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).

[yoelcortes]

Great work!

Users reading this pull might find this note helpful: The issue in BioSTEAM where temperatures do not match heating/cooling directions in condensers/reboilers is due to the way they are modeled in shortcut methods (FUG and McCabeThiele). There is nothing we can do make everything thermodynamically consistent (maintaining the overall energy balance and phase equilibrium at both outlets) because the system is overspecified internally in shortcut methods.

This pull request makes sure all results are conservative... If users what to include reboiler/condensers where the problem arises, it is better to direct them to a rigorous column.

Thank you!!