Vose SoftwareModelRisk example · Oil and gas
Well Cost and Time (AFE)
What should the AFE for well K-15 be? Days and cost phase by phase, with trouble time and the events that wreck a well budget.
From the model’s saved run
The AFE
The AFE is the cost at the confidence level on Inputs (P80 as shipped). The deterministic estimate is the usual single number.
| Measure | Unit | Value |
|---|---|---|
| Deterministic estimate, with trouble allowance | US$m | 41.5 |
| Mean cost of the well | US$m | 44.3 |
| Chance of staying within the deterministic estimate | probability | 15.6% |
| Chance of exceeding the deterministic estimate | probability | 84.4% |
| AFE (P80 cost) | US$m | 46.3 |
| Contingency over the deterministic estimate | US$m | 4.8 |
| Contingency as a share of the deterministic estimate | 12% |
S-curve (cumulative probability) of Total well cost from the saved simulation.
The business question
Well K-15 is an appraisal well, planned to 4,200 m from a jack-up rig. The drilling engineer's deterministic estimate adds up the most likely duration and cost of each phase and puts a 10% allowance on top for trouble time. But wells rarely go to plan.
Some trouble — lost circulation, a tight hole, an equipment failure, waiting on weather — happens on almost every well, more often in the difficult sections. And once in a while a major event, such as a stuck drill string that forces a sidetrack, adds weeks. Because most of the rig's cost accrues by the day, every lost day costs money.
The model builds the well phase by phase, adds trouble time as a random number of events of random size, adds the two major risk events, and turns days into cost at the spread rate. The AFE then rests on a stated confidence level instead of a single number that is exceeded far more often than not.
- Who it is for
- Drilling and well engineers, cost engineers and asset managers who prepare or approve AFEs.
- Main outputs
- Total days and total cost with P50 / P80 / P90 · the chance of exceeding the deterministic estimate · the contingency for a P80 AFE · days at the end of each phase with their range · what drives the cost.
How the model works
Three sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
The spread rate (rig, services, fuel, logistics) per day. How often trouble occurs and how many days an event costs; the chance and the size of a sidetrack and of a well-control event, and the phase each can happen in. The trouble allowance used in the deterministic estimate; and the confidence level of the AFE.
Well plan sheet
Each phase has a trouble-free duration and a cost of materials and services (PERT), and a trouble factor for how difficult it is. In every iteration the number of trouble events in a phase is Poisson with a mean proportional to its duration and its trouble factor, and VoseAggregateMC adds up the days they cost.
A major event adds its days and cost to the phase it happens in. Phase days × spread rate plus materials and services gives the phase cost.
Results sheet
Percentiles of total cost and days in the P50 / P80 / P90 form used for AFEs, the chance of exceeding the deterministic estimate, the AFE at the chosen confidence level and its contingency, days at the end of each phase, and what drives the cost.
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The results in detail
Cost and days
P50 / P80 / P90: a 50%, 80% and 90% chance of not being exceeded.
| Measure | Unit | P50 | P80 | P90 | Mean |
|---|---|---|---|---|---|
| Total cost of the well | US$m | 43.7 | 46.3 | 49.0 | 44.3 |
| Total days | days | 64.8 | 70.8 | 75.8 | 66.1 |
| Trouble time | days | 6.7 | 10.2 | 12.2 | 7.2 |
| Major event days | days | – | – | 11.1 | 1.8 |
| Materials and services | US$m | 20.0 | 20.5 | 20.8 | 20.0 |
| Chance of a sidetrack or a well-control event | probability | 12.6% |
Days at the end of each phase
The time–depth plan with its range: 10th percentile, median and 90th percentile.
