Realistic Methodology for Permeability Modelling Used for Conserving Heterogeneity During Assisted History Matching-Applied to a Turbiditic Reservoir Field Case
Authors: Botton-Dumay R. , Cogrel Y.M. , Massonnat G.J. , Eberle N. 
Published: December 2007

Realistic Methodology for Permeability Modelling Used for Conserving Heterogeneity During Assisted History Matching-Applied to a Turbiditic Reservoir Field Case. R. Botton-Dumay; Y.M. Cogrel; G.J. Massonnat; N. Eberle, SPE, Elf Exploration Production.

Abstract
Recent advances in stochastic modelling have extensively improved the representations of complex geology in unknown inter-well regions. The high level of detail provided by these models often requires several million grid-blocks, however it cannot be used in flow simulators, and hence scaling-up is necessary.
Up-scaling absolute permeability whilst maintaining a reasonable degree of detail in the representation of heterogeneity is difficult and time-consuming and should include up-scaling of relative permeabilities as well as use of a full permeability tensor.
Moreover, constraining successive modifications during history matching to be consistent with the original model appears to be challenging.
This paper presents a simplified methodology for the input of horizontal permeability anisotropy and vertical transmissibility (obtained from fine synthetic 3D models) in a coarse deterministic model.
The management of the permeability heterogeneity during the assisted history matching phase (using the method of gradients) is then simplified and consistency with the original model is maintained throughout the study.
This method is applied to a turbiditic reservoir where the main recovery process is edge water flooding.
Only key heterogeneity (drains in channels and inter-lobes barriers) is dealt with using this methodology. It was sufficient to successfully impact history matching without changing the initial geological model.
Hydrocarbon-bearing reservoirs are inherently complex and are characterized by heterogeneity: sedimentary features of different sizes, different shapes and different origins coexist within a same reservoir. This makes the scale related problems particularly delicate in reservoir engineering.
Reservoir engineers, in their concern to improve the predictions about the dynamic behavior of the reservoirs, and the recent advances achieved in geostatistics, are at the origin of the development of modelling tools which have significantly improved the representation of heterogeneity in reservoir models. The high level of detail provided by these models often requires several million grid-blocks. This degree of detail cannot however be used for flow simulation, and hence, up-scaling is necessary.
Scaling-up absolute permeability is a delicate point since averaging heterogeneous values, even isotropic at fine scale, develops anisotropy at the larger scale. The memory of the pre-upscaled heterogeneity is, therefore, included into all the members of the permeability tensor (diagonal and crossed members). However, scaling-up relative permeability curves is a more critical point in so far as it drives polyphasic flows into the reservoir and allows a good representation of the reservoir behavior. Due to the limitations related to the means of calculation, scaling up relative permeability curves for each grid-block of the flow simulation is today "a dream" in operational studies. Many authors have proposed to bypass most of this step by running simplified flow simulations in order to identify flow units and to adapt gridding and upscaling to flows. This allows use of all the stochastic simulations created from a single geological scenario and the same global statistics input into the stochastic model.
Nevertheless, when a production history is available and a history matching phase must be completed, the availability of equiprobable simulations presents a big headache for the engineer responsible for the simulation.
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