# Can Agents Model Hydrocarbon Migration for Petroleum System Analysis? A Fast Screening Tool to De-Risk Hydrocarbon Prospects

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Methods and Materials

#### 2.1. Go with the Flow—An Agent-Based Library for Modelling Secondary Hydrocarbon Migration

#### 2.2. Integration of Go with the Flow for Uncertainty Quantification

#### 2.2.1. Monte Carlo Simulation for Modelling Secondary Hydrocarbon Migration

#### 2.2.2. Implementation of Geomodel Designer and Hydrocarbon Migration Simulator within Python

#### 2.2.3. Postprocessing and Evaluation Methods

- (1)
- Detection of the accumulations

- (2)
- Metrics and methods of evaluation

- (3)
- Spatial visualisation of 3D simulation results

_{i}is the probability of an event to occur. It allows quantifying the level of surprise by the occurrence of an event (i.e., the probability of an event). Events that rarely occur carry a high load of information and events that occur more often carry a low information content. In the context of this work, entropy is treated as a measure for the uncertainty that exists around the discrete property value of each cell in the model [70]. To identify locations of highest uncertainty across all Monte Carlo realisations, the entropy for each cell across all model realisations is calculated and visualised.

## 3. Results

#### 3.1. Validation of Go with the Flow on Simple Geological Scenarios

#### 3.2. Uncertainty Quantification of a Synthetic Case Study

#### 3.2.1. Modelling Objective and Case Study Description

#### 3.2.2. Sensitivity Analyses—Identification of Main Migration Drivers and Geological Uncertainties; Evaluation of the Monte Carlo Simulations

- (1)
- Accumulation size

^{3}, a porosity of 15%, a residual water saturation of 20%, and an oil formation volume factor Bo of 1.3. The probability of discovering a fault block accumulation greater than or equal to the economic threshold is 28.0% (red line). The probability of finding an accumulation greater than 1000 mmbbl is 4.2% (green line). The probability of discovering anticline accumulation greater than or equal to the economic threshold is 26.8%. The probability of finding an accumulation greater than 1000 mmbbl is 1.6%.

- (2)
- Spearman correlation matrix

- (3)
- t-SNE visualisation

- (4)
- Entropy visualisation

- (5)
- Case study evaluation

## 4. Discussion and Future Perspectives

_{2}in the subsurface.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Flow chart showcasing the workings of the Go with the Flow algorithm. The iterators i, j, k are responsible for the generation of new agents, the movement of active agents and the number of iterations to run, respectively.

## Appendix B

**Figure A2.**(

**a**) t-SNE analysis of kitchen scenario 1 showing the most impactful geological uncertainties and their correlation with simulation evaluation metrics. Each point represents an individual model from the Monte Carlo simulation. The points are colour coded with the evaluation metric ratio of trapped agents and sized by the size of the most significant accumulation. One observation is that all the accumulations remain in the fault block area. Exemplary 2D slices of the environment and 3D plots showing the accumulation positions at the end of the simulation (red) and the barriers (purple) are also shown (

**b**) Display of the trends of the original geological parameters with colour coded arrows.

**Figure A3.**(

**a**) t-SNE analysis of kitchen scenario 2 showing the most impactful geological uncertainties and their correlation with simulation evaluation metrics. Each point represents an individual model from the Monte Carlo simulation. The points are colour coded with the evaluation metric ratio of trapped agents and sized by the size of the most significant accumulation. One observation is that accumulations are mainly located in the anticline but a significant part (~25%) is also located in the fault block. Exemplary 2D slices of the environment and 3D plots showing the accumulation positions at the end of the simulation (red) and the barriers (purple) are also shown (

**b**) Display of the trends of the original geological parameters with colour coded arrows.

**Figure A4.**(

**a**) t-SNE analysis of kitchen scenario 3 showing the most impactful geological uncertainties and their correlation with simulation evaluation metrics. Each point represents an individual model from the Monte Carlo simulation. The points are colour coded with the evaluation metric ratio of trapped agents and sized by the size of the most significant accumulation. One observation is that accumulations are located in the fault block and the anticline. Exemplary 2D slices of the environment and 3D plots showing the accumulation positions at the end of the simulation (red) and the barriers (purple) are also shown (

**b**) Display of the trends of the original geological parameters with colour coded arrows.

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**Figure 1.**(

**a**) Migration of two agents moving in a 2D environment; (

**b**) decision-making process for selecting the next move of agent A.

**Figure 3.**(

**a**) Final unprocessed agent position (red) after simulation. Significant accumulations as well as minor accumulations are present. (

**b**) Final post-processed agent position after simulation. HDBSCAN detected significant accumulations and discarded minor accumulations and dispersed agents.

