← The Process Simulation Handbook

Heat Transfer & Energy Integration

Almost every process spends most of its operating cost on heating and cooling. This chapter is the equipment that moves heat — heaters, coolers, and exchangers — and then the bigger idea that saves the money: making the hot streams heat the cold ones instead of paying for utilities twice.

6.1 Heaters and coolers

The simplest energy units add or remove a duty. You specify either the duty

or the outlet temperature, and the other follows from the energy balance:

$Q$

Duty — heat added (Q>0, a heater) or removed (Q<0, a cooler).

$F$

Molar flow through the unit.

$h_{\text{in}},\; h_{\text{out}}$

Inlet and outlet molar enthalpy, from the active thermo package.

A heater takes

, a cooler . That's the whole model — but the duty it reports is a real utility cost, and the point of the rest of this chapter is to make it smaller.

6.2 The heat exchanger

A heat exchanger couples two streams: a hot one giving up heat and a cold one taking it. No utility is consumed — the duty simply moves from one side to the other, so its energy balance is a pair of matched terms:

$F_{\text{hot}},\; F_{\text{cold}}$

Molar flow of the hot and cold streams.

$h_{\text{hot,in/out}},\; h_{\text{cold,in/out}}$

Molar enthalpy of each stream at its inlet and outlet — the duty that leaves the hot side exactly equals the duty that enters the cold side.

The example below is a crude-distillation train where the hot column products preheat the cold crude feed through a feed-effluent exchanger before it ever reaches a fired heater — recovered heat that would otherwise be paid for twice.

6.3 Rating: how big must the exchanger be?

Knowing the duty isn't the same as knowing the exchanger will fit it. The transfer rate is set by the area

, the overall coefficient , and the driving temperature difference — the log-mean temperature difference (LMTD):

$U$

Overall heat-transfer coefficient — how readily heat crosses the wall between the two fluids.

$A$

Heat-transfer area.

$\Delta T_{lm}$

Log-mean temperature difference — the effective driving force averaged over the exchanger's length.

$\Delta T_1,\; \Delta T_2$

Temperature difference between the two streams at each end of the exchanger.

$F_T$

Correction factor (≤1) for a non-pure-counter-current geometry (below).

alone only tells the truth for pure counter-current flow. A real shell-and-tube exchanger mixes some co-current pattern in (one shell pass, two-or-more tube passes), so the actual driving force is knocked down by the correction factor , read off two dimensionless temperature ratios built from the four terminal temperatures (hot in/out , cold in/out ) — the cold-side thermal effectiveness and the capacity-rate ratio :

$T_1,\; T_2$

Hot-stream inlet and outlet temperature.

$t_1,\; t_2$

Cold-stream inlet and outlet temperature.

$P$

Cold-side thermal effectiveness — how much of the maximum possible temperature rise the cold stream actually achieves.

$R$

Capacity-rate ratio — the hot-to-cold ratio of mass flow times specific heat.

In practice

comes from the standard Bowman-Mueller-Nagle charts (built for 1-shell/2-tube-pass geometry, or their closed-form fit) indexed by and — MaximaLabs' rating panel below solves it directly rather than reading a chart, and flags the case every design should avoid: means the temperature crosses are severe enough that adding a shell pass (or another shell in series) is cheaper than accepting the derated area.

Rating asks: for a given geometry, is the available area enough for the required duty? MaximaLabs' HX design panel (an EDR-style rating) takes the duty, terminal temperatures, and shell/tube/baffle geometry and returns the overall

, the LMTD, the required vs. available area, the over-surface margin (adequate or undersized), the Bell-Delaware shell-side factors, and the counter-current temperature profile:

6.4 Energy integration: the pinch

One exchanger recovers heat between two streams. A whole plant has many hot and cold streams, and the question becomes: what is the least heating and cooling utility this process could possibly need? That's pinch analysis. You combine all hot streams into a hot composite curve and all cold streams into a cold composite curve, slide them together until the closest approach equals a chosen

, and read off the answer:

$Q_{H,\min},\; Q_{C,\min}$

Minimum hot and cold utility the process could reach with a perfectly integrated network — the target.

$T_{\text{pinch}}$

The temperature where the hot and cold composite curves come closest (exactly \Delta T_min apart).

The point where the curves touch is the pinch; it divides the process into a heat-deficit region above and a heat-surplus region below, and the golden rule — don't transfer heat across the pinch — is what unlocks the minimum-utility target. MaximaLabs runs the Linnhoff targeting over the solved flowsheet and reports the minimum hot/cold utilities and the savings left on the table versus the current design:

6.5 From target to design: the heat-exchanger network

Targeting (§6.4) tells you the minimum utility a perfectly-integrated network could reach — but not which streams to match against which, or how many new exchangers to add. The pinch design method answers that with a grid diagram (hot streams left-to- right on top, cold streams below, the pinch drawn as a vertical line splitting the grid) and one governing rule: split the problem at the pinch and design each side separately, since no stream may legally cross it.

Immediately next to the pinch, a match is only feasible if it can carry the full duty without a temperature cross. That reduces to a heat-capacity-flow (

) rule, different on each side:

$CP$

Heat-capacity flow rate \dot m c_p — how much duty a stream gives up (or absorbs) per degree.

$CP_{\text{hot}},\; CP_{\text{cold}}$

The CP of the hot and cold stream in a candidate match — which one must be larger sets which side of the pinch the match is feasible on.

The tick-off heuristic then greedily matches streams pinch-outward: at each step, match the largest feasible pair, exhaust ("tick off") whichever stream runs out of duty first, and carry the other's remainder to the next match. Repeat until every stream is either fully matched against another process stream or left with a residual duty — which becomes the hot/cold utility this design actually needs. MaximaLabs runs exactly this algorithm over your solved flowsheet's real hot and cold streams and returns the match list, each exchanger's estimated area, and — honestly — a flag on any stream a stream-split would be needed to match (the one case tick-off alone can't resolve): open the same Energy panel's Network design tab (right beside the targeting view above) and it lists the proposed matches, each one's duty and estimated area, and the utility remaining after matching — the same streams §6.4 targeted, now actually assigned to exchangers.

This is screening-level, not detailed exchanger design — no stream-split optimization, no capital-cost weighting between candidate networks — but it's the real next step after a target: an actual list of exchangers to add, sized well enough to cost and specify.

6.6 Try it

Heat transfer is where a correct simulation turns into a cheaper plant: size the exchangers so they fit, then integrate them so the process heats itself. Next: turning a converged model into decisions — sensitivity, design specs, and optimization.

6.7 Exercises