Résumé -Subsidence différée : observations et analyse à partir de données de champs -L'objectif de cet article est de décrire l'effet différé de subsidence liée à la déplétion à partir des observations de terrain, dans le but d'expliquer ses origines et de mieux contraindre sa modélisation. L'évolution non linéaire de la subsidence en surface en fonction de la déplétion du réservoir peut être étudiée à partir du décalage entre le début de la production et le démarrage (différé) de la subsidence. Nous avons analysé des données provenant de huit champs d'hydrocarbures et quantifié l'effet de décalage entre la subsidence et la déplétion et le temps de retard correspondant. Les temps de retard quantifiés varient de 1,6 à 13 ans. Les champs étudiés ont été classifiés selon leur profondeur, âge et type de roche. Afin d'expliquer les observations de terrain, les données ont été confrontées à quatre mécanismes : -diffusion de la pression interstitielle ; -effet du recouvrement ; -comportement du réservoir en compaction ; -déformation du recouvrement, de la base ou de l'extension du réservoir. L'importance relative de ces mécanismes a été déterminée à partir de l'analyse des données de terrain. Certains mécanismes peuvent être éliminés à partir de principes théoriques de base alors que d'autres apparaissent comme inappropriés. Il est montré que le mécanisme de diffusion de la pression interstitielle contribue toujours à un effet différé, mais que cet effet est trop faible pour expliquer les observations de champ. Dans le cas de réservoirs contenant de l'argile, la surcompaction naturelle peut expliquer les temps de retard observés. En général, les autres mécanismes de compaction des réservoirs (tels que fluage, effet de la vitesse de chargement sur le comportement de la roche et transition élastoplastique) peuvent également être la cause principale de l'effet de décalage entre la subsidence et la déplétion. Abstract

Summary Open literature and new experimental compaction data from five reservoir and 16 outcrop sandstones are used to delineate the near-elastic, inelastic, and failure domains in 3D-stress space for porosity classes of 5 to 15%, 15 to 25%, and 25 to 35%. Applications of this compaction-domain model include the analysis of the extent of the near-elastic domain (where elasticity theory can be used to describe and predict rock deformation), the pore-volume compressibility (Cpp), and the permeability reduction as a function of reservoir stress path. This is illustrated for a well-consolidated sandstone reservoir with an average porosity of approximately 18%. Two aspects of dynamic reservoir modeling in the near-elastic domain are addressed: calculation of Cpp from raw volumetric-compaction data as a function of isotropic total stress change, and the correction of Cpp for a nonhydrostatic reservoir stress path. Open-literature work combined with our experimental data indicates that the compaction-induced permeability reduction of 15 to 25% porosity sandstone in the near-elastic domain depends predominantly on the increase of the effective mean stress, not on the reservoir stress path.

Summary The decrease of pore pressure during hydrocarbon production (depletion) leads to compaction of the reservoir, which in turn changes the stresses acting on the reservoir. The prediction of reservoir compaction and its consequences is usually based on laboratory experiments performed under uniaxial strain conditions, i.e., allowing no lateral strain during depletion. Field data of the Groningen gas field (The Netherlands) indicate that the stress development of the field deviates significantly from the stress path under uniaxial strain conditions. Laboratory experiments show that the applied stress path has a strong influence on the depletion-induced compaction behavior. We discuss the consequences of these results for the field compaction behavior by considering the responsible deformation mechanisms active in reservoir and experiment. The new Groningen field data, in combination with our experimental results, provide an explanation for the difference between the prediction of compaction and subsidence based on uniaxial experiments and the measurement of compaction and subsidence in the Groningen field. With the use of the new stress path, the predicted and measured compaction and subsidence are in agreement. Introduction The prediction of the amount of depletion-induced reservoir compaction and its adverse consequences (such as subsidence, casing deformation, and seismicity) requires three types of input parameters: The mechanical behavior of the reservoir rock and the rock surrounding the reservoir, the reservoir stress path induced by the depletion, and the dimension and depth of reservoir and overburden formations. Also, a model is required to upscale the laboratory experiments to predict reservoir compaction and the associated surface or seabed subsidence during and after depletion. The first two types of input parameters (mechanical behavior and stress path) are actually linked: The depletion leads to compaction and deformation of the reservoir, which in turn changes the total stresses acting on the reservoir. It is the combination of pore pressure change and total stress change, which alters (and generally increases) the effective normal and shear stresses acting on the load-bearing grain framework. This results in elastic (recoverable) and inelastic (permanent) deformation which, in turn, has a time-independent component, usually referred to as plasticity, and a time-dependent component, referred to as creep. The bulk rock compaction is the result of the various micro mechanisms activated by the depletion, and their dependence on stress path and stress rate (typically, a few MPa per year), stress level (<100 MPa), and temperature (<200°C) and possibly also pore fluid composition.1–3 Ideally, the laboratory experiments are performed along the same stress path that the reservoir undergoes during depletion. However, the reservoir stress path is not known before depletion starts, and analytical or numerical models for the stress development in depleting reservoirs are very sensitive to the input parameters mentioned earlier. To make things worse, field data describing depletion-induced changes in total stress are very scarce, so only a few case studies are available to guide the design of laboratory experiments. In most studies it is assumed that the reservoir compacts uniaxially; that is, there is only vertical compaction and no horizontal deformation. During uniaxial compaction of sandstone with 10 to 30% porosity, the ratio of change in total horizontal stress per change in pore pressure is typically in the range 0.7 to 0.9.3 For the Groningen gas reservoir (The Netherlands) a similar strategy was followed, and a large amount of uniaxial compaction experiments were performed, partly published.3 The tested rock types ranged from low-porosity (5 to 10%) conglomerates to highly porous (25 to 30%) coarse sandstone. However, the compaction and subsidence prediction based on these uniaxial strain experiments is larger than the measured compaction and subsidence in the Groningen field, and the reason for this is still unknown. This paper describes the important role of stress path in compaction prediction and offers a new explanation for the difference in predicted and measured compaction and subsidence in the Groningen field. We start with an analysis of the changes of the total stresses during reservoir compaction, using basic rock mechanics theory. Then, new field stress data are presented and analyzed to estimate the production-induced stress path of the Groningen gas field. Next, the results of triaxial compaction experiments on Groningen core samples are shown, indicating a strong influence of stress path on compaction. Finally, we discuss the experimental results and the consequences of the stress path to the compaction behavior by considering the underlying compaction mechanisms. Although we discuss only field data and core measurements from the Groningen gas field, we think that our conclusions can be generalized, and may be of value to other studies aimed at the prediction of depletion-induced reservoir compaction. Reservoir Stress Changes During Production Prior to production, the Earth's stress field determines the state of stress in the reservoir. Production causes a decrease of the fluid and/or gas pressure in the pores. These pressure changes also result in changes in the total vertical and horizontal stresses acting on the reservoir. Strong evidence for this comes from the occurrence of seismic events inside and close to compacting reservoirs.4,5 Geertsma6 developed a theory of the subsidence and stress changes associated with reservoir compaction, based on linear poroelastic rock behavior. Regarding the total vertical stress, the depletion-induced stress changes at the axis just above a disk-shaped compacting reservoir can be written as6 Δ σ V = h Δ p r ( 1 − 2 ν 2 − 2 ν ) f ( d r ) . ( 1 )

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