Reference ID: MET-54E9 | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
Demineralization efficiency calculation is a critical performance metric in Electrodialysis (ED) systems, particularly within the food and beverage industry. In fruit juice processing, ED is employed to reduce ash content (mineral salts) to improve flavor profiles, stabilize the product, or meet specific regulatory requirements; for related calculations on how ED can be used to lower acidity, see our fruit juice deacidification calculation. By applying an electrical potential across ion‑exchange membranes, ionic species are migrated out of the juice stream. Monitoring the efficiency of this process is essential for optimizing energy consumption, ensuring membrane longevity, and maintaining consistent product quality.
Methodology & Formulas
The following calculations translate the operational parameters of an ED stack into performance indicators. All calculations assume a steady-state, continuous flow process.
1. Concentration Conversion
The total dissolved solids (TDS) concentration is derived from the measured electrical conductivity (\(\kappa\)) using a calibration factor (\(f_{\mathrm{TDS}}\)):
\[ C = f_{\mathrm{TDS}} \cdot \kappa \]
2. Demineralization Efficiency (\(\eta_{\mathrm{dem}}\))
This represents the percentage of salt removed from the feed stream relative to the initial concentration:
\[ \eta_{\mathrm{dem}} = \left( \frac{C_{\mathrm{feed}} - C_{\mathrm{prod}}}{C_{\mathrm{feed}}} \right) \cdot 100 \]
3. Current Efficiency (\(\xi\))
The Faradaic efficiency measures how effectively the applied current (\(I\)) is utilized for ion transport compared to the theoretical current required for the observed mass removal. For NaCl, the valence factor (\(z\)) is 2 (accounting for both cation and anion transport per mole):
\[ \xi = \left( \frac{z \cdot F \cdot \Delta C \cdot Q}{M_{\mathrm{NaCl}} \cdot N \cdot I} \right) \cdot 100 \]
4. Specific Energy Consumption (\(E_{\mathrm{sp}}\))
This metric quantifies the electrical energy required to remove a unit mass of salt from the juice:
\[ E_{\mathrm{sp}} = \frac{U \cdot I \cdot 1000}{Q_{\mathrm{h}} \cdot \Delta C} \]
Parameter
Symbol
Definition
Faraday Constant
\(F\)
96485 C/eq
Molar Mass of NaCl
\(M_{\mathrm{NaCl}}\)
58.44 g/mol
Cell Pairs
\(N\)
Number of repeating units in the ED stack
Flow Rate
\(Q\)
Volumetric flow rate (m3/s or L/h)
Operational Validity Criteria
Condition
Threshold/Limit
Engineering Implication
Current Efficiency (\(\xi\))
0% < \(\xi\) < 100%
Values outside this range indicate measurement error or system bypass.
Voltage per Cell Pair
\(U / N \leq 2.5\) V
Exceeding this limit indicates high resistance, potential scaling, or membrane fouling.
Flow Rate (\(Q\))
\(Q > 0\)
System must maintain positive flow to prevent overheating and concentration polarization.
To determine the demineralization efficiency of an ED stack, compare the influent and effluent salt concentrations. Follow these steps:
Measure the feed conductivity (\(\kappa_{\mathrm{feed}}\)) and product conductivity (\(\kappa_{\mathrm{prod}}\)) with a calibrated, temperature-compensated meter.
Convert conductivity to TDS concentration using a system-specific factor: \(C = f_{\mathrm{TDS}} \cdot \kappa\).
Ensure that all measurements are taken at the same temperature, or use automatic temperature compensation (ATC).
Several operational and membrane‑related variables influence ED performance. Key factors include:
Membrane fouling or scaling, which increases electrical resistance and blocks ion migration.
Concentration polarization at the membrane surface, reducing effective driving force.
Current density and non‑uniform current distribution across the stack.
Voltage per cell pair – exceeding ~2.5 V can cause water splitting and efficiency loss.
Feed flow velocity and spacer design, which affect mass transfer and boundary layer thickness.
