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Darcy's law is an equation that describes the flow of a fluid through a porous medium and through a Hele-Shaw cell.The law was formulated by Henry Darcy based on results of experiments [1] on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences.
Before we start the conversion, we notice that both the original (single phase) the flow equation of Darcy and the generalized (or extended) multiphase flow equations of Muskat et al. are using reservoir velocity (volume flux), volume rate and densities.
Contrary to the linear reservoir, the non linear reservoir has a reaction factor A that is not a constant, [3] but it is a function of S or Q (figure 2, 3). Normally A increases with Q and S because the higher the water level is the higher the discharge capacity becomes.
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. [1] The term black-oil refers to the fluid model, in which water is modeled explicitly together with two hydrocarbon components, one (pseudo) oil ...
If the fluid is flowing out of a reservoir, the sum of all forms of energy is the same because in a reservoir the energy per unit volume (the sum of pressure and gravitational potential ρ g h) is the same everywhere. [6]: Example 3.5 and p.116 Bernoulli's principle can also be derived directly from Isaac Newton's second Law of Motion. When ...
is the bulk volume of that portion of the aquifer from which the water is released ([L 3]); is the volume of water released from storage ([L 3]); is the decline in pressure(N•m −2 or [ML −1 T −2]) ; is the decline in hydraulic head ([L]) and
Therefore, gas volume may alternatively be expressed excluding the humidity content: V d (volume dry). This fraction more accurately follows the ideal gas law. On the contrary, V s (volume saturated) is the volume a gas mixture would have if humidity was added to it until saturation (or 100% relative humidity).
Volumetric flow rate is defined by the limit [3] = ˙ = =, that is, the flow of volume of fluid V through a surface per unit time t.. Since this is only the time derivative of volume, a scalar quantity, the volumetric flow rate is also a scalar quantity.