Regeneration in steam plant with P-V and T-S

Regeneration is the heating of boiler feed water by steam bled from the turbine, instead of by the boiler fuel alone. It recovers latent heat of the bled steam that would otherwise be lost in the condenser.

Layout (one open feed water heater)

              1
  +--------+------>+---------------+   +-----+
  | Boiler |       |    Turbine    |===| Gen |
  |  + S/H |       +---------------+   +-----+
  +--------+          | m kg (2)  | (1-m) kg (3)
      ^ 7             v           v
      |         +-----------+ +-----------+
  +--------+  6 |  Open FWH | | Condenser |
  | Pump 2 |<---| (mixing)  | +-----------+
  +--------+    +-----------+       | 4
                      ^ 5           |
                 +--------+         |
                 | Pump 1 |<--------+
                 +--------+

Working

1. Steam at boiler pressure enters the turbine (1).
2. At an intermediate pressure, $m$ kg per kg of steam is bled (2) and sent to the feed water heater.
3. The rest, $(1-m)$ kg, expands to condenser pressure (3) and is condensed (4).
4. Pump 1 raises condensate to heater pressure (5). In the heater the bled steam mixes with it and condenses, giving saturated water at heater pressure (6).
5. Pump 2 raises it to boiler pressure (7) and it enters the boiler much hotter than in a simple cycle.

Why efficiency (and effective output) increases

• Heat supplied in the boiler falls from about $(h_1 - h_5)$ to $(h_1 - h_7)$; the remaining heat is added at a higher temperature, so the mean temperature of heat addition rises.
• The bled steam's latent heat goes to the feed water, not to the cooling water, so heat rejected falls to $(1-m)(h_3-h_4)$.
• Although work per kg of boiler steam falls slightly, efficiency rises by about 10-15% with several heaters; fuel per kWh falls.
• Smaller exhaust flow means smaller LP blades and condenser, and turbine size can be raised for the same exhaust area, so plant output increases.
• Hot feed water reduces thermal stresses in the boiler; an open heater also deaerates the water.

$$m = \frac{h_6 - h_5}{h_2 - h_5}, \qquad \eta = \frac{(h_1-h_2) + (1-m)(h_2-h_3) - W_p}{h_1 - h_7}$$

where $W_p = (1-m)W_{p1} + W_{p2}$ is the total pump work.

P-v diagram

  p
  ^
  | 7 ________________ 1
  |  |                 \
  |  |                  \  expansion
  |5,6_ _ _ _ _ _ _ _ _ _2 (m kg bled)
  |  |                    \
  |  |                     \___
  | 4|_________________________3
  +--------------------------------> v
  4-5, 6-7 pumps (water, very small v);
  5 and 6 are both at heater pressure
  7-1 boiler, 1-2-3 turbine, 3-4 condenser

T-s diagram

  T
  ^                    1
  |                   /|
  |      f----------g  |
  |     /              |
  |    7               |
  |    6 . . . . . . . 2  bleed (m kg)
  |   /                |
  |  5                 |
  |  4-----------------3  (1-m) kg
  +-------------------------> s
  4-5 pump 1, 5 and 2 mix in FWH -> 6,
  6-7 pump 2, 7-f-g-1 boiler,
  1-2-3 turbine, 3-4 condenser