Steam Generator Efficiency

Steam generators are designed as large counter-flow heat exchangers with extensive tube surfaces, so they transfer heat very effectively. The losses (1-2%) are due to: (1) heat loss to the environment through insulation (radiation and convection), (2) the finite temperature difference required for heat transfer (the primary coolant must be hotter than the secondary steam), which creates an irreversibility, (3) incomplete heat transfer in the tube bundle due to fouling or flow maldistribution, and (4) leakage of primary coolant to the secondary side (though this is very small in a well-maintained unit). The efficiency is defined as the actual heat transferred to the secondary divided by the heat available from the primary, which is the enthalpy drop of the primary coolant.

The steam generator efficiency is a multiplier on the Rankine cycle efficiency. The overall plant efficiency is η_plant = η_SG × η_Rankine × η_turbine × η_generator, etc. If the steam generator efficiency drops from 99% to 97% (a 2% loss), the overall plant efficiency would decrease by roughly 2% of its value. For a plant with a 33% overall efficiency, a 2% reduction in SG efficiency would reduce it to about 32.3%—a significant loss in output. Therefore, maintaining high steam generator efficiency is critical for plant economics.

The heat that is not transferred to the secondary coolant is carried away by: (1) the primary coolant exiting the steam generator at a higher temperature than the theoretical minimum (because the approach temperature is not zero), (2) radiation and convection losses from the external surfaces of the steam generator (typically <0.5%), and (3) in some designs, a small fraction of heat is lost through the tube sheet and support structures. In a PWR, the primary coolant outlet temperature from the SG is about 5-10°C above the saturation temperature of the secondary steam, which represents the 'lost' heat that is not available for electricity generation. This is the largest component of the loss.

The secondary side pressure determines the saturation temperature of the steam. A higher pressure means a higher saturation temperature, which reduces the temperature difference between the primary and secondary sides (the 'approach temperature'). This reduces the heat transfer rate for a given surface area, potentially requiring a larger SG or lowering the efficiency if the primary coolant temperature is fixed. Conversely, a lower secondary pressure increases the temperature difference, improving heat transfer but reducing the Rankine cycle efficiency because the steam is at a lower pressure. The secondary pressure is chosen to optimize the overall plant efficiency. Typically, PWRs operate with secondary steam pressures around 5-6 MPa (saturation temperature ~270-280°C).

The heat available from the primary is Q_primary = m_dot_primary × cp_primary × (T_in - T_out). The steam generator efficiency is the ratio of Q_secondary / Q_primary. If the primary ΔT is larger (i.e., the primary cools down more), more heat is transferred to the secondary, increasing the heat transferred but also lowering the average primary temperature. The efficiency is not directly affected by the ΔT; it's the ratio of heat transferred to heat available. A larger ΔT means the primary coolant is rejecting more heat, which may increase the SG efficiency if the secondary can absorb it, but it also reduces the primary loop's average temperature, which affects the reactor's power distribution. The SG efficiency is typically high regardless of the ΔT, as long as the heat exchanger is properly designed.

A new, clean steam generator has an efficiency of about 99.0-99.5%. Over the plant's life, fouling on the secondary side (from corrosion products, impurities, and deposits) can reduce the heat transfer coefficient, requiring the primary coolant to cool less, thus lowering the efficiency. Typical degradation is about 0.2-0.5% per year, depending on the water chemistry and the effectiveness of the secondary side cleanup. After 10-20 years, the efficiency may drop to 97-98%, which can reduce the plant's output by 1-2%. This is why utilities perform chemical cleaning or tube plugging to restore efficiency.

The approach temperature is the difference between the primary coolant outlet temperature and the saturation temperature of the secondary steam (at the secondary pressure). A lower approach temperature means the primary coolant is cooled closer to the secondary saturation temperature, indicating more heat is extracted, which generally implies higher efficiency. However, achieving a lower approach temperature requires a larger heat transfer surface area or a higher overall heat transfer coefficient. The efficiency is not directly a function of approach temperature but rather of the heat transferred relative to the heat available. A well-designed SG will have an approach temperature of 5-10°C, which corresponds to about 98-99% efficiency in transferring the available heat.

