Simplified Calculation Memory — User Guide

1. What is this file?#

This Excel workbook constitutes the detailed calculation memory of the Average Individual Risk of the Exposed Population (IR_av) for projects generated with TekRisk under the CCPS-4-3 §4.4.1.3 simplified method.

Purpose: to document step by step, with explicit tables and live formulas, the specific contribution of each incident outcome case to the individual risk at each (x,y) point of interest, the initial frequencies, and the applied probabilities. It is intended to be delivered to regulatory authorities (e.g. ASEA in Mexico, HSE in UK, RIVM in the Netherlands) and allows peer review.

Target audience:

• Regulatory authority reviewing.
• Process engineers performing peer validation of the calculations.
• External auditors who need to reproduce the calculation with their own assumptions.

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2. Workbook structure#

The workbook contains 7 sheets ordered sequentially. Each sheet starts with a gray introductory block explaining its content and purpose.

#	Sheet	Content
1	Summary	Project metadata, applied method, threshold, IR criteria, population, and IR_av result. Defines the named ranges THRESHOLD_PCT, INTOL_THR, TOL_THR, POBLACION_PROYECTO, DENSIDAD_PROYECTO.
2	Scenarios	One row per incident outcome case: initial frequency f_i, analytical radius r_i, directional factor, potential IR contribution.
3	Receivers	(x,y) coordinates of interest (receivers defined in the project), with population and density.
4	Point Contributions	Receivers × Scenarios matrix. Each cell with a live formula =IF(distance ≤ radius; contribution; 0). Final column IR(x,y) = SUM(contributions).
5	Average IR	For each receiver, IR(x,y) × P(x,y). IR_av Eq. 4.4.6 (exposed population) and Eq. 4.4.7 (total population).
6	Contour Levels	Application of CCPS Eq. 4.4.5 (cumulative sum per cluster) — actual iso-contour levels of the map.
7	Methodology	Canonical equations, variables/units table, and bibliographic references.

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3. How to audit IR_av step by step#

Step 1 — Sheet 1 (Summary)#

1. Verify that Method applied = Simplified (CCPS-4-3 §4.4.1.3).
2. Note the Fatality threshold (% of probit fatality that defines the binary discriminator).
3. Confirm the IR criteria (intolerable / tolerable) and the applicable country preset.
4. Observe the total population P_T and the density of the project.
5. The IR_av Exposed Population cell references the final result from Sheet 5.

Step 2 — Sheet 2 (Scenarios)#

1. Each row is a scenario (incident outcome case): combination of source + risk model + method.
2. Column E (Frequency f_i): initial frequency in events/year, entered by the engineer.
3. Column G (Radius r_i): distance precomputed by the engine where the fatality probability crosses the threshold from Step 1.
4. Column H (Directional factor): 1 for thermal / radial VCE models; θ/360 for Flash Fire (CCPS Eq. 4.4.4).
5. Column J (IR contribution): live formula =E×I = f_i × factor. This is what it contributes to the IR of any point that falls within the circle.
6. Column L (Notes): indicates special cases like "source inside LEL polygon → θ=360°".

Step 3 — Sheet 3 (Receivers)#

1. Each row is an (x,y) point of interest with its name, type, lat/lon, and population.
2. If Geometry ≠ Point, the lat/lon is the centroid of the original geometry (LineString/Polygon) — the Notes column flags it.

Step 4 — Sheet 4 (Point Contributions) — the key sheet for the authority#

1. The Reference row (row 6 approx.) brings the radii and potential contributions from Sheet 2 via INDEX(RADIOS_SCENARIOS, #) and INDEX(CONTRIBUCIONES_SCENARIOS, #).
2. For each receiver (row):
   • Distance (precomputed): haversine between the receiver and the circle center of the scenario.
   • Contribution (live formula): =IF(distance ≤ radius; contribution; 0). If the receiver falls inside the circle, the contribution is added; otherwise, 0.
3. The final column IR(x,y) sums the individual contributions: =SUM(contributions in the row). This is CCPS Eq. 4.4.1 in its binary form.

How to verify a point manually:

• Compute by hand the distance from the receiver to the scenario source.
• Compare with the radius r_i from Sheet 2.
• If distance ≤ r_i → the contribution must be f_i × directional_factor.
• Sum all contributions ≠ 0 → it should match the IR(x,y) column.

