Abstract Land subsidence due to fluid depletion is an outcome of physical processes operating across a wide range of time and length scales. Although geomechanical models are crucial to simulate reservoir compaction and predict its long-term fate, their use across large regions often bears prohibitive computational costs. To overcome this obstacle, this paper proposes a simplified modelling framework consisting of (i) a near-field numerical solver simulating the coupling between fluid flow and rock deformation with reference to a simplified one-dimensional geometry and (ii) a far-field geospatial algorithm mapping ground settlements across a region through the superposition of poroelastic computations at multiple wells. The model computes the delay between depletion history and reservoir compaction in proximity of a producing well by assuming basal depletion of a fluid-saturated deformable disk, while the Geertsma solution of nucleus of strain is used to extrapolate the impact of such time-varying reservoir compaction around the well. This approach has been used to back-analyze the spatio-temporal progression of subsidence at the Groningen gas field. The results are compared against measurements collected over 50 year of production at 25 benchmark locations scattered over an area of 900 km2. It is shown that coupled simulations based on average values of rock compressibility and permeability lead to nonlinear trends of subsidence evolution in good agreement with field measurements, while uncoupled analyses overpredict settlements by more than 70%. Lastly, synthetic forecasts based on different rates of depletion were provided. The results suggest that slower depletion rates lead to lower subsidence at a given time, and that residual subsidence may continue to develop for several decades after interruption of production activities.

中文翻译：

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用于分析由水库枯竭引起的时间相关地面沉降的地理空间模型

摘要 由于流体枯竭导致的地面沉降是在广泛的时间和长度范围内运行的物理过程的结果。尽管地质力学模型对于模拟油藏压实和预测其长期命运至关重要，但它们在大面积区域的使用通常会带来过高的计算成本。为了克服这个障碍，本文提出了一个简化的建模框架，包括 (i) 一个近场数值求解器，参考简化的一维几何模拟流体流动和岩石变形之间的耦合，以及 (ii) 一个远场地理空间通过在多口井中叠加多孔弹性计算来绘制跨区域地面沉降的算法。该模型通过假设流体饱和的可变形盘的基础耗竭来计算生产井附近的耗竭历史和储层压实之间的延迟，而应变核的格尔茨马解用于推断这种时变储层压实的影响井周围。这种方法已被用于反分析格罗宁根气田沉降的时空进展。将结果与分布在 900 平方公里区域内的 25 个基准位置在 50 年的生产过程中收集的测量结果进行比较。结果表明，基于岩石压缩率和渗透率平均值的耦合模拟导致沉降演化的非线性趋势与现场测量结果非常吻合，而非耦合分析高估了 70% 以上的沉降。最后，提供了基于不同消耗率的综合预测。结果表明，较慢的消耗速率会导致给定时间的下沉较低，并且在生产活动中断后，剩余下沉可能会继续发展数十年。