Abstract
This manuscript primarily focuses on the constraints associated with the extended version of Darcy’s law that is used to describe the multiphase flow through a porous media; and in particular, a petroleum reservoir. This manuscript clearly brings out the basics associated with the usage of Darcy’s law, and reasons out the inapplicability of the Navier-Stokes Equation in order to describe the momentum conservation in a typical petroleum reservoir. Further, this work highlights the essence of continuum-based Darcy’s macroscopic-scale equation with that of Navier-Stokes’s microscopic-scale equation. Further, the absence of capillary forces in original Darcy’s equation and extending the same by considering the concept of ‘capillary pressure’ in order to accommodate the multi-phase flow has several critical constraints associated with it. In this manuscript, all these constraints or limitations have been posed in the form of a list of basic queries that need to be addressed or at least to be understood with clarity, when applying the multi-phase fluid flow equations associated with a petroleum reservoir. This study is limited to an oil-water two-phase system.
Highlights
IntroductionFluid flow through a porous medium is of great significance in various applications that includes groundwater flow; contaminant hydrogeology; enhanced geothermal energy system; enhanced oil recovery; CO2 sequestration; mass transport in vadose zone; flow through shale gas reservoirs; flow through tight gas reservoirs, and onshore oil spill (Nitha et al, 2018; Nitha et al, 2019; Kumar and Rakesh, 2018; Kumar 2019a, 2019b; Manojkumar and Kumar, 2020; Kumar and Sekhar, 2005; Kumar et al, 2006; Sekhar and Kumar, 2006; Sekhar et al, 2006; Kumar, 2008; Kumar et al, 2008; Kumar, 2009; Natarajan and Kumar, 2010; Natarajan and Kumar, 2011a; 2011b; Natarajan and Kumar, 2012a, 2012b; Renu and Kumar, 2012; Kumar, 2014a, 2014b; Natarajan and Kumar, 2014a, 2014b; Renu and Kumar, 2014; Nikhil and Kumar, 2015a, 2015b; Natarajan and Kumar, 2015; Kumar, 2015; Kumar and Rakesh, 2015; Kumar et al, 2016; Renu and Kumar, 2016a, 2016b; Kumar, 2016; Rakesh and Kumar, 2016; Nikhil and Kumar, 2016; Natarajan and Kumar, 2016a, 2016b; Abhishek et al, 2016; Nikhil and Kumar, 2017; Renu and Kumar, 2017a, 2017b; Natarajan and Kumar, 2018; Bagalkot et al, 2018a, 2018b; Naga babu et al, 2018; Kumar and Ghassemi, 2005; Kumar and Ghassemi, 2006; Ghassemi and Kumar, 2007; Reddy and Kumar, 2014; Sharma et al, 2014a, 2014b; Sivasankar et al, 2014; Kanna et al, 2014; Reddy and Kumar, 2015a, 2015b; Sharma et al, 2015a, 2015b, 2015c; Abhishek et al, 2015; Kidambi and Kumar, 2016; Sivasankar et al, 2016; Kumar and Reddy, 2017; Sivasankar and Kumar 2017a, 2017b; Sivasankar and Kumar, 2018, 2019; Vivek and Kumar, 2016; Vivek et al, 2017, 2019; Vivek and Kumar, 2020; Mohanasundaram et al, 2013a, 2013b; Berlin et al, 2013; Berlin et al, 2014a, 2014b; Berlin et al, 2015a, 2015b, 2015c; Omkar et al, 2016a, 2016b; Mohanasundaram et al, 2017; Berlin et al, 2018a, 2018b; Omkar et al, 2019a, 2019b; Berlin and Kumar, 2019; Mohanasundaram et al, 2019, 2020; Patwardhan et al, 2014; Patwardhan et al, 2015; Patwardhan et al, 2016; Patwardhan et al, 2017a, 2017b; Kidambi et al, 2017; Vasudevan et al, 2014a, 2014b; Vasudevan et al, 2015; Vasudevan et al, 2016a, 2016b, 2016c; Vasudevan et al, 2017; Renu and Kumar 2018a, 2018b, 2018c; Rajasekhar et al, 2018; Renu and Kumar, 2019).‘Fluid flow through a porous medium’ is fundamentally different from the concept of ‘fluid flow through pipes’ in the sense that the flow through a porous medium is associated with a hydraulic head with an insignificant kinetic head
