Object$-$Oriented Programming

In this lab, we will learn to:

Overload operators

Create a representation of the mathematical concept of a vector

Perform operations on vectors.

In mathematics, a vector is a quantity with both direction and magnitude. In an Euclidean plane $($xy$-$plane$)$ a vector can be represented as the amount of movement in the x direction plus the amount in the y direction. Some examples of vectors are

$v1=3x+2y,$

$v2=-2x+6y,$ and

$v3=4x($which is the same as $v3=4x+0y).$

In this lab we are going to write a Vector class.

A generic vector is of the form $v=ax+by$ where a and $b$ are constants.

You must implement the instance variables and methods described below.

You may implement any others to make the class work more effectively.

Create the Vector class in a file named

VectorClass.py

$\backslash$table$[[$Vector$],[],[$init$\_\_],[$magnitude$],[\_],[],[$str$\_],[]]$

Download the

VectorTester.py from D$2$L$.$

In the

VectorTester.py file, you'll need to implement the three vectors defined above $(v1,v2,v3).$

Once each test passes, upload your

VectorClass.py file to D$2$L$.$Object$-$Oriented Programming

In this lab, we will learn to:

Overload operators

Create a representation of the mathematical concept of a vector

In mathematics, a vector is a quantity with both direction and magnitude. In an Euclidean plane $($xy$-$plane$)$ a vector can be represented as the amount of movement in the x direction plus the amount in the y direction. Some examples of vectors are

$v1=3x+2y,$

$v2=-2x+6y,$ and

$v3=4x($which is the same as $v3=4x+0y).$

In this lab we are going to write a Vector class.

A generic vector is of the form $v=ax+by$ where a and $b$ are constants.

You must implement the instance variables and methods described below.

You may implement any others to make the class work more effectively.

Create the Vector class in a file named

VectorClass.py

$\backslash$table$[[$Vector$],[],[$init$\_\_],[$magnitude$],[\_],[],[$str$\_],[]]$

Download the

VectorTester.py from D$2$L$.$

In the

VectorTester.py file, you'll need to implement the three vectors defined above $(v1,v2,v3).$

Once each test passes, upload your

VectorClass.py file to D$2$L$.$

A $1-$D$,$ Two$-$phase flow simulation is used to demonstrate the IMPES method

$1\mathrm{.}127{10}^{-3}\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{x}}[\frac{KA{K}_{ro}}{{}_o{B}_o}\frac{del{P}_o}{\text{d}\text{e}\text{l}\text{x}}]+q_o^{**}=\frac{\frac{O}{A}}{5\mathrm{.}615B_o}[\frac{del{S}_o}{\text{d}\text{e}\text{l}\text{t}}+S_o(C_o+C_r)\frac{del{P}_o}{\text{d}\text{e}\text{l}\text{t}}](oil$ balance$)$

$1\mathrm{.}127{10}^{-3}\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{x}}[\frac{KA{K}_{rw}}{{}_w{B}_w}\frac{del{P}_w}{\text{d}\text{e}\text{l}\text{x}}]+q_w^{**}=\frac{\frac{O}{A}}{5\mathrm{.}615B_w}[\frac{del{S}_w}{\text{d}\text{e}\text{l}\text{t}}+S_w(C_w+C_r)\frac{del{P}_w}{\text{d}\text{e}\text{l}\text{t}}](water$ balance$)$

First, the 'pressure equation' will be obtained by $(\frac{B_d}{B_w})$ oil balance $+$ water balance. If we neglect the capillary pressure and assume that $B_o=B_w=1,$ the obtained pressure equation is:

$\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{x}}[5\mathrm{.}6151\mathrm{.}127{10}^{-3}\frac{KA{K}_{ro}}{{}_o}\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{x}}]+5\mathrm{.}615q_o^{**}+\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{x}}[5\mathrm{.}6151\mathrm{.}127{10}^{-3}\frac{KA{K}_{rw}}{{}_w}\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{x}}]+5\mathrm{.}615q_w^{**}=$

$\frac{O}{A}{C}_t\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{t}}$

Then discrete the pressure equation using implicit scheme $)=(5\mathrm{.}6151\mathrm{.}127{10}^{-3}$ :

$\frac{1}{x_i}[(\frac{KA{K}_{ro}}{{}_o}\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{x}}{)}_{x_{i+0\mathrm{.}5}}-(\frac{KA{K}_{ro}}{{}_o}\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{x}}{)}_{x_{i-0\mathrm{.}5}}]+\frac{1}{x_i}[(\frac{KA{K}_{rw}}{{}_w}\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{x}}{)}_{x_{i+0\mathrm{.}5}}-(\frac{KA{K}_{rw}}{{}_w}\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{x}}{)}_{x_{i-0\mathrm{.}5}}]$

$+5\mathrm{.}615q=\frac{O}{A_i}{C}_t\frac{P_i^{n+1}-P_i^n}{t}$

Transmissibility, $T^o=\frac{KA{K}_{ro}}{{}_{o}x},T^w=\frac{KA{K}_{rw}}{{}_{w}x},T=T^o+T^w,$ then the above equation can be written as:

$[T_{i+0\mathrm{.}5}^o(P_{i+1}^{n+1}-P_i^{n+1})-T_{i-0\mathrm{.}0}^o(P_i^{n+1}-P_{i-1}^{n+1})]+[T_{i+0\mathrm{.}5}^w(P_{i+1}^{n+1}-P_i^{n+1})-T_{i-0\mathrm{.}5}^w(P_i^{n+1}-P_{i-1}^{n+1})]+5\mathrm{.}615Q$

$,=\frac{O}{V_i}{C}_t\frac{P_i^{n+1}-P_i^n}{t}$

$,-T_{i-0\mathrm{.}5}{P}_{i-1}^{n+1}+(T_{i-0\mathrm{.}5}+T_{i+0\mathrm{.}5})P_i^{n+1}-T_{i+0\mathrm{.}5}{P}_{i+1}^{n+1}+\frac{V_i{C}_t}{t}{P}_i^{n+1}=\frac{V_i{C}_t}{t}{P}_i^n+5\mathrm{.}615Q_i$

If $i=1$ :

$-T_{0\mathrm{.}5}{P}_0^{n+1}+(T_{0\mathrm{.}5}+T_{1\mathrm{.}5})P_1^{n+1}-T_{1\mathrm{.}5}{P}_2^{n+1}+\frac{V_1{C}_t}{t}{P}_1^{n+1}=\frac{\frac{O}{V_1}{C}_t}{t}{P}_1^n+5\mathrm{.}615Q_1$

If $i=2N-1$