A cylindrical pore model consists of cylindrical tubes stacked on each other. (A
ID: 1766806 • Letter: A
Question
A cylindrical pore model consists of cylindrical tubes stacked on each other. (Assume overall cross- sectional area is Au and fluid viscosity is , the porosity of the grain (shadowed area) is Note that (1) r and R are the radii but not diameters; (2) the cross-sectional areas for these two sections are not the same. a. Determine the symbolic expression for the porosity of the cylindrical pore model. b. Determine the symbolic expression for average permeability of a serial coupling of two tubes with 3. tube radius r andRExplanation / Answer
A.)
This model considers that Cylindrical consist of both macro and micropores. The magnitude of individual contribution is dependent on their effective cross-sectional areas perpendicular to the direction of diffusion..
The resultant expression for effective diffusivity De is given as
D=DmEm^2+((Eu^2(1+3Em)Du/(1-Em)).
Dm and Du are combined diffusivity in macropores and micropores respectively and obtained by applying equation for combined diffusivity D to macro and micro regions as follows.
B.)
Permeability is a property of the porous medium that measures the capacity and ability of the formation to transmit fluids. The rock permeability, k, is a very important rock property because it controls the directional movement and the flow rate of the reservoir fluids in the formation. This rock characterization was first defined mathematically by Henry D’ Arcy in 1856.
Poiseuille’s equation for viscous flow in a cylindrical tube is a well-known equation
V=D^2*P/(32UL)
v = fluid velocity, cm/sec
d = tube diameter, cm
P = pressure loss over length L,
= fluid viscosity, centipoise
L = length over which pressure loss is measured,
According to the steady state condition
(3.14r^2)-(3.14R^2)(P+P2)-4*3.14*(l+L)T=0
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