fix HXN pinch analysis: energy-consistent problem table

[sarangbhagwat]

Stacked on #253 (fix-hxn-cache-network) — it depends on tests/test_hxn.py and the cache fix there. Merge #253 first; this PR's base should then be retargeted to master (the diff shown here is only this branch's five commits).

Problem

temperature_interval_pinch_analysis (biosteam/facilities/hxn/hxn_synthesis.py) built the heat cascade from interval enthalpies that were

1. evaluated by flashing hot streams at the shifted temperature T − T_min_app, so a stream entering within T_min_app of its dew point was already liquid and lost its latent heat;
2. never clipped to the stream's actual [H_in, H_out], so non-equilibrium column outlets inflated interval duties;
3. assigned with the wrong sign for streams whose outlet temperature moves against their duty.

The resulting utility targets were physically impossible — the hot target exceeded the un-integrated heating load on the class doctest system, and hot − cold ≠ Σ unit_duty on sugarcane — so the pinch temperatures handed to synthesize_network were wrong (304 K vs 359 K on sugarcane).

Fix

The cascade is now built by a pure function problem_table(streams_inlet, streams_quenched, is_hot, T_min_app) -> ProblemTable:

• Each monotone stream is walked once down the shifted-temperature grid with a single warm-started copy, flashed at the real temperature T + shift. Its enthalpies are exact at its own end points (assigned by index) and clipped to [H_in, H_out] in between, so its interval contributions telescope exactly to sign · |H_out − H_in|.
• Isothermal streams, and streams whose outlet temperature moves against their duty (e.g. a reboiler outlet at VLE), are point loads at their outlet temperature.
• The cascade checks feasibility of the heat both arriving at each boundary (before its point loads) and leaving it — a hot point load at T cannot serve a sink above T, and checking only the leaving flow let such loads mask a deficit in the interval directly above them.
• Hence hot_util_load − cold_util_load == Σ unit_duty and both targets are non-negative by construction (rounding in the threshold branch is absorbed into the hot target to keep the identity exact).
• A failed VLE warns with the stream's ID, falls back to linear interpolation in T, and restarts the warm-started copy cleanly.

temperature_interval_pinch_analysis is now a thin wrapper; its signature and 12-tuple return are unchanged, and synthesize_network / HeatExchangerNetwork are untouched. problem_table/ProblemTable are exported with an Examples doctest.

Synthesis-side note: non-monotone streams get pinch_T = T_in in pinch_T_arr, so load_duties places their whole duty on the hot side (the old code produced a meaningless negative dH2 for them when T_in sat on the wrong side of the pinch). Reconciling that with the point-load treatment in the table is left to the planned synthesis-heuristic work.

Validation

tests/test_hxn.py (new tests):

• per-stream and net energy identities on the doctest system and a 4-stream synthetic case at ΔT_min = 5/10/20 K (also: a target can never exceed the un-integrated load; the public wrapper reports the same targets);

• two-stream closed forms (threshold problem; pinch at the cold inlet);

• isothermal / non-monotone streams handled as point loads;

• regression for the point-load masking case (condensing stream at 400 K vs. a cold stream 392 → 398 K: correct hot target = the 395–398 K segment, pinch 395 K);

• the synthetic 4-stream network reaches the corrected MER.

• HeatExchangerNetwork class doctest unchanged (same pinch on that system; ratio still 0.82).

• Full suite (pytest . --disable-numba=1 -m "not slow"): identical failure set to master — stack drift, missing optional deps, tutorial notebooks — nothing new. tests/test_biorefineries.py::test_sugarcane (full HXN synthesis) passes; test_cornstover fails with the same pre-existing numbers as on master.

🤖 Generated with Claude Code

[sarangbhagwat]

Effect on heat recovery (old vs. new problem table)

Same systems simulated with the old and new hxn_synthesis.py (biorefineries with HXN.units = None, i.e. all utility streams integrated; T_min_app = 5 K; loads are unit_duty):

Case	Hot utility (MJ/hr) old → new	Recovered (MJ/hr) old → new	Old network feasible?
HeatExchangerNetwork doctest system	282.8 → 282.8	60.1 → 60.1	yes — network unchanged; only the MER target moved (435 → 283, from impossible to feasible)
4-stream synthetic (tests)	6.53 → 2.37	10.6 → 14.7	yes — now at MER
Sugarcane	111.2 → 126.2	58.9 → 44.0	no — HX_2_7 (20.4 MJ/hr) has a −3 K internal temperature cross
Lipidcane	71.9 → 79.4	48.8 → 41.3	no — 10.0 MJ/hr in exchangers with internal approach < 5 K

The sugarcane/lipidcane results look like they worsened, but the old networks there actually "beat" the corrected MER, so they weren't actually feasible. This is an issue in HXprocess's internal counter-current H–T profile (not just the end-point approaches that HXprocess enforces): e.g., on sugarcane, H304 is a vapor whose 21.8 MJ/hr is almost all latent heat at 364 K, and the old pinch (328 K, after the shifted-temperature flash dropped that latent heat) led the greedy synthesizer to match it against a cold stream that is at 367 K at the condensation point.

With the corrected table: sugarcane recovers 43.99 of the 44.07 MJ/hr the MER allows (at MER) and lipidcane 41.3 of 43.9 (94 %), with no infeasible exchangers. In feasible heat, recovery improves on every case (sugarcane ≈ +14 %, lipidcane ≈ +6 %, synthetic +39 %, doctest unchanged).

Downstream effect (all-streams configurations): sugarcane utility cost +5.5 %, TCI −0.7 %; lipidcane +1.6 % / −0.2 %. The default configurations, which integrate a hand-picked subset, are unchanged.

Follow-ups this surfaced (out of scope here): HXprocess should check the internal approach for latent-heat streams (or the synthesizer should split condensing streams at their dew point), and the synthesizer can emit a reversed match (lipidcane HX_3_19, "hot" 374.6 → 374.1 K vs. "cold" 386 K, 0.04 MJ/hr — present before and after this PR).