Line chart: 90th percentile, Median, Mean, 10th percentile.
| Measure | Unit | 10th pct | Median | 90th pct | Mean |
|---|---|---|---|---|---|
| 1 Mobilise and rig up | days | 3.5 | 4.2 | 5.4 | 4.4 |
| 2 26-in surface hole, 20-in casing | days | 8.5 | 9.8 | 11.9 | 10.1 |
| 3 17½-in hole, 13⅜-in casing | days | 18.7 | 21.3 | 24.8 | 21.6 |
| 4 12¼-in hole, 9⅝-in casing | days | 35.1 | 39.8 | 49.2 | 41.0 |
| 5 8½-in reservoir section | days | 46.6 | 52.4 | 63.1 | 53.7 |
| 6 Logging and testing | days | 53.4 | 59.4 | 70.3 | 60.7 |
| 7 Plug, abandon and rig down | days | 58.7 | 64.8 | 75.8 | 66.1 |
What drives the cost of the well
Lowest and highest mean total cost over ten equal groups of each input (VoseSimSensitivityMean), drawn from the overall mean.
Tornado chart: the inputs ranked by how far the mean output moves across each input’s range.
The ranking as a table 10 inputs
| Input (ranked by influence) | Lowest mean | Highest mean | Rank |
|---|---|---|---|
| Sidetrack days | 43.6 | 51.4 | 1 |
| Well control days | 44.2 | 49.1 | 2 |
| Trouble time | 42.2 | 47.1 | 3 |
| Spread rate | 42.8 | 46.2 | 4 |
| Duration, 12¼-in hole | 43.3 | 45.6 | 5 |
| Duration, 8½-in hole | 43.5 | 45.3 | 6 |
| Duration, 17½-in hole | 43.6 | 45.0 | 7 |
| Materials and services, Logging | 43.8 | 45.1 | 8 |
| Materials and services, 12¼-in hole | 43.8 | 44.8 | 9 |
| Materials and services, 17½-in hole | 44.0 | 45.0 | 10 |
How to read these results
- The deterministic estimate is exceeded far more often than not, even with its trouble allowance: most likely values add up to less than the median, trouble time is almost certain and its average is larger than the allowance, and the major events can only add time.
- An AFE at P80 is exceeded in 20% of wells. The contingency is the amount the AFE adds to the deterministic estimate to get there. Companies that set the AFE at P50 should expect to need a supplement about half the time.
- The sidetrack drives the upper end of the S-curve: it happens in one well in ten, but when it does it adds two weeks and several million dollars. Reducing that risk (better stuck-pipe practices, a contingency liner) narrows the range more than shaving days off the plan.
- Most of the cost accrues by the day, so the spread rate and every lost day matter. Trouble time is one of the largest drivers: individually small events add up to about a week on average, and some wells lose nearly twice that.
See it move. Open the workbook, change an input on the Inputs sheet and run the simulation: every table and chart on this page updates in Excel.
Inputs and assumptions
Every assumption in the model, with its uncertainty and where it comes from. The figures are illustrative.
Rig and spread rate 1 input
Everything that costs money by the day.
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| Spread rateJack-up day rate with services, fuel, logistics and supervision; the range covers the service contracts still open. | US$k/d | PERT | 330 | 360 | 410 |
Trouble time 4 inputs
Frequent, smaller events: lost circulation, tight hole, equipment failure, waiting on weather.
| Assumption | Unit | Value | Uncertainty |
|---|---|---|---|
| Trouble events per 10 days of operationsOffset wells: 61 events in 610 rig days. Multiplied by each phase's trouble factor. | events | 1.00 | Fixed |
| Trouble events per day of operationsThe rate above ÷ 10. A phase expects this × its days × its trouble factor events. | events / day | 0.100 | Calculated |
| Days lost per event, meanOffset wells: average non-productive time per event. | days | 1.20 | Fixed |
| Days lost per event, standard deviationA Lognormal with this mean and spread: many short events, a few long ones. | days | 1.00 | Fixed |
Major risk events 8 inputs
Rare events that add weeks. Each happens at most once, in the section where it can occur.
