Introduction & Context

In the sugar production industry, the extraction of sucrose from sugar beet cossettes is a critical unit operation typically performed in a continuous, counter-current diffusion tower. This process relies on the principle of solid-liquid leaching, where hot water flows against the movement of beet cossettes to maximize the concentration gradient and facilitate the diffusion of sucrose out of the plant cell structures.

Monitoring extraction efficiency and juice purity is essential for process control, as these metrics directly influence the yield of the final crystalline sugar and the energy requirements of downstream evaporation and crystallization stages. Maintaining optimal operating conditions, such as temperature and chemical dosing, is vital to prevent sucrose inversion and microbial degradation.

Methodology & Formulas

The following calculations determine the mass balance of sucrose and the chemical requirements for the subsequent purification phase. The variables are defined as follows: ṁ_beet is the mass flow rate of the beet, w_suc,beet is the mass fraction of sucrose in the beet, ṁ_juice is the mass flow rate of the raw juice, w_suc,juice is the mass fraction of sucrose in the juice, w_TDS,juice is the total dissolved solids in the juice, and f_lime is the empirical lime dosing factor.

The mass flow of sucrose entering the system is calculated as:

\[ \dot{m}_{suc,in} = \dot{m}_{beet} \cdot w_{suc,beet} \]

The mass flow of sucrose recovered in the raw juice is calculated as:

\[ \dot{m}_{suc,out} = \dot{m}_{juice} \cdot w_{suc,juice} \]

The extraction efficiency (η) is defined as the ratio of recovered sucrose to input sucrose:

\[ \eta = \left( \frac{\dot{m}_{suc,out}}{\dot{m}_{suc,in}} \right) \cdot 100 \]

The purity of the raw juice, representing the ratio of sucrose to total dissolved solids, is calculated as:

\[ Purity = \left( \frac{w_{suc,juice}}{w_{TDS,juice}} \right) \cdot 100 \]

The required mass flow of lime (CaO) for purification is determined by the empirical dosing factor:

\[ \dot{m}_{lime} = \dot{m}_{beet} \cdot f_{lime} \]

Parameter	Operational Range	Significance
Extraction Efficiency (η)	95.0% - 99.0%	Indicates sucrose loss to exhausted pulp.
Raw Juice Purity	85.0% - 88.0%	High values indicate lower non-sugar impurity levels.
Diffusion Temperature	68.0°C - 72.0°C	Balances extraction rate against inversion risk.
Lime Factor (f_lime)	2.0% - 2.5%	Required for carbonatation and impurity removal.

To maximize sucrose yield during the diffusion process, process engineers must monitor and control the following variables:

Temperature profile: Maintaining the diffuser temperature between 68 and 72 degrees Celsius to ensure cell wall permeability while preventing microbial activity.
Retention time: Adjusting the screw speed to ensure optimal contact time between the cossettes and the extraction water.
Draft ratio: Managing the ratio of juice drawn off to the weight of the sliced beets to ensure efficient concentration gradients.
pH control: Maintaining a slightly acidic environment to minimize the inversion of sucrose into glucose and fructose.

High pectin content can lead to significant filtration issues and increased viscosity in the evaporators. Mitigation strategies include:

Optimizing the scalding temperature to denature pectin-methylesterase enzymes.
Adjusting the lime dosage during the carbonation stage to effectively precipitate pectin compounds.
Monitoring the quality of the incoming beet crop, as damaged or stored beets often exhibit higher pectin degradation.

Recirculating pulp press water is essential for water conservation but introduces risks of bacterial contamination. Engineers should implement the following:

Thermal sterilization: Heating the press water to at least 80 degrees Celsius before returning it to the diffuser.
Chemical treatment: Utilizing approved biocides to control thermophilic bacteria populations.
Monitoring total dissolved solids: Ensuring that the recirculation loop does not lead to an accumulation of non-sugars that could inhibit crystallization.

Worked Example: Sugar Extraction Efficiency and Juice Purity

A sugar beet processing plant operates a continuous diffusion battery under steady-state conditions. The following parameters are measured to assess the extraction performance and downstream requirements.

Known Input Parameters:

Beet processing rate, \( \dot{m}_{beet} = 100.0 \, \text{t/h} \)
Sucrose content in beet (mass fraction), \( w_{suc,beet} = 0.16 \)
Raw juice flow rate, \( \dot{m}_{juice} = 120.0 \, \text{t/h} \)
Sucrose concentration in raw juice (mass fraction), \( w_{suc,juice} = 0.13 \)
Total dissolved solids in raw juice (mass fraction), \( w_{TDS,juice} = 0.15 \)
Diffusion temperature, \( T = 70.0 \, ^{\circ}\text{C} \)
Lime factor (mass fraction on beet), \( f_{lime} = 0.022 \)

Step-by-Step Calculation:

Sucrose input from beets: The mass flow rate of sucrose entering with the beets is directly obtained as \( \dot{m}_{suc,in} = 16.000 \, \text{t/h} \).
Sucrose output in raw juice: The mass flow rate of sucrose leaving in the raw juice is directly obtained as \( \dot{m}_{suc,out} = 15.600 \, \text{t/h} \).
Extraction efficiency: The efficiency of sucrose extraction is calculated as: \[ \eta = \left( \frac{\dot{m}_{suc,out}}{\dot{m}_{suc,in}} \right) \cdot 100\% = 97.500 \, \% \] This value is within the typical empirical range of 95–99% for modern diffusers.
Raw juice purity: The purity of the raw juice, defined as the sucrose content relative to total dissolved solids, is calculated as: \[ P = \left( \frac{w_{suc,juice}}{w_{TDS,juice}} \right) \cdot 100\% = 86.667 \, \% \] This value falls within the typical empirical range of 85–88%.
Lime requirement for purification: The mass flow rate of lime (CaO) required for the subsequent carbonatation step is calculated as: \[ \dot{m}_{lime} = \dot{m}_{beet} \cdot f_{lime} = 2.200 \, \text{t/h} \] The lime factor \( f_{lime} = 0.022 \) is within the standard empirical range of 0.020–0.025.

Final Answer:

Sucrose extraction efficiency, \( \eta = 97.500 \, \% \).
Raw juice purity, \( P = 86.667 \, \% \).
Lime requirement, \( \dot{m}_{lime} = 2.200 \, \text{t/h} \).
The diffusion temperature of \( 70.0 \, ^{\circ}\text{C} \) is within the optimal operating range of 68–72°C.

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