Simulator and minimal model — move the parameters and build intuition

First, move the five parameters one at a time

The simulator in this chapter reduces temperature, pressure, catalyst activity, purge rate, and inert contamination into a simplified teaching model. The goal is not rigorous design calculation; it is to visually separate which operating parameter affects which indicator.

• Temperature: Lower is better for equilibrium, but the rate tends to drop.
• Pressure: Higher favors the equilibrium.
• Catalyst activity: Primarily affects the rate side.
• Purge rate: Too low and inerts cannot escape.
• Inert contamination: Eats into the partial pressures inside the loop and drops the apparent performance.

The JavaScript of the teaching model

The teaching-side code is also written short, without hiding the formulas or assumptions. Values outside the input ranges are not silently corrected — they stop with a RangeError.

function assertFiniteInRange(name, value, min, max) {
  if (!Number.isFinite(value) || value < min || value > max) {
    throw new RangeError(`${name} must be a finite number in [${min}, ${max}]`);
  }
}

function clamp01(value) {
  if (!Number.isFinite(value)) {
    throw new RangeError("value must be finite");
  }
  return Math.min(1, Math.max(0, value));
}

// Equilibrium favorability: scores the Chapter 3 relationship that
// "lower temperature and higher pressure favor the NH3 side" as 0..1.
function equilibriumFavorability(temperatureC, pressureBar) {
  assertFiniteInRange("temperatureC", temperatureC, 350, 550);
  assertFiniteInRange("pressureBar", pressureBar, 80, 280);

  // Bonus for being below 520 degC (0..1). 170 scales the 350-520 degC span.
  const temperatureBonus = clamp01((520 - temperatureC) / 170);
  // Bonus for being above 80 bar (0..1). 170 scales the 80-250 bar span.
  const pressureBonus = clamp01((pressureBar - 80) / 170);
  // 0.18 = floor, 0.52 = temperature contribution, 0.30 = pressure contribution.
  // Their ratio reflects the qualitative claim that temperature has a slightly
  // stronger effect than pressure, as a teaching choice.
  return clamp01(0.18 + 0.52 * temperatureBonus + 0.30 * pressureBonus);
}

// Rate score: scores the Chapter 4 relationship that
// "higher temperature and higher activity make the reaction faster" as 0..1.
function rateScore(temperatureC, catalystActivityPct) {
  assertFiniteInRange("temperatureC", temperatureC, 350, 550);
  assertFiniteInRange("catalystActivityPct", catalystActivityPct, 40, 120);

  // From 360 degC up, the drive grows with temperature (0..1).
  const temperatureDrive = clamp01((temperatureC - 360) / 140);
  const activity = catalystActivityPct / 100;
  // 0.12 = floor, 0.78 = product of temperature x activity (so "both must be
  // present together" before the rate goes up).
  return clamp01(0.12 + 0.78 * temperatureDrive * activity);
}

// Inert accumulation risk: scores the Chapter 5 relationship that
// "high inert load + low purge" raises risk, as 0..1.
function inertRisk(purgePct, inertPct) {
  assertFiniteInRange("purgePct", purgePct, 0.5, 8);
  assertFiniteInRange("inertPct", inertPct, 0, 8);

  // Below 4.5%, lowPurge climbs.
  const lowPurge = clamp01((4.5 - purgePct) / 4);
  const inertLoad = clamp01(inertPct / 8);
  // 0.04 = floor, 0.64 = inert contamination contribution (primary driver),
  // 0.22 = low-purge contribution (secondary).
  return clamp01(0.04 + 0.64 * inertLoad + 0.22 * lowPurge);
}

// Estimated single-pass (one-through) conversion.
function estimateSinglePassConversion(temperatureC, pressureBar, catalystActivityPct, purgePct, inertPct) {
  const equilibrium = equilibriumFavorability(temperatureC, pressureBar);
  const rate = rateScore(temperatureC, catalystActivityPct);
  const risk = inertRisk(purgePct, inertPct);
  // Symmetric design around 4% purge:
  //   - increasing purge helps inerts leave, slightly raising conversion (max +0.02);
  //   - increasing purge too far loses feed H2, slightly lowering effective conversion (max -0.02).
  // The result is an apparent "sweet spot" near 4% purge.
  const purgeBenefit = clamp01(purgePct / 4) * 0.02;
  const purgeLoss = clamp01((purgePct - 4) / 4) * 0.02;
  // 0.05 = base conversion, 0.23 = equilibrium x rate contribution
  // (product so "both must be present"), -0.05 = penalty from inert risk.
  const raw = 0.05 + 0.23 * equilibrium * rate - 0.05 * risk + purgeBenefit - purgeLoss;
  // Clip output to 3..28% as a sanity guard for a teaching model.
  return Math.min(0.28, Math.max(0.03, raw));
}

We split equilibriumFavorability and rateScore first, then layer inertRisk on top to produce estimateSinglePassConversion. For a teaching codebase, having it decomposed at this level makes it easier to see "which part of the explanation corresponds to which piece of the code."

How to use this simulator

The recommended approach is to press "Textbook" first to get a baseline, then change only temperature, only pressure, or only catalyst activity. Moving multiple parameters at once makes it hard to tell which change produced which effect.