In mathematics, de Moivre's formula states that for any real number x and integer n it holds that
Permeability in fluid mechanics and the Earth sciences is a measure of the ability of a porous material to allow fluids to pass through it.
Darcy's law is an equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences. It is analogous to Ohm's law in electrostatics, linearly relating the volume flow rate of the fluid to the hydraulic head difference via the hydraulic conductivity.
In fluid statics, capillary pressure is the pressure between two immiscible fluids in a thin tube, resulting from the interactions of forces between the fluids and solid walls of the tube. Capillary pressure can serve as both an opposing or driving force for fluid transport and is a significant property for research and industrial purposes. It is also observed in natural phenomena.
In petrophysics, Archie's law relates the in-situ electrical conductivity (C) of a porous rock to its porosity and fluid saturation of the pores:
Effective porosity is most commonly considered to represent the porosity of a rock or sediment available to contribute to fluid flow through the rock or sediment, or often in terms of "flow to a borehole". Porosity that is not considered "effective porosity" includes water bound to clay particles and isolated "vuggy" porosity. The effective porosity is of great importance in considering the suitability of rocks or sediments as oil or gas reservoirs, or as aquifers.
In multiphase flow in porous media, the relative permeability of a phase is a dimensionless measure of the effective permeability of that phase. It is the ratio of the effective permeability of that phase to the absolute permeability. It can be viewed as an adaptation of Darcy's law to multiphase flow.
In fluid dynamics, the Buckley–Leverett equation is a conservation equation used to model two-phase flow in porous media. The Buckley–Leverett equation or the Buckley–Leverett displacement describes an immiscible displacement process, such as the displacement of oil by water, in a one-dimensional or quasi-one-dimensional reservoir. This equation can be derived from the mass conservation equations of two-phase flow, under the assumptions listed below.
HydroGeoSphere (HGS) is a 3D control-volume finite element groundwater model, and is based on a rigorous conceptualization of the hydrologic system consisting of surface and subsurface flow regimes. The model is designed to take into account all key components of the hydrologic cycle. For each time step, the model solves surface and subsurface flow, solute and energy transport equations simultaneously, and provides a complete water and solute balance.
Porosity or void fraction is a measure of the void spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure the "accessible void", the total amount of void space accessible from the surface.
The Amott test is one of the most widely used empirical wettability measurements for reservoir cores in petroleum engineering. The method combines two spontaneous imbibition measurements and two forced displacement measurements. This test defines two different indices: the Amott water index and the Amott oil index.
Nuclear magnetic resonance (NMR) in porous materials covers the application of using NMR as a tool to study the structure of porous media and various processes occurring in them. This technique allows the determination of characteristics such as the porosity and pore size distribution, the permeability, the water saturation, the wettability, etc.
In the petroleum industry, special core analysis, often abbreviated SCAL or SPCAN, is a laboratory procedure for conducting flow experiments on core plugs taken from a petroleum reservoir. Special core analysis is distinguished from "routine (RCAL) or conventional (CCAL) core analysis" by adding more experiments, in particular including measurements of two-phase flow properties, determining relative permeability, capillary pressure, wettability, and electrical properties. Due to the time-consuming and costly character of SCAL measurements, routine core analysis (RCAL) data should be inspected thoroughly to select a representative subset of samples for SCAL.
The black-oil equations are a set of partial differential equations that describe fluid flow in a petroleum reservoir, constituting the mathematical framework for a black-oil reservoir simulator. The term black-oil refers to the fluid model, in which water is modeled explicitly together with two hydrocarbon components, one (pseudo) oil phase and one (pseudo-)gas phase. This is in contrast with a compositional formulation, in which each hydrocarbon component is handled separately.
In fluid mechanics, fluid flow through porous media is the manner in which fluids behave when flowing through a porous medium, for example sponge or wood, or when filtering water using sand or another porous material. As commonly observed, some fluid flows through the media while some mass of the fluid is stored in the pores present in the media.
In physics and engineering, the radiative heat transfer from one surface to another is the equal to the difference of incoming and outgoing radiation from the first surface. In general, the heat transfer between surfaces is governed by temperature, surface emissivity properties and the geometry of the surfaces. The relation for heat transfer can be written as an integral equation with boundary conditions based upon surface conditions. Kernel functions can be useful in approximating and solving this integral equation.
Morris Muskat et al. developed the governing equations for multiphase flow in porous media as a generalisation of Darcy's equation for water flow in porous media. The porous media are usually sedimentary rocks such as clastic rocks or carbonate rocks.
In petroleum engineering, TEM, also called TEM-function developed by Abouzar Mirzaei-Paiaman, is a criterion to characterize dynamic two-phase flow characteristics of rocks. TEM is a function of relative permeability, porosity, absolute permeability and fluid viscosity, and can be determined for each fluid phase separately. TEM-function has been derived from Darcy's law for multiphase flow.
In petroleum engineering, Lak wettability index, developed by Abouzar Mirzaei-Paiaman is a quantitative indicator to measure wettability of rocks from relative permeability data. This index is based on a combination of Craig's first rule. and modified Craig's second rule
The Bigoni–Piccolroaz yield criterion is a yielding model, based on a phenomenological approach, capable of describing the mechanical behavior of a broad class of pressure-sensitive granular materials such as soil, concrete, porous metals and ceramics.
