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arxiv: 2604.26802 · v1 · submitted 2026-04-29 · 📡 eess.SY · cs.SY

A Control Framework for Induced Seismicity Mitigation in Groningen Gas Reservoir

Diego Guti\'errez-Oribio , Ioannis Stefanou This is my paper

Pith reviewed 2026-05-07 11:30 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords induced seismicityGroningen gas fieldfeedback controlpore-pressure diffusionseismicity rateactuator saturationrobust controllergas production
0
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The pith

A feedback controller regulates induced seismicity rates in the Groningen gas reservoir by commanding well rates under production and saturation limits.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a control framework that treats seismicity mitigation as an active regulation problem rather than a forecasting exercise. It links a model of pressure diffusion through the rock to the rate at which earthquakes occur, then converts the continuous rate field into a catalog of synthetic events so that regional seismicity measurements can be fed back to a controller. The controller issues rate commands to wells that drive the measured seismicity toward a chosen target while obeying limits on how much gas can be produced and how quickly the wells can change their flow. Numerical tests show the architecture works across different update intervals and gain choices, including cases that combine extraction with nitrogen reinjection. If the approach holds in the field, operators gain a practical tool to keep earthquake activity within acceptable bounds without halting production.

Core claim

We employ a cascade model coupling pore-pressure diffusion with seismicity rate dynamics and complement it with a stochastic event-generation procedure to convert the continuous SR field into a synthetic earthquake catalog. From this catalog we estimate regional SR measurements and design a robust feedback controller that computes well-rate commands to regulate the SR toward a desired reference while satisfying operational requirements, including prescribed production constraints and actuator saturation. The well fluxes are updated at discrete-time intervals and the framework is validated against Groningen data through numerical experiments under various scenarios.

What carries the argument

Cascade model of pore-pressure diffusion coupled to seismicity rate dynamics, paired with a robust feedback controller that handles flux limits and discrete updates.

Load-bearing premise

The cascade model together with the stochastic event procedure produces seismicity rate measurements that are accurate and timely enough for the feedback controller to work reliably on the actual reservoir.

What would settle it

Applying the controller's rate commands in the real Groningen field and checking whether the observed seismicity rates track the commanded target without large unpredicted events or major production shortfalls.

Figures

Figures reproduced from arXiv: 2604.26802 by Diego Guti\'errez-Oribio, Ioannis Stefanou.

