Abstract
Porous media like hydrocarbon reservoirs may be composed of a wide variety of rocks with different porosity and permeability. Our study shows in algorithms and in synthetic numerical simulations that the flow pattern of any particular porous medium, assuming constant fluid properties and standardized boundary and initial conditions, is not affected by any spatial porosity changes but will vary only according to spatial permeability changes. In contrast, the time of flight along the streamline will be affected by both the permeability and porosity, albeit in opposite directions. A theoretical framework is presented with evidence from flow visualizations. A series of strategically chosen streamline simulations, including systematic spatial variations of porosity and permeability, visualizes the respective effects on the flight path and time of flight. Two practical rules are formulated. Rule 1 states that an increase in permeability decreases the time of flight, whereas an increase in porosity increases the time of flight. Rule 2 states that the permeability uniquely controls the flight path of fluid flow in porous media; local porosity variations do not affect the streamline path. The two rules are essential for understanding fluid transport mechanisms, and their rigorous validation therefore is merited.
Highlights
Flow analysis in porous media is at the macroscopic scale governed by Darcy’s law
flow paths (FP) are fixated by the particle paths for transient flows and by streamlines for steady flows. Our work provides such proof and validation for the fact that the time of flight (TOF) is controlled by the integrated velocities of fluid particles as they move along the flight path
The aim of our study is to investigate the effect of permeability and porosity on FP and TOF by some systematically designed numerical experiments
Summary
The local flux and velocity are controlled by reservoir parameters such as permeability and porosity and by fluid properties such as density and viscosity. Permeability [m2] is an independent dynamic scaling parameter in Darcy’s law that relates the fluid transmission flux [m−3 s1] through a unit area [m2] by the ratio of the applied pressure gradient [Pa m−1] and the transmitted fluid’s dynamic viscosity [Pa s]. There often exists an empirical relationship between the permeability and porosity for a given porous medium [1,2,3,4]. The Carman-Kozeny relationship is a theoretical model which has limited practical value for reservoirs comprised of rock types with exceptional high porosity and relatively low permeability [8, 9]. Reservoirs properties are often dominated by certain rock types with petrophysical properties that correlate permeability and porosity in certain domains (Figure 1(b))
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