Modelling Uncertainty in Pore Pressure Using Dynamic Bayesian Networks

Pore pressure prediction is vital when drilling a well, as unexpected overpressure can cause drilling challenges and uncontrolled hydrocarbon leakage. Predictions often use porosity-based techniques, relying on an idealised compaction trend and using a single wireline log as a proxy for porosity, ignoring the many sources of uncertainty and the system’s multivariate nature. 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 etc.), capturing their joint behaviour using conditional probability distributions. A compaction model is central to the SDBN, relating porosity to vertical effective stress with uncertainty, so that the logic resembles that of the equivalent depth method. Given data, the probability distribution for each quantity is updated, so that instead of a single-valued prediction for pore pressure, the SDBN gives a full specification of uncertainty that takes into account the whole system, knowledge and data. We can use this to analyse the model’s sensitivity to its parameters, through sensitivity analysis. The vertical correlation in the SDBN makes it suitable for real-time analysis of logging while drilling data. We show examples using real well data.