For sediments and rocks, intrinsic permeability (k) includes the influence of all properties of the medium that influence flow, not just the average grain diameter, as was the case with uniform glass spheres. It has L2 units. Intrinsic permeability represents the magnitude of variation in interconnected pore diameters, as well as the extent of branching and reconnecting pore pathways via a linear trajectory called the degree of tortuosity. Tortuosity is a measure of the actual distance travelled, divided by the shortest distance between two places. In general, the larger the diameter of the pores and the more efficiently they are connected to each other (less tortuosity), the greater the intrinsic permeability. In contrast, a porous material with small diameter pores and many bulky interconnected paths (high tortuosity) would have lower intrinsic permeability. Intrinsic permeability can also be calculated if hydraulic conductivity and fluid properties are known by rearranging equation 31. The density and dynamic viscosity of the fluid also influence hydraulic conductivity. The higher the density of a fluid (γ = gρ) and the lower the dynamic viscosity (μ), the higher the hydraulic conductivity. The density of a fluid, γ, is its density multiplied by the gravitational constant ρg, and the dynamic viscosity, μ, is the ratio of the shear stress in a plane to the rate at which the velocity of the fluid changes through the plane (internal resistance to flow). The influence of fluid properties on the value of hydraulic conductivity can be illustrated by visualizing how flow would be affected if two columns filled with Darcy sand were placed under the same hydraulic gradients so that water flows into one and molasses into the other (Freeze and Cherry, 1979). It is believed that the sand in each column has the same structure and number of interconnected pores.

Obviously, the flow of molasses would be slower than that of water. This is because the viscosity of molasses is usually more than a thousand times higher than that of water, while the density of molasses is only about 1.5 times higher than that of water. Amanat U. Chaudhry, in Gas Well Testing Handbook, 2003 Effective permeability is the product of absolute rock permeability and relative permeability. The absolute permeability of the rock is usually measured with 100% water or gas occupying the pore space. However, if there are two or more phases in the pores, the flow of each phase is limited by the other phases. When the saturation of the water or gaseous phases is increased and the oil saturation decreases, the resistance to oil flow increases until the oil stops flowing with its residual oil saturation. Here ∇2 is the Laplace differential operator Σi ∂2/∂xi2, p is the microscopic pressure of the fluid and u is the microscopic velocity vector of the fluid. Consider the porous medium as a stationary and ergodic random set and let ω(x) be the microscopic porosity (ω(x) = 1 in the pores and 0 in the grains).

The solution to the microscopic flow problem across the gamut can be described as the discovery of a stationary random velocity u(x), which satisfies Bruce Hobbs, Alison Ord, in Structural Geology, 2015. For example: If a sand has an intrinsic permeability of 1 × 10-7 cm2 and the water moving through the sand has a temperature of 10 °C, then (from Figure 28): In the above equations, the definitions of sCA and c′ depend on the type of vacuum as defined above. D is the turbulence factor in units of 1/mscfd and is defined in equation 3-18. Equations 3-93 and 3-94 tell us that the influence of turbulence is to increase the pressure drop or pressure drop needed to produce the given gas production rate. Thus, the presence of turbulence reduces the net production of a well. Reducing the velocity of the fluid near the well can minimize the effect of turbulence. If there is no turbulence near the well, there is no turbulence in the reservoir. The fluid velocity near the well can be minimized by increasing the perforated production length hP. Horizontal drilling has the potential to significantly improve the perforated gap and reduce turbulence in the vicinity of the well. The substrate flows through a small part of the porous medium (e.g.

macropores, pipes, fractures or other larger cavities) and moves much faster than the flow through the rest of the porous medium.