Temperature variations that alter conductivity, membrane properties, and solubility limits.
A decline in ED efficiency often points to physical or chemical changes inside the stack. Investigate the following potential causes:
Membrane fouling or scale accumulation – inspect and perform cleaning‑in‑place (CIP) if required.
Increased stack resistance due to aged membranes or loose electrical connections.
Drift or failure of conductivity sensors used for the calculation; verify calibration.
Changes in feed composition (e.g., higher hardness or silica) that promote scaling.
Operating outside recommended limits – check that voltage per cell pair stays below 2.5 V and that flow rates are adequate.
Temperature shifts that affect conductivity readings if not properly compensated.
Worked Example: Demineralization Efficiency of an Electrodialysis Unit for Apple Juice
An electrodialysis (ED) unit is used to reduce the ash content of apple juice. The feed conductivity is 1667 µS/cm, corresponding to a total dissolved solids (TDS) concentration of 1000.2 mg/L. The target product conductivity is 500 µS/cm, indicating a TDS of 300.0 mg/L. The stack has 20 cell pairs, operates at a flow rate of 1000 L/h, and is powered by a DC supply of 40 A and 40 V. The temperature is stable at 25°C.
Molar mass of NaCl, \(M_{\mathrm{NaCl}} = 58.44\ \mathrm{g/mol}\)
Step-by-step calculation:
Demineralization efficiency:
\[
\eta_{\mathrm{dem}} = \frac{C_{\mathrm{feed}} - C_{\mathrm{prod}}}{C_{\mathrm{feed}}} \times 100\%
\]
Using \(C_{\mathrm{feed}} = 1000.2\ \mathrm{mg/L}\) and \(C_{\mathrm{prod}} = 300.0\ \mathrm{mg/L}\), the concentration difference is \(\Delta C = 700.2\ \mathrm{mg/L}\). Therefore,
\[
\eta_{\mathrm{dem}} = \frac{700.2}{1000.2} \times 100\% = 70.006\%.
\]
Current efficiency (Faradaic):
The theoretical current required for desalting is:
\[
I_{\mathrm{theoretical}} = \frac{z \cdot F \cdot \Delta C \cdot Q}{M_{\mathrm{NaCl}} \cdot N}
\]
with \(z = 2\) (NaCl provides 2 equivalents per mole). Inserting values \(F = 96485\ \mathrm{C/eq}\), \(\Delta C = 700.2\ \mathrm{g/m^3}\) (1 mg/L = 1 g/m³), \(Q = 0.000278\ \mathrm{m^3/s}\), \(M_{\mathrm{NaCl}} = 58.44\ \mathrm{g/mol}\), and \(N = 20\), the theoretical current is \(I_{\mathrm{theoretical}} = 32.112\ \mathrm{A}\). Then,
\[
\xi = \frac{I_{\mathrm{theoretical}}}{I} \times 100\% = \frac{32.112}{40} \times 100\% = 80.28\%.
\]
Specific energy consumption:
The energy consumed per kilogram of salt removed is:
\[
E_{\mathrm{sp}} = \frac{U \cdot I \cdot 1000}{Q_{\mathrm{h}} \cdot \Delta C}
\]
where \(U = 40\ \mathrm{V}\), \(I = 40\ \mathrm{A}\), \(Q_{\mathrm{h}} = 1000\ \mathrm{L/h}\), and \(\Delta C = 700.2\ \mathrm{mg/L}\). Substituting the values,
\[
E_{\mathrm{sp}} = \frac{40 \cdot 40 \cdot 1000}{1000 \cdot 700.2} = 2.285\ \mathrm{kWh/kg}.
\]
Final Answer:
The electrodialysis unit achieves a demineralization efficiency of 70.006%, a current efficiency of 80.28%, and a specific energy consumption of 2.285 kWh/kg of salt removed.
"Un projet n'est jamais trop grand s'il est bien conçu."— André Citroën
"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise."— Charles de Gaulle
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