Graph-based determination of structural controllability and observability for pressure and temperature dynamics during steam-assisted gravity drainage operation

Abstract

Steam assisted gravity drainage (SAGD), which is used for the in-situ extraction and recovery of oil sands bitumen, is represented by a distributed parameter system (DPS). The problem of sensor placement and the control of steam chamber growth and oil production, respectively, require analysis of the observability and controllability of the system. In this type of system, parametric sensitivity is traditionally used in lieu of observability, and controllability has not been explored rigorously. In this work, we analyze the pressure and temperature fields of a SAGD model based on detailed reservoir simulations and present a data-driven technique to assess the structural controllability and observability of the system, with a view to determine optimal locations of actuators and sensors. An agglomerative hierarchical clustering technique is used to obtain a spanning tree of the clusters which is partitioned based on an objective function to arrive at a set of spatially contiguous clusters that display similar pressure/temperature dynamics. A Granger causality measure is used to create the linkage amongst the clusters to build a digraph model of the data. The driver nodes of the graph identify locations for actuation which provide full control over the graph, and the root strongly connected components indicate sensor locations which ensure structural observability over the entire graph. We demonstrate the method using data generated from SAGD simulations using the CMG-STARS simulator, identify the sensor and actuator locations required for complete structural observability and controllability of the system, and also provide a method of assessment of partial actuation and in-sensor ranges.