Figure 1
Figure 1. Figure 1: Groningen gas reservoir with wells location. Back￾ground image obtained https://zoek.officielebekendmakingen. nl/stcrt-2017-28922.html. : Preprint submitted to Elsevier Page 1 of 13 view at source ↗
Figure 2
Figure 2. Figure 2: Block diagram (closed control loop) of the methodology proposed of this work. The loop is executed in discrete-time intervals during which the well fluxes remain constant. 𝑢𝑡 = − 1 𝛽 ∇⋅ 𝑞 + 𝑠, (1) where 𝑢 = 𝑢(𝑥, 𝑡) is the change in pore fluid pressure induced by the injection/extraction of fluid 𝑠. 𝑥 ∈ 𝑉 denotes space, 𝑡 ≥ 0 is time, and 𝑢𝑡 is the partial derivative of 𝑢 with respect to time. The flux vari… view at source ↗
Figure 3
Figure 3. Figure 3: shows the total gas extraction history, 𝑓(𝑡) = − ∑29 𝑖=1 𝑄𝑖 (𝑡), over the full reservoir. The spatial distribution of all recorded events over this period is shown on the left of view at source ↗
Figure 4
Figure 4. Figure 4: Spatial density maps of the seismicity density in the reservoir representing the 790 events that occurred between 12-1991 and 01-2023. Synthetic density correspond to Realization 1 in view at source ↗
Figure 5
Figure 5. Figure 5: Spatial average SR over the reservoir and cumulative number of seismic events. Real data (blue line) and simulated data (orange line). values Λ(𝑡1 ) and Λ(𝑡2 ). This is a reasonable approximation for sufficiently small time intervals and allows us to draw 𝑁 events at time instances 𝑠𝑖 , 𝑖 = 1, 2, ..., 𝑁 in the interval [𝑡1 , 𝑡2 ] by inversion of the cumulative intensity (9). The drawn events are then sorte… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison between the real and two different stochastic catalogs (realizations) of Groningen simulated according to the system (1)–(7) and interpreted as a non-homogeneous Poisson process (8)–(11). preserves both the time-varying domain-wide activity level through Λ(𝑡) and the instantaneous spatial distribution en￾coded by 𝑅(⋅, 𝑡), while naturally incorporating the intrinsic randomness of non-homogeneous … view at source ↗
Figure 7
Figure 7. Figure 7: Multiple runs of the stochastic process showing convergence around the mean. 𝑄𝑖 (𝑡) < 𝑄𝑀𝑖 , i.e., 𝑄𝑖 (𝑡) is “clamped" (saturated) for all 𝑡 ≥ 0 as sat(𝑄𝑖 ) = ⎧ ⎪ ⎨ ⎪ ⎩ 𝑄𝑖 for 𝑄𝑚𝑖 < 𝑄𝑖 < 𝑄𝑀𝑖 , 𝑄𝑀𝑖 for 𝑄𝑖 ≥ 𝑄𝑀𝑖 , 𝑄𝑚𝑖 for 𝑄𝑖 ≤ 𝑄𝑚𝑖 , . (13) The objective is to design the well-rate control input 𝑄𝑐 (𝑡)so that the average SR over the whole reservoir follows a prescribed target profile. This will be performed sin… view at source ↗
Figure 8
Figure 8. Figure 8: Synthetic Groningen seismic catalogs at the end of the simulation for the considered control scenarios. a) Production-only control: all wells constrained to extraction. b) Production with compensating injection: a subset of wells allowed to inject while the remaining wells follow the reference extraction profile. See view at source ↗
Figure 9
Figure 9. Figure 9: Fluxes of the wells in the extraction-only scenario. The effect of the ZOH is visble in the inset image. 0 5 10 15 20 25 30 t [years] 14 12 10 8 6 4 2 0 P r o du c tio n [1 0 6 m 3 / m o n t h] XQ(t) f(t) view at source ↗
Figure 10
Figure 10. Figure 10: Total reservoir flux ∑ 𝑄(𝑡) compared with the reference extraction profile in the extraction-only scenario (𝑘3 = 36.05, Δ𝑡 𝑐 = 1 month). The controller reduces induced seismicity by redistributing and limiting extraction, which leads to deviations from the reference demand. Another important parameter is the control update period Δ𝑡 𝑐 (ZOH sampling time interval) view at source ↗
Figure 12
Figure 12. Figure 12: Effect of the sampling interval Δ𝑡 𝑐 at the end of the simulation. 3.2. Scenario 2: Combined production and injection In this scenario, half of the total wells is assigned to injection only and the remaining wells to extraction only (see view at source ↗
Figure 13
Figure 13. Figure 13: Fluxes of the wells in Scenario 2. Half of the wells can only extract to satisfy the gas production demand, while the others are only injecting. The effect of the ZOH is also visible in the inset images. See view at source ↗
Figure 14
Figure 14. Figure 14: Scenario 2 (combined production and injection): total extraction from production wells, total injection from injection wells, and reference production target 𝑓(𝑡). The pro￾duction constraint (20) enforces exact tracking of the historical gas-production profile using the production-well subset, while the injection wells provide the degrees of freedom needed for seismicity mitigation. among wells and by tem… view at source ↗
read the original abstract

Induced seismicity associated with gas production poses major operational and societal challenges, as illustrated by the Groningen field in the Netherlands. While many studies have focused on forecasting seismicity under prescribed production scenarios, fewer works address the inverse problem: designing operational strategies that minimize seismicity while maintaining production objectives. In this paper, we propose a control-oriented methodology for operating Groningen under induced-seismicity mitigation constraints. We employ a cascade model coupling pore-pressure diffusion with seismicity rate (SR) dynamics, and complement it with a stochastic event-generation procedure to convert the continuous SR field into a synthetic earthquake catalog with event times, locations, and magnitudes. From this catalog, we estimate regional SR measurements and design a robust feedback controller that computes well-rate commands to regulate the SR toward a desired reference while satisfying operational requirements, including prescribed production constraints. The proposed control architecture explicitly accounts for injection and extraction flux limits (actuator saturation). The well fluxes generated by the controller are updated at discrete-time intervals (digital control). We validate the modeling components against Groningen data and illustrate the approach through numerical experiments under different scenarios, including various control update periods and gain selections, as well as combined production with compensating injection (e.g., reinjection of nitrogen). The results illustrate how the proposed framework can reduce seismicity levels in a controlled manner while maximizing production targets.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript proposes a control-oriented framework for mitigating induced seismicity in the Groningen gas reservoir. It employs a cascade model coupling pore-pressure diffusion with seismicity rate (SR) dynamics, augmented by a stochastic event-generation procedure that converts the continuous SR field into a synthetic earthquake catalog (with times, locations, and magnitudes). Regional SR measurements are then estimated from this catalog to design a robust feedback controller that computes well-rate commands, regulating SR toward a reference while respecting production targets, actuator saturation (injection/extraction flux limits), and discrete-time updates. The modeling components are validated against Groningen data, and the framework is illustrated via numerical experiments under scenarios including varying control periods, gains, and combined production with compensating injection.

