- #1

roesbak

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Hi there,

I am working on a project in a subject called "Multiphase Flow in Pipes." We are to make a "simulator", describing the pressure (step-wise) in a pipe inserted vertically into water. Air is injected at the bottom of the pipe with a given mass rate, m, and for simplicity, ideal gas, no slip conditions, and a given QL (liquid flow rate) are assumed. The pressure-losses taken into account are hydrostatic and friction only. (I can explain further on request, but my problem is, I hope, code-related, and not physics :P)

I started writing what I thought was a fairly simple piece of "code", and decided to test my program with one given m and QL. However, based on my graph, it looks as though the pressure-drop upwards in the pipe is constant, and does not change, no matter what m and QL I try.

I think I may have done something wrong in my "for" loop, but since I am very inexperienced with Matlab, I thought I would ask if anyone might give me a small pointer..

Code follows:

------------------------------

clf

% First, we set up the main constants

g = 9.81;

h = 50;

D = 0.15;

rhoL = 1000;

P(1) = 1*10^5 + (rhoL*h*g);

Ptop = 1.013*10^5;

Pref = 1.013*10^5;

nu = 1.5*10^-5;

viscL = 0.001;

rhoref = 1.2;

% Then we start entering the equations necessary to iterate.

dH = 0.5;

H = 0:dH:h;

NH = length(H);

m = 1;

ql = 0.001;

for i = 2:NH % Loop, upwards in the well.

% Calculate gas density and friction pressure drop

rhoG = rhoref * (P(i-1)/Pref); % density of gas

qg = (m/rhoG); % volumetric flow rate of gas

EG = (qg)/(qg + ql); % gas fraction

EL = (ql)/(qg + ql); % liquid fraction

rhom = (EL * rhoL) + (EG * rhoG); % density of gas/liquid mixture

viscm = (EL * viscL) + (EG * rhoG * nu); % viscosity of gas/liquid mixture

U = (ql+qg)/((pi/4)*D^2); % flow speed

phyd = rhom * g; % hydrostatic pressure loss

pfrict = (4/D) * 0.046 * ((rhom*U*D)/(viscm))^(-0.2); % frictional pressure loss

ptot = phyd + pfrict; % total pressure loss

P(i) = P(i-1) - (ptot*dH)

end

figure(1)

plot(H,P)

---------------------------------------

Thank you very much for your time.

Yours

André Røsbak

I am working on a project in a subject called "Multiphase Flow in Pipes." We are to make a "simulator", describing the pressure (step-wise) in a pipe inserted vertically into water. Air is injected at the bottom of the pipe with a given mass rate, m, and for simplicity, ideal gas, no slip conditions, and a given QL (liquid flow rate) are assumed. The pressure-losses taken into account are hydrostatic and friction only. (I can explain further on request, but my problem is, I hope, code-related, and not physics :P)

I started writing what I thought was a fairly simple piece of "code", and decided to test my program with one given m and QL. However, based on my graph, it looks as though the pressure-drop upwards in the pipe is constant, and does not change, no matter what m and QL I try.

I think I may have done something wrong in my "for" loop, but since I am very inexperienced with Matlab, I thought I would ask if anyone might give me a small pointer..

Code follows:

------------------------------

clf

% First, we set up the main constants

g = 9.81;

h = 50;

D = 0.15;

rhoL = 1000;

P(1) = 1*10^5 + (rhoL*h*g);

Ptop = 1.013*10^5;

Pref = 1.013*10^5;

nu = 1.5*10^-5;

viscL = 0.001;

rhoref = 1.2;

% Then we start entering the equations necessary to iterate.

dH = 0.5;

H = 0:dH:h;

NH = length(H);

m = 1;

ql = 0.001;

for i = 2:NH % Loop, upwards in the well.

% Calculate gas density and friction pressure drop

rhoG = rhoref * (P(i-1)/Pref); % density of gas

qg = (m/rhoG); % volumetric flow rate of gas

EG = (qg)/(qg + ql); % gas fraction

EL = (ql)/(qg + ql); % liquid fraction

rhom = (EL * rhoL) + (EG * rhoG); % density of gas/liquid mixture

viscm = (EL * viscL) + (EG * rhoG * nu); % viscosity of gas/liquid mixture

U = (ql+qg)/((pi/4)*D^2); % flow speed

phyd = rhom * g; % hydrostatic pressure loss

pfrict = (4/D) * 0.046 * ((rhom*U*D)/(viscm))^(-0.2); % frictional pressure loss

ptot = phyd + pfrict; % total pressure loss

P(i) = P(i-1) - (ptot*dH)

end

figure(1)

plot(H,P)

---------------------------------------

Thank you very much for your time.

Yours

André Røsbak

Last edited: