Introduction & Context
In edible oil refining, bleaching earth is utilized to remove pigments, oxidation products, and trace impurities from crude oil, a critical stage in edible oil extraction from oilseeds. As the adsorbent is filtered out, it forms a spent filter cake that retains a significant portion of the processed oil. This calculation is essential for process engineers to perform accurate mass balances, estimate waste disposal costs, and evaluate the economic impact of oil loss within the filtration stage, and it is typically applied during the design of waste management systems, environmental compliance reporting, and operational efficiency audits.
Methodology & Formulas
The mass balance is determined by calculating the mass of fresh adsorbent added per batch and accounting for the oil trapped within the interstitial spaces of the filter cake. The following steps define the mathematical framework:
1. Calculate the mass of fresh adsorbent per batch:
\[ m_{\text{fresh}} = d \cdot m_{\text{oil}} \]
2. Calculate the mass of oil retained within the spent cake, derived from the oil mass fraction:
\[ m_{\text{retained}} = \left( \frac{f_{\text{oil}}}{1 - f_{\text{oil}}} \right) \cdot m_{\text{fresh}} \]
3. Determine the total mass of the spent cake per batch:
\[ m_{\text{spent}} = m_{\text{fresh}} + m_{\text{retained}} \]
4. Calculate the total annual waste mass in tonnes:
\[ m_{\text{annual}} = \frac{m_{\text{spent}} \cdot N}{1000} \]
| Parameter |
Description |
Typical Empirical Range |
| d |
Adsorbent dosage (fraction of oil mass) |
0.005 – 0.020 |
| foil |
Oil retention fraction in spent cake |
0.20 – 0.40 |
| N |
Annual batch cycles |
200 – 300 |
Worked Example: Mass Balance for Spent Bleaching Earth Disposal
Consider a vegetable oil refinery that processes 100 tonnes of oil per batch in a batch bleaching operation using an agitated filter press. Fresh bleaching earth is added at a dosage of 1.2% by weight of the oil. After filtration, the spent filter cake retains 35% by weight of oil. The plant operates 200 batches per year. The following mass balance calculates the annual mass of spent bleaching earth waste generated.
Known Parameters
- Mass of oil processed per batch: \( m_{\text{oil}} = 100{,}000 \, \text{kg} \)
- Fresh adsorbent dosage (by weight of oil): \( d_{\%} = 1.2 \, \% \)
- Oil retention fraction in spent cake: \( f_{\text{oil}} = 0.35 \)
- Number of batches per year: \( N = 200 \)
Step-by-Step Calculation
- Convert the dosage percentage to a decimal fraction:
\[
d = \frac{d_{\%}}{100} = 0.012
\]
- Compute the mass of fresh adsorbent per batch:
\[
m_{\text{fresh}} = d \cdot m_{\text{oil}} = 0.012 \cdot 100{,}000 \, \text{kg} = 1200.0 \, \text{kg}
\]
- Compute the mass of oil retained in the spent cake:
\[
m_{\text{retained}} = \frac{f_{\text{oil}}}{1 - f_{\text{oil}}} \cdot m_{\text{fresh}} = \frac{0.35}{0.65} \cdot 1200.0 \, \text{kg} = 646.154 \, \text{kg}
\]
- Compute the total spent cake mass per batch:
\[
m_{\text{spent}} = m_{\text{fresh}} + m_{\text{retained}} = 1200.0 \, \text{kg} + 646.154 \, \text{kg} = 1846.154 \, \text{kg}
\]
- Compute the annual waste mass in tonnes:
\[
m_{\text{annual}} = \frac{m_{\text{spent}} \cdot N}{1000} = \frac{1846.154 \, \text{kg} \cdot 200}{1000} = 369.231 \, \text{tonnes/year}
\]
Final Answer
The annual generation of spent bleaching earth waste is 369.231 tonnes per year.
