Wellbore State Estimation Using Particle Filtering in Real Time
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Solution Overview
Problem
Existing Bayesian inference methods face challenges in accurately estimating system states and parameters from uncertain measurements, particularly in nonlinear models and real-time applications, due to computational complexity and the need for numerous forward simulations, which limits their effectiveness in industries like oil and gas for detecting gas kicks and other critical events.
Innovation Solution
A method employing probabilistic Markov sequences, particle filtering, and Single Component Metropolis Hastings sampling, combined with piecewise model approximation, to efficiently estimate system states and parameters by sampling from a reduced posterior distribution and using approximate models for faster computation, enabling real-time monitoring and control of wellbores.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If particle filtering and Bayesian inference are used to estimate system states from uncertain measurements, then measurement precision and reliability are improved, but computational complexity and processing time increase significantly
Solution Approach 1:
The patent segments the complex Bayesian inference problem into discrete time intervals and uses particle filtering to divide the continuous state space into discrete particles. This segmentation allows the system to handle complex nonlinear models by breaking them into manageable computational units that can be processed sequentially, reducing overall computational complexity while maintaining estimation accuracy.
Solution Approach 2:
The patent introduces an intermediary computational framework that bridges the gap between complex Bayesian inference and real-time processing. This framework uses approximate inference methods and efficient particle sampling techniques as intermediaries to translate complex probabilistic models into computationally tractable form, enabling real-time state estimation without sacrificing measurement precision.
2Reliability
If numerous forward simulations are performed for Bayesian inference, then reliability of parameter estimation is improved, but productivity and real-time processing capability deteriorate
Solution Approach 1:
The patent performs preliminary actions by pre-computing certain components of the Bayesian inference framework, such as pre-defining particle distributions and pre-calculating likelihood functions where possible. This preliminary preparation reduces the computational burden during real-time processing, allowing the system to maintain high reliability through thorough simulations while achieving real-time processing speeds.
Solution Approach 2:
The patent applies partial action by performing a sufficient number of forward simulations to achieve the required reliability threshold without performing excessive simulations that would unnecessarily slow down processing. The system dynamically adjusts the number of particles and simulation iterations to achieve just enough accuracy for real-time decision-making, balancing reliability and productivity.
3Measurement precision
If complex nonlinear models are used to represent system behavior, then measurement precision and state estimation accuracy are improved, but computational complexity and processing time increase
Solution Approach 1:
The patent employs dynamic adaptive techniques where the complexity of the nonlinear model is adjusted based on the current processing requirements and available computational resources. The particle filtering framework dynamically adapts the number of particles and model complexity to maintain accurate state estimation while minimizing processing time, allowing the system to handle complex nonlinear models efficiently in real-time applications.
Data Source
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AI summary
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.