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An areal model of a fractured/faulted reservoir with 49 wells is developed that incorporates fully-coupled geo-mechanics and fluid flow. It is a generic example of a pattern waterflood although it is inspired by a parallel study of the Gullfaks reservoir in the North Sea, in which stress-related, fault-related and long-range correlations in rate fluctuations are observed. Based on this model, three scenarios are examined in terms of different initial stress states prior to production, each of which involves 36 months of production and injection in the presence of fracture sets and faults. The results support the concept that the long-range, stress-related and fault-related characteristics of correlations in rate fluctuations, observed not only in the Gullfaks data, but also in several other fields worldwide, are symptomatic of a system near a geomechanical critical point. These characteristics are not observed in models that are sub-critical. Short-range rate correlations are likely to exist where there are highly permeable zones between producers and injectors. Long-range rate correlations occur only within critically-stressed regions where there is active shearing or fault reactivation. The modelling results are consistent with field evidence suggesting that incipient shearing is an important mechanism coupled with reservoir flow behaviour.

Abstract. Centrifuge experiments modeling single-phase flow in prototype porous media typically use the same porous medium and permeant. Then, well-known scaling laws are used to transfer the results to the prototype. More general scaling laws that relax these restrictions are presented. For permeants that are immiscible with an accompanying gas phase, model-prototype (i.e., centrifuge model experiment-target system) scaling is demonstrated. Scaling is shown to be feasible for Miller-similar (or geometrically similar) media. Scalings are presented for a more general class, Lisle-similar media, based on the equivalence mapping of Richards' equation onto itself. Whereas model-prototype scaling of Miller-similar media can be realized easily for arbitrary boundary conditions, Lislesimilarity in a finite length medium generally, but not always, involves a mapping to a moving boundary problem. An exception occurs for redistribution in Lisle-similar porous media, which is shown to map to spatially fixed boundary conditions. Complete modelprototype scalings for this example are derived.

This paper describes the new concept of a ‘Statistical Reservoir Model’ to determine significant well-pair correlations. We solve this conceptual problem using a predictive error filter, combined with Bayesian methods that identify those well pairs that are related to each other with statistical significance, for the Gullfaks reservoir in the North Sea. Significant, long-range, correlations in the whole field are found at an optimal time lag of one month. The correlation function for significantly-correlated well pairs, after normalization for the distribution of available wells, shows a long-range power-law decay that is consistent with a critical-point response at the reservoir scale. A principal component analysis shows a strong correlation with the location and orientation of faults that intersect the main producing horizon. A predictive experiment shows that the model performs very well both in history matching and predictive mode on a time scale of about one month.

[1] We attempt to generate new solutions for the moisture content form of the onedimensional Richards ' [1931] equation using the Lisle [1992] equivalence mapping. This mapping is used as no more general set of transformations exists for mapping the onedimensional Richards' equation into itself. Starting from a given solution, the mapping has the potential to generate an infinite number of new solutions for a series of nonlinear diffusivity and hydraulic conductivity functions. We first seek new analytical solutions satisfying Richards' equation subject to a constant flux surface boundary condition for a semi-infinite dry soil, starting with the Burgers model. The first iteration produces an existing solution, while subsequent iterations are shown to endlessly reproduce this same solution. Next, we briefly consider the problem of redistribution in a finite-length soil. In this case, Lisle's equivalence mapping is generalized to account for arbitrary initial conditions. As was the case for infiltration, however, it is found that new analytical solutions are not generated using the equivalence mapping, although existing solutions are recovered.