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Insights of using Control Theory for minimizing Induced Seismicity in Underground Reservoirs

Diego Gutierrez-Oribio, Ioannis Stefanou

Abstract

Deep Geothermal Energy, Carbon Capture, and Storage and Hydrogen Storage have significant potential to meet the large-scale needs of the energy sector and reduce the CO$_2$ emissions. However, the injection of fluids into the earth's crust, upon which these activities rely, can lead to the formation of new seismogenic faults or the reactivation of existing ones, thereby causing earthquakes. In this study, we propose a novel approach based on control theory to address this issue. First, we obtain a simplified model of induced seismicity due to fluid injections in an underground reservoir using a diffusion equation in three dimensions. Then, we design a robust tracking control approach to force the seismicity rate to follow desired references. In this way, the induced seismicity is minimized while ensuring fluid circulation for the needs of renewable energy production and storage. The designed control guarantees the achievement of the control objectives even in the presence of system uncertainties and unknown dynamics. Finally, we present simulations of a simplified geothermal reservoir under different scenarios of energy demand to show the reliability and performance of the control approach, opening new perspectives for field experiments based on real-time regulators.

Insights of using Control Theory for minimizing Induced Seismicity in Underground Reservoirs

Abstract

Deep Geothermal Energy, Carbon Capture, and Storage and Hydrogen Storage have significant potential to meet the large-scale needs of the energy sector and reduce the CO emissions. However, the injection of fluids into the earth's crust, upon which these activities rely, can lead to the formation of new seismogenic faults or the reactivation of existing ones, thereby causing earthquakes. In this study, we propose a novel approach based on control theory to address this issue. First, we obtain a simplified model of induced seismicity due to fluid injections in an underground reservoir using a diffusion equation in three dimensions. Then, we design a robust tracking control approach to force the seismicity rate to follow desired references. In this way, the induced seismicity is minimized while ensuring fluid circulation for the needs of renewable energy production and storage. The designed control guarantees the achievement of the control objectives even in the presence of system uncertainties and unknown dynamics. Finally, we present simulations of a simplified geothermal reservoir under different scenarios of energy demand to show the reliability and performance of the control approach, opening new perspectives for field experiments based on real-time regulators.
Paper Structure (16 sections, 2 theorems, 41 equations, 20 figures, 1 table)

This paper contains 16 sections, 2 theorems, 41 equations, 20 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. EXAMPLE OF INDUCED SEISMICITY IN A RESERVOIR DUE TO FLUID INJECTIONS
  3. PROBLEM STATEMENT AND CONTROL DESIGN
  4. Energy demand and production constraints
  5. SIMULATIONS
  6. Scenario 1: SR tracking without demand
  7. Scenario 2: SR tracking with constant demand
  8. Scenario 3: SR tracking with intermittent demand
  9. Scenario 4: SR tracking with heterogeneities
  10. CONCLUSIONS AND LIMITATIONS
  11. Notation
  12. Weak solution of the 3D diffusion equation
  13. Depth average of the 3D diffusion equation
  14. Spectral Decomposition of the 2D diffusion equation
  15. Output Feedback Tracking Control Design
  16. ...and 1 more sections

Key Result

Lemma 1

The term $\Psi(t)$ in system eq:errordyn2,eq:BPsi2 fulfils the condition eq:bounds if Assumption A1 is fulfilled.

Figures (20)

  • Figure 1: Underground reservoir diagram.
  • Figure 2: Regions $V_1$ and $V_2$ and location of the injection well with flux $Q_{s_1}$ inside of region $V_2$.
  • Figure 3: Seismicity rate in both regions, $V_1,V_2$ with constant injection rate, $Q_{s_1}$. $7975$ more earthquakes of a given magnitude in a given time window are expected over the outer region of the reservoir due to the constant fluid injection.
  • Figure 4: Solution, $u(x,t)$, of the pressure's reservoir at different times, with constant injection rate, $Q_{s_1}$. The solution presents high pressure profiles in wide areas next to the point of injection.
  • Figure 5: Regions $V_1$ and $V_2$ and location of the injection wells in the cases without demand (top) and with demand (bottom).
  • ...and 15 more figures

Theorems & Definitions (3)

  • Definition 1
  • Lemma 1
  • Theorem 1