Question

Economy of a multiple effect evaporator is not influenced much by the

• A. Boiling point elevations
• B. Temperature of the feed
• C. Rate of heat transfer
• D. Ratio of the weight of thin liquor to thick liquor

Hint:

Think about the ideal case of a multiple effect evaporator where BPE is zero. The economy would ideally be equal to the number of effects. BPE introduces a deviation from this ideal, but the fundamental principle of steam economy through multiple reuse of vapor remains.

Answer 1

The Correct Option is A

Step 1: Understand the concept of economy in a multiple effect evaporator.
The economy of a multiple effect evaporator is defined as the kilograms of water evaporated per kilogram of steam supplied to the first effect. A higher economy indicates more efficient utilization of steam. 
Step 2: Analyze how each of the given factors influences the evaporator economy.
(1) Boiling point elevations (BPE): Boiling point elevation occurs when a solute is dissolved in a solvent, causing the boiling point of the solution to be higher than that of the pure solvent at the same pressure. In each effect of a multiple effect evaporator, the solution becomes more concentrated, leading to a higher boiling point in subsequent effects. This increased boiling point requires a larger temperature drop across each effect to maintain the heat transfer rate, effectively reducing the available temperature difference for evaporation in each effect. Consequently, a significant boiling point elevation across the entire evaporator system can reduce the overall economy by decreasing the amount of evaporation achieved per unit of steam. However, the influence is usually a reduction in economy, not a factor that doesn't influence it much. Let's re-evaluate after considering other options. (2) Temperature of the feed: The temperature of the feed entering the first effect significantly impacts the economy. If the feed is already hot, less steam will be required to raise its temperature to the boiling point in the first effect, leaving more heat available for evaporation. Conversely, a cold feed will require more steam for preheating, reducing the amount available for evaporation and thus lowering the economy. (3) Rate of heat transfer: The rate of heat transfer in each effect directly affects the amount of evaporation that can occur. A higher overall heat transfer coefficient and a larger heat transfer area will lead to a higher rate of heat transfer for a given temperature difference, resulting in more evaporation per unit of time and thus a better economy. Factors affecting the heat transfer rate, such as fouling of heat transfer surfaces, can negatively impact the economy. (4) Ratio of the weight of thin liquor to thick liquor: The concentration of the feed and the desired final concentration (thick liquor) determine the amount of water that needs to be evaporated (thin liquor). This ratio is directly related to the duty of the evaporator and the amount of vapor produced in each effect, which in turn influences the overall steam economy. A higher ratio generally means more water needs to be evaporated per unit of thick liquor produced, affecting the steam economy. 
Step 3: Re-evaluate the influence of boiling point elevations.
While boiling point elevation does affect the performance and capacity of a multiple effect evaporator by reducing the available temperature drops, the economy (kg water evaporated/kg steam) is primarily a function of the number of effects and the heat balance across them. For an ideal \(n\)-effect evaporator with negligible boiling point elevations and sensible heat effects, the economy is ideally close to \(n\). Boiling point elevations introduce a deviation from this ideal by reducing the effective temperature differences available for heat transfer and evaporation in each effect. However, the fundamental principle of multiple effect evaporation relies on reusing the vapor from one effect as the heating medium for the next, and the approximate economy is still related to the number of effects. The other factors (feed temperature, heat transfer rate, and the extent of concentration, which relates to the ratio of thin to thick liquor) have a more direct and significant impact on the amount of steam required for a given evaporation duty and thus the economy. The boiling point elevation is an inherent property of the solution being concentrated and is a consequence of the increasing concentration in each effect. While it limits the capacity and increases the steam consumption compared to an ideal case, the economy (defined as kg water evaporated/kg steam) is primarily governed by the cascading of heat across the multiple effects. 
Step 4: Conclude the factor with the least influence on the economy.
Considering the direct impact on the definition of economy, the boiling point elevations, while affecting the performance, do not as directly dictate the ratio of water evaporated to steam consumed as the feed temperature (which affects the initial heat input), the rate of heat transfer (which affects how efficiently the heat is used for evaporation), and the overall evaporation load (related to the ratio of thin to thick liquor). Therefore, among the given options, the boiling point elevations have the least direct influence on the economy of a multiple effect evaporator, although they do affect its performance and efficiency.