With a clear discontinuity at the flood front, will it be feasible to deduce a reasonable Representative Elementary Volume (REV) in the vicinity of the flood front that will make the multi-phase fluid flow system to be treated at the continuum scale that includes the location of flood front interface, where both oil pressure and water pressure can be treated to remain as a continuous phase? It is known that the discontinuity of the immiscible fluid phase pressures on either side of the flood front depends on the magnitude of the capillary pressure and depends on the complete hysteresis of the drainage-imbibition capillary pressure curves
This work has made an attempt to provide an overview that describes a physical system with multi-phase fluid flow
Summary
Fluid flow through a porous medium is of great significance in various applications that includes groundwater flow; contaminant hydrogeology; enhanced geothermal energy system; enhanced oil recovery; CO2 sequestration; mass transport in vadose zone; flow through shale gas reservoirs; flow through tight gas reservoirs, and onshore oil spill (Nitha et al, 2018; Nitha et al, 2019; Kumar and Rakesh, 2018; Kumar 2019a, 2019b; Manojkumar and Kumar, 2020; Kumar and Sekhar, 2005; Kumar et al, 2006; Sekhar and Kumar, 2006; Sekhar et al, 2006; Kumar, 2008; Kumar et al, 2008; Kumar, 2009; Natarajan and Kumar, 2010; Natarajan and Kumar, 2011a; 2011b; Natarajan and Kumar, 2012a, 2012b; Renu and Kumar, 2012; Kumar, 2014a, 2014b; Natarajan and Kumar, 2014a, 2014b; Renu and Kumar, 2014; Nikhil and Kumar, 2015a, 2015b; Natarajan and Kumar, 2015; Kumar, 2015; Kumar and Rakesh, 2015; Kumar et al, 2016; Renu and Kumar, 2016a, 2016b; Kumar, 2016; Rakesh and Kumar, 2016; Nikhil and Kumar, 2016; Natarajan and Kumar, 2016a, 2016b; Abhishek et al, 2016; Nikhil and Kumar, 2017; Renu and Kumar, 2017a, 2017b; Natarajan and Kumar, 2018; Bagalkot et al, 2018a, 2018b; Naga babu et al, 2018; Kumar and Ghassemi, 2005; Kumar and Ghassemi, 2006; Ghassemi and Kumar, 2007; Reddy and Kumar, 2014; Sharma et al, 2014a, 2014b; Sivasankar et al, 2014; Kanna et al, 2014; Reddy and Kumar, 2015a, 2015b; Sharma et al, 2015a, 2015b, 2015c; Abhishek et al, 2015; Kidambi and Kumar, 2016; Sivasankar et al, 2016; Kumar and Reddy, 2017; Sivasankar and Kumar 2017a, 2017b; Sivasankar and Kumar, 2018, 2019; Vivek and Kumar, 2016; Vivek et al, 2017, 2019; Vivek and Kumar, 2020; Mohanasundaram et al, 2013a, 2013b; Berlin et al, 2013; Berlin et al, 2014a, 2014b; Berlin et al, 2015a, 2015b, 2015c; Omkar et al, 2016a, 2016b; Mohanasundaram et al, 2017; Berlin et al, 2018a, 2018b; Omkar et al, 2019a, 2019b; Berlin and Kumar, 2019; Mohanasundaram et al, 2019, 2020; Patwardhan et al, 2014; Patwardhan et al, 2015; Patwardhan et al, 2016; Patwardhan et al, 2017a, 2017b; Kidambi et al, 2017; Vasudevan et al, 2014a, 2014b; Vasudevan et al, 2015; Vasudevan et al, 2016a, 2016b, 2016c; Vasudevan et al, 2017; Renu and Kumar 2018a, 2018b, 2018c; Rajasekhar et al, 2018; Renu and Kumar, 2019).‘Fluid flow through a porous medium’ is fundamentally different from the concept of ‘fluid flow through pipes’ in the sense that the flow through a porous medium is associated with a hydraulic head with an insignificant kinetic head. All the kinetic head in a porous medium gets dissipated as it passes through the complex network of solid grains. The presence of these solid grains or solid phase within the flow regime is fundamental to the concept of ‘porosity’ that makes distinct from the concept of ‘fluid flow through pipes’. Since, these solid grains do not form a regular solid boundary
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