Darcy s Law

Keywords compressibility, primary-, secondary- and enhanced oil-recovery, drive mechanisms (solution gas-, gas cap-, water-drive), secondary gas cap, first production date, build-up period, plateau period, production decline, water cut, Darcy s law, recovery factor, sweep efficiency, by-passing of oil, residual oil, relative permeability, production forecasts, offtake rate, coning, cusping, horizontal wells, reservoir simulation, material balance, rate dependent processes, pre-drilling. 

On a microscopic scale, the most important equation governing fluid flow in the reservoir is Darcy s law, which was derived from the following situation. 

A simple law, known as Darcy s law (1936), states that the volume flow rate per unit area is proportional to the pressure gradient if applied to the case of viscous flow through a porous medium treated as a bundle of capillaries,... 

Darcy s Law and the Basic Filtration Equation. Darcy s law combines the constants in the last term of equation 1 into one factor K known as the permeabiHty of the bed, ie. 

Modem filtration theory tends to prefer the Ruth form of Darcy s law, ie,... 

The fundamental case for pressure filters may be made using equation 10 for dry cake production capacity Y (kg/m s) derived from Darcy s law when the filter medium resistance is neglected. Eor the same cycle time (same speed), if the pressure drop is increased by a factor of four, production capacity is doubled. In other words, filtration area can be halved for the same capacity but only if is constant. If increases with pressure drop, and depending how fast it increases, the increased pressure drop may not give much more capacity and may actually cause capacity reductions. 

This form of Darcy s law is appHcable only to saturated flow. As discussed earlier, there are distinctions between the state of soil water in the saturated and unsaturated regions. These distinctions lead to an alternative form of Darcy s law for the case of unsaturated flow (2,5). 

When pure water is forced through a porous ultrafiltration membrane, Darcy s law states that the flow rate is direcdy proportional to the pressure gradient ... 

Creeping flow (Re <- 1) through porous media is often described in terms or the permeability k and Darcy s Law ... 

Darcy s law has been used to derive an expression which reflects not only the effect of a change in elevation, but also provides a means for estimating changes in air rate resulting from changes in vacuum level and cake thickness (or cake weight per unit areaj. In order for this relationship to hold for changes in vacuum and cake thickness, it must be assumed that both cakes have the same specific resistance. 

The governing flow equation describing flow through as porous medium is known as Darcy s law, which is a relationship between the volumetric flow rate of a fluid flowing linearly through a porous medium and the energy loss of the fluid in motion. 

Darcy s law is considered valid for creeping flow where the Reynolds number is less than one. The Reynolds number in open conduit flow is the ratio of inertial to viscous forces and is defined in terms of a characteristic length perpendicular to flow for the system. Using four times the hydraulic radius to replace the length perpendicular to flow and conecting the velocity with porosity yields a Reynolds number in the form ... 

Heterogeneity, nonuniformity and anisotropy are terms which are defined in the volume-average sense. They may be defined at the level of Darcy s law in terms of permeability. Permeability, however, is more sensitive to conductance, mixing and capillary pressure than to porosity. 

Heterogeneity, nonuniformity and anisotropy are defined as follows. On a macroscopic basis, they imply averaging over elemental volumes of radius e about a point in the media, where e is sufficiently large that Darcy s law can be applied for appropriate Reynolds numbers. In other words, volumes are large relative to that of a single pore. Further, e is the minimum radius that satisfies such a condition. If e is too large, certain nonidealities may be obscured by burying their effects far within the elemental volume. 

Heterogeneity, nonuniformity and anisotropy are based on the probability density distribution of permeability of random macroscopic elemental volumes selected from the medium, where the permeability is expressed by the one-dimensional form of Darcy s law. 

Permeability is the conductance of the medium and has direct relevance to Darcy s law. Permeability is related to the pore size distribution, since the distribution of the sizes of entrances, exits and lengths of the pore walls constitutes the primary resistance to flow. This parameter reflects the conductance of a given pore structure. 

Since flow is through parallel elements of different constant area, Darcy s law for each element, assuming the overall length of each element is equal, is ... 

Go to a standard handbook like Perry s Chemical Engineer s Handbook and obtain several hydraulic conductivities (say for sand, crushed stone, gravel, diatomaceous earth, other). Assume a constant head of fluid over a bed of each material, and apply Darcy s law to calculate flowrates and compare the results. Try several hydraulic head calculations and plot the results. Which of the materials studied shows the highest hydraulic resistance ... 

Sephadex G-lO-G-50 behave as rigid spheres and the maximum linear velocity may be calculated by Darcy s law where U = K i p/L) U is the linear velocity... 

Estimation of the pressure-drop The system is designed to work within a given pressure limit thus, one needs a relation giving the pressure-drop in the column (per unit length). Darcy s law gives the relation of AP/L versus the mobile phase velocity u. However, the Kozeny-Carman equation is best adapted for laminar flows as described ... 

Column length and diameter these are set according to the minimum number of plates required and the maximum acceptable pressure-drop, and calculated by taking into account the constraints given by the Van Deemter and Darcy s laws. 

For accurate determination of pressure drop, the flowrate is measured at 20 ml min f A pressure drop of 5.5 bar was measured, allowing Darcy s law to be expressed as ... 

In the fluid flow model, simulation is based on Darcy s law for the steady flow of Newtonian fluids through porous media. This law states that the average... 

The filtration, or superficial face, velocities used in fabric filters are generally in the range of 1 to 10 feet per minute, depending on the type of fabric, fabric supports, and cleaning methods used. In this range, pressure drops conform to Darcy s law for streamline flow in porous media, which states that the pressure drop is directly proportional to the flow rate. The pressure drop across the... 

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