**Figure 4.**Spatial visualisation of exemplary 3D simulation results. (

**a**) Agents’ final positions and flow barriers; (

**b**) pathways (scaled between 0 and 1) of the agents where high values are associated with more agents passing in the cell and vice versa. Accumulations are highlighted in red.

**Figure 5.**(

**a**) Anticline scenario with barrier layer completely sealing the structure; (

**b**) anticline scenario leaking on the right side of the structure; (

**c**) fault block scenario with an impermeable fault on the top left side of the environment. For each scenario, the agents are initialised from the bottom layer of the environment.

**Figure 7.**Accumulation size distribution of the most significant accumulation in the fault block trap (

**a**) and anticlinal trapping structure (

**b**). The red vertical line shows the limit for accumulations of economic value (300 mmbbl); the green line shows the limit for accumulation greater than 1000 mmbbl.

**Figure 8.**Spearman correlation matrix showing the correlation of the geological uncertainties with the evaluation metrics.

**Figure 9.**t-SNE visualisation showing the most impactful geological uncertainties and their correlation with simulation evaluation metrics. Each point represents an individual model from the Monte Carlo simulation. (

**a**) The points are colour coded with the evaluation metric ratio of trapped agents and sized by the size of the most significant accumulation. (

**b**) Display of the trends of the original geological parameters with colour coded arrows.

**Figure 10.**t-SNE visualisation showing the most impactful geological uncertainties and their correlation with simulation evaluation metrics, colour coded by ratio of agents in anticlinal accumulations (

**a**) and fault block accumulations (

**b**) and sized by the size of the largest accumulation.

**Figure 11.**Two-dimensional slices through the model of the entropy distribution of all simulation runs for facies (

**a**), accumulation location (

**b**), and migration pathways (

**c**).

**Table 1.**Uncertain parameters related to either the structural modelling, the property modelling, or the initiation of an agent (related to the source rock), as seen in Figure 6. To each uncertain parameter, a range of uncertainty is associated (+/− 2σ, if applicable).

Type of Uncertainty | Location | Parameter | Range of Uncertainty |
---|---|---|---|

Structural | A | Fault dip | Normal distribution 45–55° |

A | Fault offset | Normal distribution 0–200 m | |

B | Fault block tilt | Normal distribution 0–40° | |

Property modelling | A | Fault critically stressed | True (50%) or False (50%) |

C | Shale facies proportion—proportion of barriers | Normal distribution 50–90% | |

C | Shale anisotropy direction (y/x anisotropy) | Normal distribution 0.5–2 | |

D | Silt facies proportion—proportion of pathways | Normal distribution 50–80% | |

D | Silt anisotropy direction (y/x anisotropy) | Normal distribution 0.5–2 | |

Source rock | E | Kitchen location | Right side of the fault (1/3), left side (1/3) or all bottom layer (1/3) |

E | New agents per turns | Normal distribution 10–100 agents | |

E | Number of turns | Normal distribution 200–2000 turns |

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## Share and Cite

**MDPI and ACS Style**

Steffens, B.; Corlay, Q.; Suurmeyer, N.; Noglows, J.; Arnold, D.; Demyanov, V.
Can Agents Model Hydrocarbon Migration for Petroleum System Analysis? A Fast Screening Tool to De-Risk Hydrocarbon Prospects. *Energies* **2022**, *15*, 902.
https://doi.org/10.3390/en15030902

**AMA Style**

Steffens B, Corlay Q, Suurmeyer N, Noglows J, Arnold D, Demyanov V.
Can Agents Model Hydrocarbon Migration for Petroleum System Analysis? A Fast Screening Tool to De-Risk Hydrocarbon Prospects. *Energies*. 2022; 15(3):902.
https://doi.org/10.3390/en15030902

**Chicago/Turabian Style**

Steffens, Bastian, Quentin Corlay, Nathan Suurmeyer, Jessica Noglows, Dan Arnold, and Vasily Demyanov.
2022. "Can Agents Model Hydrocarbon Migration for Petroleum System Analysis? A Fast Screening Tool to De-Risk Hydrocarbon Prospects" *Energies* 15, no. 3: 902.
https://doi.org/10.3390/en15030902