Monte Carlo Simulation Overview
Introduction
Monte Carlo simulation quantifies uncertainty by running thousands of calculations with randomly sampled input parameters. Instead of a single deterministic answer, Monte Carlo produces a probability distribution of outcomes.
In petroleum engineering, Monte Carlo is used for:
- Probabilistic reserves — P10/P50/P90 estimates of OOIP, OGIP, EUR
- Economic risk analysis — NPV distributions, probability of economic success
- Decision analysis — comparing development alternatives under uncertainty
- Sensitivity studies — identifying which parameters most affect outcomes
- Well planning — uncertainty in drilling targets and well placement
Why Monte Carlo?
The Problem with Deterministic Analysis
Key Advantages
| Advantage | Description |
|---|---|
| Handles non-linearity | Complex formulas with interacting variables |
| Multiple uncertainties | Combine all uncertain parameters simultaneously |
| Correlation support | Model dependencies between variables |
| Risk quantification | Probability of exceeding thresholds |
| Decision support | Compare alternatives on a risk-adjusted basis |
Methodology
Basic Steps
Sampling Methods
| Method | Description | Advantage |
|---|---|---|
| Random (Monte Carlo) | Pure random sampling | Simple, unbiased |
| Latin Hypercube | Stratified sampling | Better coverage with fewer iterations |
Latin Hypercube sampling divides each distribution into equal-probability intervals and ensures exactly one sample from each interval. This provides better coverage of the input space and faster convergence.
Probability Distributions
Common Distribution Types
| Distribution | Shape | Best For |
|---|---|---|
| Normal | Symmetric bell curve | Well-measured properties with symmetric uncertainty |
| Lognormal | Right-skewed | Permeability, reserves, costs (always positive) |
| Triangular | Three-point estimate | Expert judgment (min, most likely, max) |
| Uniform | Flat | Equal probability across a range |
| PERT | Modified triangular | Expert judgment with less weight on extremes |
| Truncated Normal | Bell curve with bounds | Properties with physical limits |
📖 Full Documentation: Distributions
Selecting Distributions
| Parameter | Typical Distribution | Rationale |
|---|---|---|
| Porosity | Normal or Triangular | Well-constrained from logs/core |
| Permeability | Lognormal | Known to be log-distributed |
| Net pay | Triangular or Uniform | Limited data, wide uncertainty |
| Oil price | Lognormal or Triangular | Market uncertainty, always positive |
| Recovery factor | Triangular | Bounded (0-1), expert estimate |
Output Analysis
Percentile Reporting
| Percentile | Meaning | SPE/PRMS Term |
|---|---|---|
| P90 | 90% probability of exceeding | Proved (1P) |
| P50 | 50% probability of exceeding | Proved + Probable (2P) |
| P10 | 10% probability of exceeding | Proved + Probable + Possible (3P) |
| Mean | Expected value | Used for economic analysis |
Convention: In petroleum reserves, P90 is the low estimate (conservative) and P10 is the high estimate (optimistic). This follows the "probability of exceeding" convention.
Sensitivity Analysis
Tornado charts rank input parameters by their impact on the output:
- Run the model with each parameter at its P10 and P90 values while holding others at P50
- Plot the resulting output range for each parameter
- Parameters with the widest bars have the most influence
Correlation Handling
Why Correlations Matter
Some input parameters are physically related:
- Porosity and permeability — higher porosity often means higher permeability
- Net pay and gross thickness — net-to-gross constrains both
- Oil price and gas price — commodity prices are correlated
Ignoring correlations can produce physically impossible combinations (e.g., high porosity with zero permeability).
Correlation Methods
| Method | Description |
|---|---|
| Rank correlation | Spearman correlation between sampled values |
| Gaussian copula | Preserves marginal distributions while imposing correlation structure |
Convergence
How Many Iterations?
| Application | Minimum Iterations | Notes |
|---|---|---|
| Screening | 1,000 | Quick estimates |
| Standard analysis | 5,000-10,000 | Most applications |
| High-precision | 50,000-100,000 | When tail probabilities matter |
Convergence Check
Monitor P10, P50, P90 as iterations increase. When these percentiles stabilize (change < 1-2%), the simulation has converged.
Related Documentation
MC Details
- Distributions — Distribution types and parameter estimation
Supporting Topics
- DCA Overview — Decline parameters as Monte Carlo inputs
- MBE Overview — Reserves estimation to be probabilistically analyzed
References
Rose, P.R. (2001). Risk Analysis and Management of Petroleum Exploration Ventures. AAPG Methods in Exploration No. 12.
Murtha, J.A. (1997). "Monte Carlo Simulation: Its Status and Future." Journal of Petroleum Technology, 49(4), 361-373. SPE-37932-JPT.
Metropolis, N. and Ulam, S. (1949). "The Monte Carlo Method." Journal of the American Statistical Association, 44(247), 335-341.
McKay, M.D., Beckman, R.J., and Conover, W.J. (1979). "A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code." Technometrics, 21(2), 239-245.
SPE/WPC/AAPG/SPEE/SEG (2018). Petroleum Resources Management System (PRMS).