Control of Human-Induced Seismicity in Underground Reservoirs Governed by a Nonlinear 3D PDE-ODE System

TL;DR

This paper develops a nonlinear, robust control method for mitigating human-induced seismicity in underground reservoirs, ensuring safety and operational goals despite uncertainties and heterogeneity.

Contribution

It introduces a novel output-feedback controller based on a nonlinear MIMO Super-Twisting design for coupled 3D PDE-ODE reservoir models, with proven finite-time convergence.

Findings

Effective seismicity and pressure regulation in simulations

Robust performance under parameter uncertainties

Applicable to real-world gas and CO2 injection scenarios

Abstract

Induced seismicity caused by fluid extraction or injection in underground reservoirs is a major challenge for safe energy production and storage. This paper presents a robust output-feedback controller for induced seismicity mitigation in geological reservoirs described by a coupled 3D PDE-ODE model. The controller is nonlinear and robust (MIMO Super-Twisting design), producing a continuous control signal and requiring minimal model information, while accommodating parameter uncertainties and spatial heterogeneity. Two operational outputs are regulated simultaneously: regional pressures and seismicity rates computed over reservoir sub-regions. Closed-loop properties are established via explicit bounds on the solution and its time derivative for both the infinite-dimensional dynamics and the nonlinear ODE system, yielding finite-time or exponential convergence of the tracking errors. The method is evaluated on the Groningen gas-field case study in two scenarios: gas production while not exceeding the intrinsic seismicity of the region, and combined production with CO$_2$ injection toward net-zero carbon operation. Simulations demonstrate accurate tracking of pressure and seismicity targets across regions under significant parameter uncertainty, supporting safer reservoir operation while preserving production objectives.