Abstract: A method of determining a parameter and state of a system from a time series of a system measurement, comprising using a processor to: a) build an approximate model of the system; b) sample a plurality of approximate system parameters for a current time interval from a posterior probability distribution; c) determine an estimate of the system parameter at the current time interval from the distribution of the plurality of approximate system parameters; d) determine an estimate of the system state at the current time interval given the estimate of the system parameter; e) repeat b) to d) for the next time interval. An apparatus for performing the method is disclosed, and application of the method to drilling and wellbores is discussed.

Abstract: A method is provided for controlling a managed pressure drilling system. The method comprises providing a fast system interpretation model for the operation of the managed pressure drilling system, obtaining real-time measurements from one or more sensors regarding the operation of the managed pressure drilling system, using the measurements to calibrate the fast system interpretation model for the managed pressure drilling system in real-time and using a predictive controller to run the calibrated fast system interpretation model to a time horizon in the future.

Abstract: A method of determining a parameter and state of a system from a time series of a system measurement, comprising using a processor to: a) build an approximate model of the system; b) sample a plurality of approximate system parameters for a current time interval from a posterior probability distribution; c) determine an estimate of the system parameter at the current time interval from the distribution of the plurality of approximate system parameters; d) determine an estimate of the system state at the current time interval given the estimate of the system parameter; e) repeat b) to d) for the next time interval. An apparatus for performing the method is disclosed, and application of the method to drilling and wellbores is discussed.

Abstract: A method is provided for controlling a managed pressure drilling system. The method comprises providing a fast system interpretation model for the operation of the managed pressure drilling system, obtaining real-time measurements from one or more sensors regarding the operation of the managed pressure drilling system, using the measurements to calibrate the fast system interpretation model for the managed pressure drilling system in real-time and using a predictive controller to run the calibrated fast system interpretation model to a time horizon in the future.

Abstract: In monitoring/control of drilling operation a dimensionality of a full-scale model (e.g., characterizing variables related to cuttings transport, gas migration and/or the like) is reduced and data from a plurality of geographically distributed (e.g., depth varying) sensors is received, and a surrogate model is used to estimate variables in real-time. Use of the surrogate model may enable, e.g., particle-filtering processes to be employed during the estimation while still allowing for real-time estimations, avoiding excessive use of reasonable computational resources (e.g., memory and processing speeds) and/or the like. Operating controls or the like may then be set based on the estimated variables. For example, drilling control parameters may be adjusted based on estimated variables to avoid lost circulation, kicks, stuck pipe, and catastrophic events, optimize drilling parameters such as rate of penetration, improve drilling success probabilities and efficiency and/or the like.