Mathematical Modelling in Petroleum Exploration and Prospect Generation: An Integrated Review of Quantitative and Computational Methods
Keywords:
Petroleum exploration, Prospect generation, Petroleum systems modelling, Geostatistics, GIS prospectivity, Machine learning, Exploration risk assessment.Abstract
Petroleum exploration is becoming more difficult and more capital-intensive as conventional basins mature and the remaining targets grow structurally and stratigraphically subtler. Persistently low exploration success rates have made formal quantitative methods central to reducing pre-drill uncertainty. This paper reviews the principal mathematical and computational modelling approaches applied across the exploration and prospect generation workflow. Although individual techniques are well documented in the literature, they have rarely been assessed together as a coherent, integrated framework spanning the full workflow, and this review addresses that gap. The methods are organized around the petroleum systems concept and grouped into three areas. The first covers mathematical and statistical modelling, including basin modelling and thermal maturity assessment through kinetic models such as EASY%Ro, probabilistic volumetric estimation based on Monte Carlo simulation, and Bayesian risk analysis, together with geostatistical techniques spanning variogram analysis, kriging, and sequential Gaussian simulation. The second examines GIS-based prospectivity mapping through play fairway analysis (PFA) and common risk segment (CRS) methods, alongside the expanding role of machine learning (ML) and deep learning in seismic interpretation, facies classification, and spatial risk prediction. The third evaluates the limitations shared across these methods, including data sparsity, model non-uniqueness, validation constraints, and the limited transferability of data-driven models between geological settings. The review finds that the integration of physics-based process modelling with data-driven analytics, increasingly enabled by digital twin and hybrid modelling concepts, offers the most defensible path toward more reliable and auditable exploration decisions.
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Copyright (c) 2026 Farrukh Inayat, Mohamed Dafalla, Faisal Mehmood Shah
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