Modelling the Impact of Anisotropy on Hydrocarbon Production in Heterogeneous Reservoirs

Effective and optimal hydrocarbon production from heterogeneous and anisotropic reservoirs is a developing challenge in the hydrocarbon industry. While experience leads us to intuitive decisions for the production of these heterogeneous and anisotropic reservoirs, there is a lack of information concerning how hydrocarbon and water production rate and cumulative production as well as water cut and water breakthrough time depend on quantitative measures of heterogeneity and anisotropy. In this work, we have used Generic Advanced Fractal Reservoir Models (GAFRMs) to model reservoirs with controlled heterogeneity and vertical and/or horizontal anisotropy, following the approach of Al-Zainaldin et al. (Transp Porous Media 116(1):181–212, 2017). This Generic approach uses fractal mathematics which captures the spatial variability of real reservoirs at all scales. The results clearly show that some anisotropy in hydrocarbon production and water cut can occur in an isotropic heterogeneous reservoir and is caused by the chance placing of wells in high-quality reservoir rock or vice versa. However, when horizontal anisotropy is introduced into the porosity, cementation exponent and grain size (and hence also into the permeability, capillary pressure, water saturation) in the reservoir model, all measures of early stage and middle stage hydrocarbon and water production become anisotropic, with isotropic flow returning towards the end of the reservoir’s lifetime. Specifically, hydrocarbon production rate and cumulative production are increased in the direction of anisotropy, as is water cut, while the time to water breakthrough is reduced. We found no such relationship when varying vertical anisotropy because we were using vertical wells but expect there to be an effect if horizontal wells were used

Calibrating transmissivities from piezometric heads with the gradual deformation method: An application to the Culebra Dolomite unit at the Waste Isolation Pilot Plant (WIPP), New Mexico, USA

International audienc

Combining the Pilot Point and Gradual Deformation Methods for Calibrating Permeability Models to Dynamic Data

We focus on specific parameterization techniques developed in inverse stochastic modeling for determining permeability fields from dynamic data using a reduced number of parameters. Two major contributions are the pilot point method and the gradual deformation method. They were designed to reduce the number of parameters and to respect the inferred spatial structure. Weaknesses have been revealed for the pilot point method: pilot points can be assigned unreasonably extreme values and possible correlations among the pilot points are neglected. To bypass these limitations, a new approach, called the gradual pilot point method, is suggested. It follows the basic workflow of the pilot point method, but the pilot point values are not driven by the optimization procedure. Intermediate gradual deformation parameters are introduced which govern the pilot point values. Compared to the original pilot point method, the gradual pilot point method does not produce extreme variations. Moreover, when the whole set of pilot points is modified simultaneously from a single deformation parameter, the correlations among the pilot points are accounted for. Thus, many pilot points can be placed on the permeability field, whatever their locations. They can produce local and global deformation. The performed numerical experiments show that a two-step approach for calibrating permeability fields is useful. First, the gradual deformation method is used to globally deform the permeability fields. Once the permeability fields have been globally improved, they can be locally refined using the gradual pilot point method

Simultaneous Inversion of Production Data and Seismic Attributes: Application to a Synthetic SAGD Produced Field Case Inversion simultanée des données de production et des attributs sismiques : application à un champ synthétique produit par injection de vapeur

The joint use of production data and time-lapse seismic attributes can help to understand fluid flows within geological formations and to build reliable numerical models for representing these formations. This concern recently motivated the development of dedicated inversion or matching techniques for identifying models consistent with all collected data. The methodology presented in this paper makes it possible to map petrophysical properties such as facies, porosity and permeability into reservoirs from production data and seismic attributes. It is successfully applied to a synthetic case describing a heavy oil field produced from steam assisted gravity drainage. This case study generated from a real case shows how to design the inversion methodology to match the entire set of available data. A few key points are highlighted since they drive the success of the proposed matching methodology. First, parameterization is essential. It must allow for locally varying petrophysical properties from a reduced number of parameters. Second, this study stresses the need for alternative formulations for quantifying the mismatch between reference seismic attributes and simulated seismic attributes. Last, two methods are compared for integrating reference seismic attributes either in time or in depth (after a time-to-depth conversion). In the case studied, it is shown that the two approaches are equivalent since time-to depth-conversion error is quite small. L’utilisation conjointe des données de production et des attributs de sismique répétée facilite la compréhension des mouvements de fluide dans les formations géologiques et aide à la construction de modèles numériques fiables représentant ces formations. Ceci a récemment motivé le développement de techniques d’inversion ou de calage dédiées à l’identification de modèles cohérents avec l’ensemble des données disponibles. La méthodologie décrite dans ce papier permet de déterminer les cartes de propriétés pétrophysiques comme les faciès, les porosités ou les perméabilités à partir des données de production et des attributs de sismique répétée. Elle est appliquée avec succès à un champ synthétique d’huile lourde produite par injection de vapeur. Ce cas d’étude, inspiré d’un cas réel, illustre comment définir une méthodologie d’inversion qui respecte l’ensemble des données disponibles. L’étude est centrée sur trois points particuliers de la méthodologie qui sont les clés du succès. Premièrement, le choix de la paramétrisation est essentiel. La paramétrisation doit permettre des variations locales avec peu de paramètres. Deuxièmement, cette étude met en évidence la nécessité d’une formulation alternative pour mesurer l’erreur entre les attributs sismiques de référence et les attributs sismiques simulés. Finalement, nous étudions deux approches pour l’intégration des attributs sismiques de référence. Ils peuvent être intégrés en temps ou bien en profondeur. Nous montrons que, dans le cas étudié, ce dernier point n’influence pas la qualité du résultat obtenu car l’erreur de conversion temps-profondeur est faible

Elements for an Integrated Geostatistical Modeling of Heterogeneous Reservoirs

The geostatistical approach for modeling heterogeneous reservoirs allows, on one hand, to integrate data of various natures and scales, and on the other hand, to evaluate uncertainties by generating multiple possible scenarios of the reservoir heterogeneity. Building a geostatistical reservoir model must account for the geological depositional environment of the reservoir, so as to represent the major heterogeneities that control fluid flow. The quantitative information from wells, seismic and well tests, etc., must be used for the inference of the model structural parameters. Constraining model realizations to the hydrodynamic data from production allows to further increase the model reliability for production forecasts. This paper presents the elements of an integrated methodology for modeling heterogeneous reservoirs. We first introduce the basic geostatistical models used to describe the heterogeneous reservoirs. This is followed by an outline on the inference of the model structural parameters. Then, we present an inverse approach based on the gradual deformation method for history matching