An Integrated Workflow to Account for Multi-Scale Fractures in Reservoir Simulation Models: Implementation and Benefits

Abstract

Quantitative systems pharmacology (QSP) modeling has become increasingly important in pharmaceutical research and development, and is a powerful tool to gain mechanistic insights into the complex dynamics of biological systems in response to drug treatment. However, even once a suitable mathematical framework to describe the pathophysiology and mechanisms of interest is established, final model calibration and the exploration of variability can be challenging and time consuming. QSP models are often formulated as multi-scale, multi-compartment nonlinear systems of ordinary differential equations. Commonly accepted modeling strategies, workflows, and tools have promise to greatly improve the efficiency of QSP methods and improve productivity. In this paper, we present the QSP Toolbox, a set of functions, structure array conventions, and class definitions that computationally implement critical elements of QSP workflows including data integration, model calibration, and variability exploration. We present the application of the toolbox to an ordinary differential equations-based model for antibody drug conjugates. As opposed to a single stepwise reference model calibration, the toolbox also facilitates simultaneous parameter optimization and variation across multiple in vitro, in vivo, and clinical assays to more comprehensively generate alternate mechanistic hypotheses that are in quantitative agreement with available data. The toolbox also includes scripts for developing and applying virtual populations to mechanistic exploration of biomarkers and efficacy. We anticipate that the QSP Toolbox will be a useful resource that will facilitate implementation, evaluation, and sharing of new methodologies in a common framework that will greatly benefit the community.

Effective Permeability of Media with a Dense Network of Long and Micro Fractures

“…The permeability is computed for several values of the total density and compared to numerical simulations on explicit discrete fracture networks by means of the software FRACA developed by IFP. Among many functionalities aiming at analyzing the characteristics of fractured reservoirs, this software allows to randomly generate fractures according to length, orientation and conductivity laws and compute an effective permeability according to the methodology presented in Bourbiaux et al (1998), Sarda et al (2001), Lange et al (2002) and Bourbiaux et al (2002). In the present case, the length, orientation and conductivity laws are deterministic.…”

“…Indeed the latter can be composed of several geological entities of different orders of length magnitude which can all play a very important role in the overall hydraulic behavior of the field. In addition to the pores and fractures at very small scale (decimetric or less) accounting for the intrinsic porosity and permeability of the rock matrix, several fracturation scales are put in evidence in Bourbiaux et al (2002). On the one hand, large scale faults observable by seismic surveys, sub-seismic faults and fracture swarms consisting in clusters of fractures can all be considered as large scale fractures (hectometric or more) taken explicitly into account in flow simulation models.…”

“…A workflow incorporating the hydraulic effects of fractures at all scales and their possible interactions is detailed in Bourbiaux et al (2002) so as to build a complete flow simulation model. An example of model built and calibrated from available static and dynamic data and containing fractures at different scales can be found in de Galard et al (2005).…”

Matrix–fracture transfer shape factor for modeling flow of a compressible fluid in dual-porosity media

“…There have also been recent attempts to find the shape factors for two-phase flow and thermal processes, which are beyond the scope of this work and are not reviewed here [7,10,34]. As an example, Civan and Rasmussen [10] developed an analytical model for rectangular shape matrix blocks.…”

Integrated Fractured Reservoir Characterization and Connectivity Study in the Cantarell Field

“…Cacas et al [3] proposed a methodology to build consistent geological models of fracture networks based on three nested models. Bourbiaux et al [2] proposed an integrated workflow to account for multiscale fractures in reservoir simulation models. Characterizing fractured reservoirs involves modeling two main scales of fractures, fracture corridors and layer bounded diffuse fractures.…”