A Sequential Dynamic Bayesian Network for Pore Pressure Prediction and Quantification of Uncertainty.

Abstract:

Pore pressure prediction is vital when drilling a well, as unexpected overpressure can cause drilling challenges and uncontrolled hydrocarbon leakage. One cause of overpressure is when pore fluid is trapped during burial and takes on part of the lithostatic load. Predictions often use porosity-based techniques, such as the Eaton Ratio method and equivalent depth method. These rely on an idealised compaction trend and use a single wireline log as a proxy for porosity. Such methods do not account for the many sources of uncertainty, or for the multivariate nature of the system. We propose a sequential dynamic Bayesian network (SDBN) as a solution to these issues.

The SDBN models the quantities in the system (such as pressures, porosity, lithology, wireline logs, fluid properties and so on) using conditional probability distributions to capture their joint behaviour. A compaction model is central to the SDBN, relating porosity to vertical effective stress, with uncertainty in the relationship, so that the logic is similar to that of the equivalent depth method. The probability distribution for porosity depends on VES and lithology, with much more uncertainty in sandstone-like rocks than in shales to reflect a general lack of understanding of sandstone compaction. The distributions of the wireline logs depend on porosity and lithology, along with other quantities, and so when they are observed the SDBN learns about porosity and lithology and in turn VES and pore pressure, using Bayes theorem. The probability distribution for each quantity in the SDBN is updated in light of any data, so that rather than giving a single-valued prediction for pore pressure, the SDBN gives a prediction with uncertainty that takes into account the whole system, knowledge and data. The dynamic nature of the SDBN enables it to use the bulk density to calculate total vertical stress, and to account for the dissipation of pore pressure. The vertical correlation in the SDBN means it is suited to the real-time analysis of logging while drilling data.

We show examples using wells from the Gulf of Mexico and West Africa. The SDBN's shale pore pressure predictions are aligned with independent direct measurements on pore pressure in thin sandstone beds encountered during drilling, and the estimated lithology from the SDBN is in agreement with experts' analyses.