Unified Oil and Water Fractional-Flow Functions: Improving Waterflood Performance Analytical Modeling Techniques

Summary Foam, a dispersion of gas in liquid, has been investigated as a tool for gas-mobility and conformance control in porous media for a variety of applications since the late 1950s. These applications include enhanced oil recovery, matrix-acidization treatments, gas-leakage prevention, as well as contaminated-aquifer remediation. To understand the complex physics of foam in porous media and to implement foam processes in a more-controllable way, various foam-modeling techniques were developed in the past 3 decades. This paper reviews modeling approaches obtained from different publications for describing foam flow through porous media. Specifically, we tabulate models on the basis of their respective characteristics, including implicit-texture as well as mechanistic population-balance foam models. In various population-balance models, how foam texture is obtained and how gas mobility is altered as a function of foam texture, among other variables, are presented and compared. It is generally understood that both the gas relative permeability and viscosity vary in the reduction of gas mobility through foam generation in porous media. However, because the two parameters appear together in the Darcy equation, different approaches were taken to alter the mobility in the various models: only reduction of gas relative permeability, increasing of effective gas viscosity, or a combination of both. The applicability and limitations of each approach are discussed. How various foam-generation mechanisms play a role in the foam-generation function in mechanistic models is also discussed in this review, which is indispensable to reconcile the findings from different publications. In addition, other foam-modeling methods, such as the approaches that use fractional-flow theory and those that use percolation theory, are also reviewed in this work. Several challenges for foam modeling, including model selection and enhancement, fitting parameters to data, modeling oil effect on foam behavior, and scaling up of foam models, are also discussed at the end of this paper.

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Application of Fractional Flow Theory for Analytical Modeling of Surfactant Flooding, Polymer Flooding, and Surfactant/Polymer Flooding for Chemical Enhanced Oil Recovery

Water ◽

10.3390/w12082195 ◽

2020 ◽

Vol 12 (8) ◽

pp. 2195

Author(s):

Lei Ding ◽

Qianhui Wu ◽

Lei Zhang ◽

Dominique Guérillot

Keyword(s):

Enhanced Oil Recovery ◽

Oil Recovery ◽

Analytical Modeling ◽

Flow Theory ◽

Polymer Flooding ◽

Surfactant Flooding ◽

Fractional Flow ◽

Oil Saturation ◽

Polymer Retention ◽

Fractional Flow Theory

Fractional flow theory still serves as a powerful tool for validation of numerical reservoir models, understanding of the mechanisms, and interpretation of transport behavior in porous media during the Chemical-Enhanced Oil Recovery (CEOR) process. With the enrichment of CEOR mechanisms, it is important to revisit the application of fractional flow theory to CEOR at this stage. For surfactant flooding, the effects of surfactant adsorption, surfactant partition, initial oil saturation, interfacial tension, and injection slug size have been systematically investigated. In terms of polymer flooding, the effects of polymer viscosity, initial oil saturation, polymer viscoelasticity, slug size, polymer inaccessible pore volume (IPV), and polymer retention are also reviewed extensively. Finally, the fractional flow theory is applied to surfactant/polymer flooding to evaluate its effectiveness in CEOR. This paper provides insight into the CEOR mechanism and serves as an up-to-date reference for analytical modeling of the surfactant flooding, polymer flooding, and surfactant/polymer flooding CEOR process.

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Robust Nonlinear Newton Solver With Adaptive Interface-Localized Trust Regions

SPE Journal ◽

10.2118/195682-pa ◽

2019 ◽

Vol 24 (04) ◽

pp. 1576-1594 ◽

Cited By ~ 2

Author(s):

Øystein S. Klemetsdal ◽

Olav Møyner ◽

Knut-Andreas Lie

Keyword(s):

Systems Approach ◽

Unconditional Convergence ◽

Trust Regions ◽

Fractional Flow ◽

Strongly Coupled ◽

Reservoir Simulations ◽

Industry Standard ◽

Inflection Points ◽

Flow Effects ◽

Flow Functions

Summary The interplay of multiphase-flow effects and pressure/volume/temperature behavior encountered in reservoir simulations often provides strongly coupled nonlinear systems that are challenging to solve numerically. In a sequentially implicit method, many of the essential nonlinearities are associated with the transport equation, and convergence failure for the Newton solver is often caused by steps that pass inflection points and discontinuities in the fractional-flow functions. The industry-standard approach is to heuristically chop timesteps and/or dampen updates suggested by the Newton solver if these exceed a predefined limit. Alternatively, one can use trust regions (TRs) to determine safe updates that stay within regions that have the same curvature for numerical flux. This approach has previously been shown to give unconditional convergence for polymer- and waterflooding problems, also when property curves have kinks or near-discontinuous behavior. Although unconditionally convergent, this method tends to be overly restrictive. Herein, we show how the detection of oscillations in the Newton updates can be used to adaptively switch on and off TRs, resulting in a less-restrictive method better suited for realistic reservoir simulations. We demonstrate the performance of the method for a series of challenging test cases ranging from conceptual 2D setups to realistic (and publicly available) geomodels such as the Norne Field and the recent Olympus model from the Integrated Systems Approach for Petroleum Production (ISAPP) optimization challenge.

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