Validation and Improvement of Numerical Methods to Simulate the Well-Test Response of Reservoir Models for Model Calibration Purposes
Authors: Scapolo Matteo , Garcia Michel H. , Mathieu Jean-Baptiste , Siffert Deborah , Gosselin Olivier R. , Ackerer Philippe 
Published: April 2019

Abstract
Using geostatistical modelling to populate reservoir properties is nowadays the most common approach in the industry and it has received a great deal of attention. A geostatistical reservoir model defines a space of spatial uncertainty, which can be explored by generating many equiprobable reservoir property realisations that are as many possible reservoir models complying with static data. Among them, the relevant models are those that also match the dynamic data, which complete the available data for reservoir model calibration. Finding the relevant reservoir models in the space of spatial uncertainty is a time-consuming process that requires simulating the dynamic (flow) response of many reservoir models. Having a fast and reliable simulation method is then highly desirable to speed up the process of reservoir model calibration. In this context, a new approach has been developed and tested. The method allows easy and fast comparison between interpreted well-test results and equivalent (average) reservoir model properties in terms of transmissivity (k.h) and permeability. The comparison can be used to validate or reject a reservoir model, and to obtain indications on how to modify it to fit the well-test data. This paper presents the method and the results obtained to evaluate its performances and to validate it.
Well-test-interpreted permeabilities (or transmissivities) are nothing but weighted average permeabilities that are to be calculated from permeabilities defined over closed surfaces properly defined around the well, the weights depending on the flow geometry. The proposed method is based on steady-state flow simulation that is carried out by making the tested well a source term (producing or injecting well) in the centre of a simulation domain (reservoir model region). The latter must be extended enough to contain, or at least overlap, the stabilisation area of the well test in which average transmissivities are to be estimated. The method relies on three key aspects: defining a simulation domain (extension and shape) that is consistent with the actual well-test drainage area, defining relevant boundary conditions to reproduce flow paths that are consistent with those generated by the actual well test, using the new effective-gradient based averaging method to compute average permeabilities over closed surfaces properly defined.
The method is tested on various synthetic and partly real field cases, for which the transient well-test responses are first simulated and interpreted, then compared with the transmissivities that are predicted using the new method. Sensitivity analysis is also carried out on calculation parameters (flow simulation domain, flow rates…) to check the robustness of the method and identify improvement avenues. All these results tend to confirm the effectiveness of the method, which can combine speed and accuracy. This method is intended to be used as an objective function to perform automatic or assisted reservoir model calibration on interpreted well-test data. It is expected to be particularly useful to calibrate naturally fractured reservoir models for which permeability tensors are to be calculated from uncertain locally defined fracture property statistics.