Significance. If the results hold, the work is significant because it addresses the inverse problem of designing operational strategies to minimize seismicity while meeting production goals, moving beyond pure forecasting. The explicit incorporation of actuator saturation and digital control, together with validation of the open-loop cascade model against historical data and numerical closed-loop demonstrations, provides a practical foundation that could inform real reservoir management. The stochastic catalog step enables feedback from discrete events, which is a strength for bridging continuous models to observable seismicity.

major comments (1)
  1. [Numerical experiments (and associated controller design)] The central claim that the framework can reduce seismicity levels in a controlled manner while maximizing production targets relies on the catalog-derived regional SR estimate serving as a sufficiently accurate and timely feedback signal for the discrete-time controller. However, the manuscript does not quantify how variance, bias, or lag in the SR estimate (arising from the stochastic event-generation procedure, especially in low-event-rate regimes) propagates through the feedback law or affects closed-loop stability under parameter mismatch. This is load-bearing for the reliability claim in the numerical experiments.
minor comments (2)
  1. The description of how the stochastic procedure converts the SR field into discrete events could be expanded with a brief algorithmic outline or pseudocode to improve reproducibility.
  2. Figure captions for the closed-loop trajectories should explicitly note the control update period and gain values used in each panel for easier cross-reference with the text.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive review and for recognizing the significance of the control-oriented framework, including the handling of actuator saturation, discrete-time updates, and the stochastic catalog generation for bridging to observable seismicity. We address the single major comment below.

read point-by-point responses

  1. Referee: The central claim that the framework can reduce seismicity levels in a controlled manner while maximizing production targets relies on the catalog-derived regional SR estimate serving as a sufficiently accurate and timely feedback signal for the discrete-time controller. However, the manuscript does not quantify how variance, bias, or lag in the SR estimate (arising from the stochastic event-generation procedure, especially in low-event-rate regimes) propagates through the feedback law or affects closed-loop stability under parameter mismatch. This is load-bearing for the reliability claim in the numerical experiments.

    Authors: We agree that the manuscript does not include a dedicated quantitative analysis of how variance, bias, or lag in the catalog-derived regional SR estimate propagates through the feedback controller, nor does it explicitly examine effects on closed-loop stability under parameter mismatch in the cascade model. The stochastic event-generation procedure is calibrated to reproduce historical event statistics, and the controller is formulated as a robust design to accommodate uncertainties, but these elements do not substitute for a sensitivity study, particularly in low-event-rate regimes. In the revised manuscript we will add Monte Carlo simulations over multiple independent realizations of the stochastic catalog. These experiments will quantify the resulting variability in regulated SR levels and production metrics, evaluate the influence of control update periods on estimation lag, and test closed-loop behavior under deliberate mismatches in the pore-pressure and SR model parameters. The results will be presented in an expanded numerical experiments section to directly support the reliability of the central claims. revision: yes

Circularity Check

0 steps flagged

No circularity: model-based controller design with independent validation and simulation

full rationale

The paper validates the cascade pore-pressure/SR model and stochastic catalog generator against historical Groningen data, then designs a robust feedback controller on that model and demonstrates its behavior via numerical closed-loop simulations. No derivation step reduces a claimed result to a fitted parameter or self-citation by construction; the controller synthesis and performance illustrations are standard model-based control outputs, not tautological re-statements of inputs. The central claims concern the architecture's ability to respect actuator limits while tracking an SR reference, which follows directly from the stated design procedure without circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract does not enumerate free parameters, axioms, or invented entities. The cascade model and stochastic event-generation procedure are invoked but their internal assumptions and any fitted quantities are not specified.

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Reference graph

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