HRSG pinch

[PabloMBarral]

Hi, community! I hope you're doing well.

When performing a thermal balance on an HRSG, the usual approach is to define two parameters, pinch and approach, which characterize the boiler without the need to specify the UA for the evaporator or economizer.

The issue arises when there is heavy supplemental firing, as the pinch point location can shift from the evaporator outlet to the stack.

One way to address this is by performing two consecutive and separate balances, plotting the T-Q diagram, and ensuring that the gas curve does not intersect the steam/water curve. However, I was wondering if this approach could be improved by redefining the pinch point not as a single temperature difference between the gas and steam, but rather as the minimum of two differences (between gas and water/steam at two different locations, the two mentioned above).

I'm not entirely sure if such a minimum function can be implemented using this:

https://tespy.readthedocs.io/en/main/modules/ude.html#tespy-ude-label

Any insight would be appreciated!

Regards,

[fwitte]

Hi @PabloMBarral,

thank you for reaching out with this suggestion, it is absolutely possible to implement this with the UserDefinedEquation. Essentially, you have to pass all the relevant connections to the ude and then just return the minimum temperature difference. That list can directly be derived from the actual heat exchangers, e.g.:

def get_conn_list(heat_exchangers):
    hot_side_conns = [
        c for heat_exchanger in heat_exchangers
        for c in (heat_exchanger.outl[0], heat_exchanger.inl[0])
    ]
    # switched order for counter current flow
    cold_side_conns = [
        c for heat_exchanger in heat_exchangers
        for c in (heat_exchanger.inl[1], heat_exchanger.outl[1])
    ]
    return hot_side_conns, cold_side_conns


def pinch_ude(ude):
    pinch = ude.params["pinch"]
    heat_exchangers = ude.params["heat_exchanger_list"]
    hot_side_conns, cold_side_conns = get_conn_list(heat_exchangers)

    ttd_list = []
    for hsc, csc in zip(hot_side_conns, cold_side_conns):
        ttd_list += [hsc.calc_T() - csc.calc_T()]

    return pinch - min(ttd_list)

def pinch_ude_deriv(ude):
    heat_exchangers = ude.params["heat_exchanger_list"]
    hot_side_conns, cold_side_conns = get_conn_list(heat_exchangers)

    for c in hot_side_conns + cold_side_conns:
        if c.p.is_var:
            ude.jacobian[c.p.J_col] = ude.numeric_deriv('p', c)
        if c.h.is_var:
            ude.jacobian[c.h.J_col] = ude.numeric_deriv('h', c)


from tespy.tools import UserDefinedEquation

ude = UserDefinedEquation(
    "minimum pinch equation",
    func=pinch_ude,
    deriv=pinch_ude_deriv,
    conns=[],
    params={"pinch": 5, "heat_exchanger_list": [preheater, evaporator]}
)

nw.add_ude(ude)

If the heat exchangers are sharing the same connections (i.e. preheater cold side outlet = evaporator cold side inlet and evaporator hot side outlet = preheater hot side inlet) you can make some simplifications, which will result in less temperature values to be calculated.

def get_conn_list(heat_exchangers):
    hot_side_conns = [heat_exchangers[0].outl[0]] + [heat_exchanger.inl[0] for heat_exchanger in heat_exchangers]
    cold_side_conns = [heat_exchanger.inl[1] for heat_exchanger in heat_exchangers] + [heat_exchangers[-1].outl[1]]
    return hot_side_conns, cold_side_conns

Best

Francesco