−1, cell lifetime: 2 years, installation depreciation: 10 year at 4% rate of investment, yearly maintenance cost: 5% of investment). Where required electrode surface (*Ael*) is determined from lab cell electrode surface (*Acel*) and flow (Equation (4)).

$$A\_{cl} = \frac{A\_{cl}}{Q\_{in}}\tag{4}$$

Selectivity [25] is calculated as the ratio of the molar ratio of hardness of the MCDI feed water and the MCDI product water (Equation (5)).

$$\text{S}^{\circ} = \frac{\frac{M\_{\text{CaCO3}} \cdot T H\_{\text{in}}}{M\_{\text{CaCO3}} \cdot T H\_{\text{iv}} + M\_{\text{NaCl1}} \cdot [\text{NaCl}]\_{\text{iv}}}}{\frac{M\_{\text{CaCO3}} \cdot T H\_{\text{out}} \cdot (M)}{M\_{\text{CaCO3}} \cdot T H\_{\text{out}} + M\_{\text{NaCl}} \cdot [\text{NaCl}]\_{\text{out}}}} \tag{5}$$

where *Mi* (g mol−1) indicates the molar masses of CaCO3 and NaCl, respectively. Least-squares multiple regression analysis (Anova) is applied to determine the functional relationship between factors and responses using following polynomial equation (Equation (6)):

$$Y = b\_0 + \sum\_i b\_i X\_i + \sum\_{ij} b\_{ij} X\_i X\_j + \varepsilon \tag{6}$$

where *Y* represents a response variable, *b* regression coefficients, *X* factors, ε experimental error and *i*, *j* running variables. The significance of the generated response surface (RS) equations and model terms are evaluated from Anova table (α > 0.05), adjusted coefficient of performance (*R*<sup>2</sup>*adj.*), residuals distribution and Pareto analysis. Insignificant terms are removed in a stepwise model reduction procedure until a fully reduced model is obtained [26]. Experimental design and statistical analysis are performed with Dell Inc. (2015) Statistica (data analysis software system), visualization with Matlab 2016 version 12 (The MathWorks, Natick, MA, USA) and data preprocessing with MS office (Microsoft).

**Table 1.** Experimental design: factor levels and ranges.


## *2.4. CT Feed Water*

Cooling tower feed water samples are collected from 3 existing thermal power plant locations (Brussels-Charleroi (BC) Canal, Belgium; Gent-Terneuzen (GT) Canal, Belgium; Eume river, Spain) and treated municipal sewage water (STP effluent; Mol, Belgium). MCDI tests are performed with real cooling water samples to compare the effect of different feed water types on MCDI-CT process parameters (*E*, *S*, *Umax* and *Cost*). Following process settings are used: (*tads*, *Iads*) = (900 s, 2.5 A) and (*tads*, *Iads*) = (2000 s, 1 A), for each setting two flowrates are selected (60 and 120 mL min−1).
