Active production in oil and gas fields tends to cause reservoir compaction and consequent surface subsidence. The compaction and the associated subsidence are often time-dependent in various reasons, and are reported, in some cases, to accelerate even after depletion of reservoir. In order to explain the accelerated post-depletion subsidence, we propose a possibility of compaction in the reservoir-bounding shale, which is induced by slow drainage of pore fluid from shale to reservoir sands after depletion. To examine the significance of the compaction in the reservoir-bounding shale, we build a simple one-dimensional compaction model that consists of sand reservoir embedded within the surrounding shale. The model assumes a poroelastic compaction in sand reservoir during production, and then shale compaction due to pore pressure diffusion in the bounding shale after depletion. The shale compaction is described by a superposition of two rheological constitutive laws: time-dependent poroelasticity and time-dependent viscoplasticity. The analytical result shows that despite extremely low permeability of shale, the total amount of shale compaction associated with a slow drainage of pore fluid can be comparable to that of the sand compaction within a decade, and that the resulting subsidence rate can accelerate even after depletion.

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