Reverse Osmosis Calculator

What is Reverse Osmosis?

Reverse osmosis (RO) is a water purification process that uses a partially permeable membrane to separate ions, unwanted molecules and larger particles from drinking water. In reverse osmosis, an applied pressure is used to overcome osmotic pressure, a colligative property that is driven by chemical potential differences of the solvent, a thermodynamic parameter.

Formula and Parameters

The key formulas used in reverse osmosis calculations are:

1. Rejection Rate (R): \[ R = \frac{C_f - C_p}{C_f} \times 100\% \]
2. Recovery Rate (Y): \[ Y = \frac{Q_p}{Q_f} \times 100\% \]
3. Concentrate Flow Rate (Q_c): \[ Q_c = Q_f - Q_p \]
4. Concentrate Concentration (C_c): \[ C_c = \frac{C_f \times Q_f - C_p \times Q_p}{Q_c} \]

Where:

• C_f = Feed Concentration
• C_p = Permeate Concentration
• Q_f = Feed Flow Rate
• Q_p = Permeate Flow Rate
• Q_c = Concentrate Flow Rate
• C_c = Concentrate Concentration

Calculation Steps

Let's calculate the reverse osmosis parameters using an example:

Given:

• Feed Concentration (C_f) = 1000 mg/L
• Permeate Concentration (C_p) = 50 mg/L
• Feed Flow Rate (Q_f) = 100 L/min
• Permeate Flow Rate (Q_p) = 75 L/min

1. Calculate Rejection Rate: \[ R = \frac{1000 - 50}{1000} \times 100\% = 95\% \]
2. Calculate Recovery Rate: \[ Y = \frac{75}{100} \times 100\% = 75\% \]
3. Calculate Concentrate Flow Rate: \[ Q_c = 100 - 75 = 25 \text{ L/min} \]
4. Calculate Concentrate Concentration: \[ C_c = \frac{1000 \times 100 - 50 \times 75}{25} = 3800 \text{ mg/L} \]

Example and Visual Representation

Let's visualize the reverse osmosis process with our example:

This visual representation shows:

• The feed water entering the system with its initial concentration and flow rate
• The semi-permeable membrane separating the feed into permeate and concentrate
• The permeate (purified water) with lower concentration and reduced flow rate
• The concentrate with higher concentration and reduced flow rate
• The rejection rate of 95% and recovery rate of 75%