Heat-exchanger network design

const part = (s, above) => {
  if (above) {
    if (s.hot) { if (s.Ts <= Th + EPS) return null; const near = Math.max(s.Tt, Th); return { near, far: s.Ts, duty: s.CP * (s.Ts - near) }; }
    if (s.Tt <= Tc + EPS) return null; const near = Math.max(s.Ts, Tc); return { near, far: s.Tt, duty: s.CP * (s.Tt - near) };
  }
  if (s.hot) { if (s.Tt >= Th - EPS) return null; const near = Math.min(s.Ts, Th); return { near, far: s.Tt, duty: s.CP * (near - s.Tt) }; }
  if (s.Ts >= Tc - EPS) return null; const near = Math.min(s.Tt, Tc); return { near, far: s.Ts, duty: s.CP * (near - s.Ts) };
};

const cpOk = above ? h.s.CP <= c.s.CP + EPS : h.s.CP >= c.s.CP - EPS;
if (h.atPinch && c.atPinch && !cpOk) continue;                      // the CP rule binds a match of two streams that both touch the pinch
const q = Math.min(h.rem, c.rem), pinchTouch = (h.atPinch ? 1 : 0) + (c.atPinch ? 1 : 0);
const score = (pinchTouch * 1e9) + q;
if (!best || score > best.score) best = { h, c, q, score, cpOk };

const { h, c, q } = best, dh = q / h.s.CP, dc = q / c.s.CP;
const hotT = [h.T, h.T + sign * dh], coldT = [c.T, c.T + sign * dc];
// counter-current ends: the pinch-side end of the hot stream faces the pinch-side end of the cold one
const d1 = Math.abs(hotT[0] - coldT[0]), d2 = Math.abs(hotT[1] - coldT[1]);
const ok = Math.min(d1, d2) >= dTmin - 1e-6;
if (!ok) problems.push(prob('hen.dtmin', 'warning', `Match ${h.s.id}/${c.s.id} (${region} the pinch) leaves ${Math.min(d1, d2).toFixed(2)} between the streams at one end, below the minimum ${dTmin}.`));
matches.push({ region, hot: h.s.id, cold: c.s.id, Q: q, hotT, coldT, ok, dT: [d1, d2], cpRule: best.cpOk });
h.rem -= q; c.rem -= q; h.T += sign * dh; c.T += sign * dc; h.atPinch = false; c.atPinch = false;

  for (const c of cs) if (c.rem > 1e-6 && above) heaters.push({ stream: c.s.id, Q: c.rem, from: c.T, to: c.far });
  for (const h of hs) if (h.rem > 1e-6 && !above) coolers.push({ stream: h.s.id, Q: h.rem, from: h.T, to: h.far });
  // what no match and no allowed utility can take: a hot stream left above the pinch, a cold one left below (that would cross the pinch with a utility)
  for (const h of hs) if (h.rem > 1e-6 && above) { problems.push(prob('hen.hotleft', 'warning', `Stream ${h.s.id} has ${h.rem.toFixed(2)} kW left above the pinch that no allowed match took (a cooler there would cost energy); split the stream or accept the penalty.`)); coolers.push({ stream: h.s.id, Q: h.rem, from: h.T, to: h.far, crosses: true }); }
  for (const c of cs) if (c.rem > 1e-6 && !above) { problems.push(prob('hen.coldleft', 'warning', `Stream ${c.s.id} has ${c.rem.toFixed(2)} kW left below the pinch that no allowed match took (a heater there would cost energy); split the stream or accept the penalty.`)); heaters.push({ stream: c.s.id, Q: c.rem, from: c.T, to: c.far, crosses: true }); }
}
const sumQ = (l) => l.reduce((a, x) => a + x.Q, 0), QH = sumQ(heaters), QC = sumQ(coolers), mu = minUnits(S, dTmin).total, units = matches.length + heaters.length + coolers.length;
if (QH > pt.QHmin + 1e-6 || QC > pt.QCmin + 1e-6) problems.push(prob('hen.target', 'warning', `The network uses ${QH.toFixed(2)} of heating and ${QC.toFixed(2)} of cooling; the targets are ${pt.QHmin.toFixed(2)} and ${pt.QCmin.toFixed(2)}.`));

const f = (v) => +Number(v).toFixed(1);