Steerable Drill String Control with Stochastic Path Prediction
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Solution Overview
Problem
Steerable drill strings face uncertainties in controlling the drill bit path due to unmeasurable directional parameters, leading to deviations from the desired wellbore path as the drill advances through varying substrates, which existing deterministic models fail to account for effectively.
Innovation Solution
A stochastic model predictive controller (SMPC) is developed using generalized polynomial chaos theory to convert a continuous stochastic differential equation into a discrete problem, allowing real-time prediction of mean and variance of drill bit behavior, incorporating feedback and constraints to optimize control inputs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If deterministic models are used to control steerable drill strings, then the control system is simple and easy to implement, but the accuracy of drill bit path control deteriorates due to unmeasurable directional parameters and parameter variations
Solution Approach 1:
The patent transforms fixed deterministic parameters into stochastic parameters with probability distributions. The directional parameters (e.g., drill string inclination, azimuth) are modeled as random variables with mean values and variances that evolve as the drill advances through different substrate types. This allows the control system to account for parameter uncertainties and variations without requiring direct measurement of each parameter.
Solution Approach 2:
The patent implements a feedback mechanism where the stochastic model is continuously updated based on actual drilling data. The measured drill bit position and orientation are compared with predicted positions from the stochastic model, and the parameter distributions are adjusted accordingly. This closed-loop feedback reduces the uncertainty in parameter estimates and improves path control accuracy over time.
2Productivity
If fixed parameter estimates are used in deterministic models, then the control computation is fast and efficient, but the reliability of path control deteriorates as wellbore depth increases and substrate types vary
Solution Approach 1:
The patent makes the control model dynamic by allowing parameters to change as functions of depth and substrate type. Instead of using fixed parameter values, the stochastic parameters are updated at each depth interval based on the substrate characteristics encountered. This dynamic adaptation maintains reliability as the drill progresses through varying geological formations while keeping computation efficient through pre-characterized substrate models.
Solution Approach 2:
The patent performs preliminary characterization of substrate types and their associated parameter distributions before drilling begins. Geological data and historical drilling information are used to pre-establish probability distributions for directional parameters in different substrate zones. This preliminary action allows the control system to quickly select appropriate parameter models during drilling without real-time complex computations, maintaining both speed and reliability.
3Manufacturing precision
If stochastic models with probability distributions are used, then the accuracy of drill bit path prediction improves by accounting for parameter uncertainties, but the device complexity and computational requirements increase
Solution Approach 1:
The patent segments the wellbore into discrete depth intervals or zones based on substrate type transitions. Within each segment, the stochastic parameters are assumed to have relatively stable distributions. This segmentation reduces the overall computational complexity by breaking down the continuous stochastic model into manageable discrete segments, while still capturing the essential uncertainties and variations in drill bit path prediction.
Data Source
AI summary
Aspects of the subject technology relate to systems and methods of controlling a drill string having a steerable bit when drilling a wellbore through a substrate. A deterministic model of a directional behavior of the drill string is developed that includes a drill string state, one or more drill parameters associated with the drill string, and one or more substrate parameters associated with the substrate. A stochastic differential model of the directional behavior of the drill string is then developed by replacing the state and each of the parameters of the deterministic model with respective probability distributions and adding feedback. The stochastic differential model is reduced to a truncated stochastic model by substituting a predetermined number of terms of a generalized polynomial chaos expansion for each probability distribution and then evaluating the expectations.