Step 5 — Sheet 5 (Average IR)#

1. For each receiver: IR(x,y) is referenced from Sheet 4 (INDEX(IR_POR_RECEPTOR, #)).
2. IR × P is a live formula.
3. If there is background population (density × area per band outside receivers), an additional block appears below.
4. TOTAL row: Σ(P) and Σ(IR×P) with SUM formulas.
5. IR_av (Eq. 4.4.6) = Σ(IR×P) / Σ(P) — average individual risk of the exposed population.
6. IR_av (Eq. 4.4.7) = Σ(IR×P) / P_T — average individual risk over the total project population.

Step 6 — Sheet 6 (Contour Levels)#

1. For each cluster of concentric disks (scenarios at the same source), the disks are sorted by descending radius.
2. The Cumulative IR column applies CCPS Eq. 4.4.5: F = F_previous + E_current (cumulative sum).
3. Each cumulative corresponds to an actual iso-contour level drawn on the map.
4. The last value of each cluster (bold red) = maximum IR of the cluster.

Step 7 — Sheet 7 (Methodology)#

1. Table of canonical equations with their mathematical form and description.
2. Table of variables with SI units.
3. List of bibliographic references (CCPS QRA 2nd Ed., NTE-002, etc.).

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4. How to do a sensitivity analysis#

The workbook contains live formulas that recalculate automatically when opened. To audit sensitivities:

• Change the fatality threshold: modify the THRESHOLD_PCT cell in Sheet 1. This affects labeling only; the radii r_i are precomputed by the engine for the threshold fixed at calculation time. To reflect a new threshold you must regenerate the Excel from the application.
• Change an initial frequency: modify the corresponding cell E in Sheet 2. The contribution (Column J) and the IR(x,y) of each receiver (Sheet 4) recalculate instantly.
• Change the directional factor: modify column H in Sheet 2. Useful to evaluate scenarios where θ is uncertain in FF.
• Change a receiver's population: modify column D in Sheet 5. Σ(P) and IR_av recalculate.
• Change the tolerability criteria: modify INTOL_THR / TOL_THR in Sheet 1. The Band in Sheet 5 changes category.

Note: the workbook has fullCalcOnLoad = true, so Excel recalculates all formulas when opened. If cells appear blank, press F9 to force recalculation.

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5. Glossary#

Symbol	Meaning	Unit
IR(x,y)	Individual risk at location (x,y)	yr⁻¹
IR_av	Average individual risk (population-weighted)	yr⁻¹
Pf	Fatality probability (0–1). In the simplified method: 0 or 1.	—
f_i	Initial frequency of scenario i (events/year)	yr⁻¹
P(x,y)	People at location (x,y)	persons
P_T	Predetermined total project population	persons
r_i	Analytical radius where Pf crosses the threshold	m
θ	Angle enclosed by the LEL polygon from the source	degrees
θ/360	Flash Fire directional factor (CCPS Eq. 4.4.4)	—
Cluster	Group of concentric scenarios at the same source	—
Analytical circle	Circular approximation of the scenario in the simplified method	—
Tolerability band	Intolerable / ALARP / Acceptable per criteria	—

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6. References#

• CCPS, Guidelines for Chemical Process Quantitative Risk Analysis, 2nd Ed., AIChE/CCPS, 2000. Chapter 4 §4.4.1.3.
• CCPS QRA 2nd Ed., Equations 4.4.1, 4.4.4, 4.4.5, 4.4.6, 4.4.7.
• Applicable technical standard per project jurisdiction (e.g. NTE-002, ASEA Guidelines).

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7. Limitations and assumptions#

1. Binary discriminator: in the simplified method, Pf = 1 if probit fatality ≥ threshold, otherwise Pf = 0. The continuous probit curve from the general method is not used.
2. Simplified Flash Fire: for FF scenarios, the engine forces CCPS Eq. 4.4.4 (circular zone of radius R with factor θ/360), regardless of the individual model's wind rose setting.
3. Directional VCE: for VCE scenarios with SLAB dispersion, the engine collapses the directional envelope to a worst-case circle centered at the source.
4. Receivers with complex geometry: for LineString/Polygon the centroid is used as the evaluation point. This may underestimate IR for extended receivers near the circle boundary.
5. Source inside LEL polygon: if the source falls inside the LEL polygon in FF, θ saturates to 360° (directional factor = 1).
6. Background population: when using population density, the calculation assumes uniform people distribution within the band. This may not reflect actual concentrations (urban vs rural zones).
7. Workbook recalculation: live formulas recalculate automatically when the file is opened in Excel/LibreOffice. If the file is opened in viewers that do not evaluate formulas, the cached values show the original result.

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Generated by TekRisk — Simplified Method Calculation Memory (CCPS-4-3 §4.4.1.3).