Actually, it is exactly that. The efficiency is η_SG = (m_secondary × (h_steam_out - h_feedwater_in)) / (m_primary × cp_primary × (T_in - T_out)). The primary heat available is the enthalpy drop of the primary coolant, and the heat transferred is the enthalpy rise of the secondary coolant, including the latent heat of vaporization. The formula accounts for the mass flow rates and the specific heats. In practice, the primary enthalpy drop is determined by the primary flow and the temperature difference, while the secondary heat transfer is determined by the steam production rate. The efficiency is simply the ratio of these two quantities, accounting for any external heat losses.

When tubes are plugged, the effective heat transfer area decreases. To transfer the same amount of heat, the remaining tubes must operate at a higher heat flux, which increases the temperature difference required, leading to a higher primary outlet temperature (i.e., less heat extracted). This lowers the steam generator efficiency because the primary coolant leaves with more residual heat, reducing the heat transferred. Each plugged tube reduces the total heat transfer capacity proportionally. If a significant number of tubes are plugged (e.g., >5-10%), the efficiency may drop noticeably, potentially requiring a derating of the reactor power to avoid overheating the remaining tubes.

In the context of nuclear engineering, the terms are often used interchangeably, but they can have subtle differences. 'Heat transfer efficiency' usually refers to the effectiveness of the heat exchanger: the ratio of actual heat transfer to the maximum possible heat transfer (given the inlet temperatures and heat capacities). 'Thermal efficiency' of the steam generator is the ratio of heat transferred to the secondary to the heat available from the primary, which includes losses to the environment. In practice, for a well-insulated steam generator, the two are nearly equal because losses are small. The formula η_SG = (heat transferred) / (heat available from primary) captures the thermodynamic efficiency of the component.

If the steam generator efficiency drops, the primary coolant must be pumped at a higher flow rate or the reactor power must be reduced to maintain the same secondary steam production. Higher flow increases pump power consumption, which is a parasitic load that reduces the net electrical output. Conversely, a higher efficiency allows the same heat transfer with lower primary flow, reducing pump power. However, the primary flow is usually set by the reactor's thermal-hydraulic design and is not directly adjusted to compensate for SG efficiency changes. If efficiency degrades, the plant may need to reduce power to stay within thermal limits, which directly affects revenue.

Once-through steam generators (OTSG) have the feedwater enter at the bottom and completely evaporate as it flows upward, producing superheated steam at the outlet. This design eliminates the recirculation loop of the U-tube SG, reduces the inventory of water in the secondary side, and allows higher steam temperatures (and thus higher Rankine efficiency) because the feedwater is heated directly. The efficiency of an OTSG is similar to a U-tube SG (both >98%), but the OTSG can achieve a slightly lower approach temperature due to the counter-flow arrangement and the ability to superheat the steam. This improves the overall plant efficiency by about 1-2%.

The efficiency is calculated from plant data: the primary side heat removal is determined from the primary coolant flow rate and the temperature drop across the SG (using calibrated flow meters and RTDs). The secondary heat absorption is determined from the feedwater flow rate and the enthalpy rise (using feedwater temperature and steam pressure). The ratio gives the efficiency. Additionally, the heat balance is verified by comparing the sum of heat removed by all SGs to the reactor thermal power. This calculation is part of the plant's performance monitoring system and is used to detect fouling, tube plugging, or instrument drift. Regular heat balance tests are performed to track efficiency trends.

Feedwater heating increases the temperature of the water entering the steam generator, reducing the amount of heat that must be added to bring it to saturation. This raises the average temperature of heat addition in the Rankine cycle, improving the overall plant efficiency. However, the steam generator efficiency itself is the ratio of heat transferred to the secondary (which includes the feedwater heating) to the heat available from the primary. If the feedwater temperature is higher, the enthalpy rise in the SG is smaller for the same steam production, but the primary heat available is unchanged. The SG efficiency might appear to increase because the secondary absorbs the same amount of heat, but the denominator (heat available from primary) is unchanged. The benefit of feedwater heating is in the Rankine cycle efficiency, not in the SG efficiency per se.

During transient conditions (such as reactor power changes or load following), the energy stored in the steam generator metal mass can be released or absorbed, temporarily causing the calculated efficiency to exceed 100% if the formula uses steady-state assumptions. For example, if the primary flow decreases and the secondary flow remains constant, the metal temperature may drop, releasing stored heat that adds to the secondary heat. The instantaneous efficiency based on the heat transfer rate could appear >100% for a short time. However, over a steady-state period, the efficiency will be <100%. In practice, efficiency is calculated only at stable conditions, and any value >100% indicates a data inconsistency or a transient not accounted for in the energy balance.