How to correctly code the expression with Ei function?

[Ein Krieger]

Hi,

I am trying to incorporate the following equation into Matlab in the red:

http://http://www.radikal.ru][PLAIN]http://s018.radikal.ru/i518/1305/16/1cc0d2a72d38.jpg

The following data is to be used:
t=3000000
nr=nx=161
q=0.02
k=5e-13
mu=0.00035
c=1.5e-8
phi=0.25
rw=0.1
h=4.5


My code is below:
st=size(t)
nr=nx;
for i=1:1:st(1)
rd=r(1:nr)/wb
td=0.0036*k*t(i)/(phi*mu*c*wb^2)
pd=((pi*h*k)/(1.842*q*1.1*mu))*(IP-p(i,1:nr))
Ei_from_mfun=mfun('Ei',1,-rd^2/(4*td))
pd=1/2*Ei_from_mfun
plot(time,pd,'bo')
end

But it gives the following command :
"? Index exceeds matrix dimensions."

Can you please help to fix the problem for every time, t and pressure,p?

Thanks

 

[Solkar]

Provide the analytic formulation and tidy your code a little, pls.
E.g. comments and indentation would not hurt; there a "code tags" button in the editor widget you can use to preserve indentation blanks in the code block.

 

[Ein Krieger]

Provide the analytic formulation and tidy your code a little, pls.
E.g. comments and indentation would not hurt; there a "code tags" button in the editor widget you can use to preserve indentation blanks in the code block.

Here is the equation to be solved :

The red equation belowi the analytical solution I want to get solution for.

The data to be used:
The following data is to be used:
t=3000000
r=nr=nx=161
q=0.02
k=5e-13
mu=0.00035
c=1.5e-8
phi=0.25
rw=0.1
h=4.5

My code is below:

st=size(t)
nr=nx;
for i=1:1:st(1)
rd=r(1:nr)/wb
td=0.0036*k*t(i)/(phi*mu*c*wb^2)
pd=((pi*h*k)/(1.842*q*1.1*mu))*(IP-p(i,1:nr))
Ei_from_mfun=mfun('Ei',1,-rd^2/(4*td))
pd=1/2*Ei_from_mfun
plot(time,pd,'bo')
end

But it gives the following command :
"? Index exceeds matrix dimensions."

 

[kreil]

t is a constant.

st=size(t) is then equal to [1 1]

the for loop runs through for i=1, but then halts on i=2 because you have t(i), and t(2) doesn't exist.

 

[alphy]

for reaching out! I can definitely help you with your code.

First, let's take a look at the equation that you are trying to code:

http://s018.radikal.ru/i518/1305/16/1cc0d2a72d38.jpg

This equation involves several variables, including t, nr, q, k, mu, c, phi, rw, and h. It also includes the Ei function, which is the exponential integral function.

To correctly code this expression, you will need to first define all of the variables and their corresponding values, as you have already done in your code. Then, you will need to use the Ei function to calculate the value of pd for each time step.

Here is an example of how you can code this expression in Matlab:

% Define variables
t = 3000000; % time
nr = 161; % number of points
q = 0.02; % flow rate
k = 5e-13; % permeability
mu = 0.00035; % viscosity
c = 1.5e-8; % compressibility
phi = 0.25; % porosity
rw = 0.1; % well radius
h = 4.5; % height

% Calculate pd for each time step
for i = 1:length(t)
rd = (1:nr)/wb;
td = 0.0036*k*t(i)/(phi*mu*c*wb^2);
pd = ((pi*h*k)/(1.842*q*1.1*mu))*(IP - p(i,1:nr));
pd = 1/2*expint(-rd.^2/(4*td));
plot(time,pd,'bo');
end

Note that I have used the "expint" function in place of the "Ei" function, as it is the equivalent in Matlab. Also, I have used the "length" function to determine the number of time steps instead of "size", as it returns the total number of elements in the vector t.

I hope this helps and please let me know if you have any further questions or if you encounter any other issues with your code.