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| Chance of a sidetrackStuck pipe in the 12¼-in section that cannot be freed: 2 of 18 offset wells. | probability | Fixed | 10% | ||
| Days lost to a sidetrackFishing, plugging back and re-drilling the section. | days | Risk event · PERT | 8.0 | 14.0 | 25.0 |
| Direct cost of a sidetrackEquipment lost in the hole, cement plugs, extra casing; on top of the rig days. | US$m | Fixed | 2.5 | ||
| Phase in which a sidetrack can happenPhase number on the Well plan sheet: 4 = the 12¼-in section. | 1 – 7 | Fixed | 4 | ||
| Chance of a well-control eventInflux in the reservoir section; pressure is better known after the 2024 appraisal well. | probability | Fixed | 3% | ||
| Days lost to a well-control eventShut in, circulate out the influx, raise the mud weight. | days | Risk event · PERT | 5.0 | 10.0 | 20.0 |
| Direct cost of a well-control eventKill mud, specialist services. | US$m | Fixed | 1.5 | ||
| Phase in which a well-control event can happenPhase number on the Well plan sheet: 5 = the 8½-in reservoir section. | 1 – 7 | Fixed | 5 | ||
Deterministic estimate and AFE 2 inputs
The single-number estimate the simulation is compared with, and the AFE's confidence level.
| Assumption | Unit | Value |
|---|---|---|
| Trouble-time allowance in the deterministic estimateAdded to the sum of the most likely phase durations, as many deterministic AFEs do. | of trouble-free days | 10% |
| AFE confidence levelThe AFE is the total cost with this chance of not being exceeded: 80% (P80) is common; some companies use 50% or 90%. | probability | 80% |
Units and conventions
- Money
- US$ million (US$m); the spread rate is in US$ thousand per day (US$k/d).
- Time
- Days of rig time, 24 hours a day.
- P50 / P80 / P90
- Cost-estimating convention: P80 is the value with an 80% chance of not being exceeded.
- Trouble time
- Non-productive time (NPT): rig time lost to unplanned events.
Key assumptions and limitations
- Trouble time
- Events occur at random (Poisson) at a rate proportional to time spent in each phase; event sizes are independent and Lognormal.
- Major events
- Each happens at most once, in one phase: as shipped, a sidetrack in the 12¼-in section and a well-control event in the reservoir section.
- Costs
- Every day costs the spread rate; materials and services are independent of days. No escalation or exchange-rate risk.
- Data
- Phases, durations, costs and rates are invented for this example.
How to use it
- Enter your well's phases, durations and costs on the Well plan sheet, and the spread rate and risk events on the Inputs sheet.
- Calibrate the trouble rate and event size from offset wells (non-productive time per 10 days, days per event).
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set).
- Set the AFE confidence level on the Inputs sheet (80% as shipped), simulate again, and read the AFE and its contingency on the Results sheet.
The tornado chart fills in after a simulation with ModelRisk’s classic engine.
ModelRisk functions used
- VosePERT
- Trouble-free duration and the cost of materials and services of each phase, and the spread rate.
- VosePoisson, VoseAggregateMC, VoseLognormalObject
- Trouble time: a Poisson number of events per phase, each of Lognormal size, summed by VoseAggregateMC.
- VoseRiskEvent, VosePERTObject
- The sidetrack and the well-control event: zero, or a PERT number of days.
- VoseInput, VoseOutput
- Name the uncertain quantities and the outputs for the Results Viewer and the sensitivity analysis.
- VoseSimMean, VoseSimPercentile, VoseSimProbability
- Statistics of the simulation for the tables and charts on the Results sheet.
- VoseSimSensitivityMean
- The tornado chart: the ten VoseInputs that move the mean total cost most across their range, ranked.
Further reading
- How to calculate cost contingency (Vose guide)
- Sensitivity analysis in Excel: a tornado chart step by step (Vose guide)
- Adams, N. J. (1985). Drilling Engineering: A Complete Well Planning Approach. PennWell.
- Vose, D. (2008). Risk Analysis: A Quantitative Guide, 3rd edition. Wiley — chapters on aggregate distributions and project risk.
Download the workbook and run it yourself. It opens in Excel with ModelRisk. The free trial runs every example model.
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An illustrative example: the figures are invented for teaching and do not describe a real company, project or asset. Last updated 9 October 2026.