WRITE AN ESSAY OF UP TO 100 KB, 2-4 PAGES, REGARDING THE USE OR USEFULNESS OF FIRST ORDER OR SECOND...

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WRITE AN ESSAY OF UP TO 100 KB, 2-4 PAGES, REGARDING THE USE OR USEFULNESS OF FIRST ORDER OR SECOND ORDER DIFFERENTIAL EQUATIONS FOR Petroleum Engineering. You do not have to write any equations, but real-world examples (or statements of problems) are encouraged. If you write any equations, use an editor so that the doc will not exceed 100KB. "

David · Accepted Answer

Usefulness of Differential Equation for Petroleum Engineering 
Let say a function y=f(x) represents some process or some phenomenon. Most of the time it can 
happen that it may not be possible to establish direct explicit relation between  y and s x, but it is 
possible to give the relation between the quantities x and y and the derivatives of y with respect 
to x: y’, y”,….y
(n)
. That is, we are able to write a differential equation. From the relationship 
established between the variables x, y and the derivatives it is required to determine the direct 
dependence of y on x. They have wide range of applications in physics and engg. Here we are 
going to discuss application of differential equation in petroleum Engg. 
The dynamics of fluids in porous materials is a phenomenon of curiosity in many disciplines, 
amongst them soil science, ground water hydrology, petroleum reservoir engineering and 
chemical engineering.  
Darcy’s law is the one of the basic laws which governs dynamics of fluids in porous material 
 Q =CAΔ(P −ρgz)/L, 
where: P = pressure [Pa], ρ = density [kg/m3], g = gravitational acceleration [m/s2], z = vertical 
coordinate (measured downwards) [m], L = length of sample [m], Q = volumetric flowrate 
[m3/s], C = constant of proportionality [m2/Pa s], A = cross-sectional area of sample [m2].  
Darcy’s law in itself does not contain sufficient information to allow us to solve transient 
dynamics (i.e., time-dependent) problems involving subsurface flow. In order to develop a 
complete equation we must consider conservation of mass.

WRITE AN ESSAY OF UP TO 100 KB, 2-4 PAGES, REGARDING THE USE OR USEFULNESS OF FIRST ORDER OR SECOND ORDER DIFFERENTIAL EQUATIONS FOR Petroleum Engineering. You do not have to write any equations, but...

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