Critical aspect of hydraulic fracturing

The hydraulic fracturing is usually referred to the fracking and also it is a gas and oil well development process. In the development process many steps involves like injecting sand, water and other chemicals that is carried out under high pressure into the bedrock formation through the well. Through repeating this process the fractures can be extended and new fractures can be created. By repeating the process new fractures can be created in the rock for increasing the size, Connectivity and extent of the existing fractures. This well simulation technique is used in low permeability rocks to make a proper flow for the oil and gas to a well from the petroleum bearing rock formation (Zhao, 2010).

MATLAB code for the calculation of all 1600 Fractures

(R.Masoomi, 2014)

Given data

Pore pressure= 2500 psi

Minimum horizontal stress around the lateral= 6500 psi

Minimum horizontal stress around = 6900 psi

Maximum horizontal stress = N57 0E

Fraction dip angle = 90o

Coefficient of fraction u= 0.6

function fracture2DP3D

G=2500;             % Shear modulus        [psi]

v=.2;               % Drained Poisson's ratio

mu=1;               % Fluid viscosity      [cp]

Zi=6500;            % In-situ stress       [psi]

Q=75;               % Pumping rate         [bbl/min]

h=3;                % Fracture height      [ft]

rw=.3;              % Wellbore radius      [ft]

tf=input('How much time is passed? \n hint best results 0.5<t<10 \n Enter time as min(0.25<=t):');

tic;

 [Tkgd, pkgd]= KGD (tf,G,Q,v,mu,Zi);

[Tpkn, ppkn]= PKN (tf,G,Q,v,mu,h);

[T3,p3]=TD(tf,G,Q,mu,Zi,rw,h);

figure(1)

set(1,'name','WELLBORE PRESSURE vs TIME in 2D and P3D MODELS','numbertitle','off')

    subplot(311)

      plot(pkgd,Tkgd);

       ylabel('Pressure [psi], KGD MODEL');

       xlabel('time [min]');

    subplot(312)

       plot(ppkn,Tpkn)

       ylabel('net Pressure [psi], PKN MODEL');

       xlabel('time[min]');

    subplot(313)

       plot(p3,T3)

       ylabel('Wellbore Pressure [psi], P3D')

       xlabel('time [min]')    

toc

disp('Auf wieder sehen')

end

MATLAB Code for the Mohr’s Plot

function [sigma_mohr,tau_mohr,sigma_1,sigma_2,tau_1,tau_2...

    ,center_circle,phi]=mohr(sigma_x,sigma_y,tau_xy,gridsize)

phi=linspace(0,pi,gridsize);

sigma_mohr=(sigma_x+sigma_y)/2+(sigma_x-sigma_y)/2*cos(2*phi)+...

    tau_xy*sin(2*phi);

tau_mohr=-(sigma_x-sigma_y)/2*sin(2*phi)+...

    tau_xy*cos(2*phi);

sigma_1=(sigma_x+sigma_y)/2-sqrt(((sigma_x-sigma_y)/2)^2+tau_xy^2);

sigma_2=(sigma_x+sigma_y)/2+sqrt(((sigma_x-sigma_y)/2)^2+tau_xy^2);

tau_1=sqrt(((sigma_x-sigma_y)/2)^2+tau_xy^2);

tau_2=-tau_1;

center_circle=(sigma_x+sigma_y)/2;

%phi_p=atan(2*tau_xy/(sigma_x-sigma_y))/2;

end

 sigma_x=150;sigma_y=50;tau_xy=50;

gridsize=1000;

[sigma_mohr,tau_mohr,sigma_1,sigma_2,tau_1,tau_2,...

    center_circle,phi]=mohr(sigma_x,sigma_y,tau_xy,gridsize);

%%

figure;

plot(sigma_mohr,tau_mohr);

grid on;

axis equal;

xlabel('Normal Stess, MPa');

ylabel('Shear Stress, MPA');

title('Mohr 2D Circle');

hold on;

plot(sigma_1,0,'r*',sigma_2,0,'r*',...

    center_circle,tau_1,'ro',center_circle,tau_2,'ro',...

    center_circle,0,'r^');

%%

figure;

plot(phi*180/pi,sigma_mohr,'b',phi*180/pi,tau_mohr,'g');grid on;

xlabel('Cut plane angle (deg)');

ylabel('Stress, MPA');

legend('Normal Stress','Shear Stress')

title('Mohr 2D Circle');

Reference of Critical aspect of hydraulic fracturing

R.Masoomi, I. B. (2014). New Technique for Calculation of Well Flowing Performance in Hydraulically Fractured Wells. International Journal of Petroleum and Geoscience Engineering (IJPGE), ISSN , 2289-4713.

Zhao, X. (2010). Imaging the mechanics of hydraulic fracturing in naturally-fractured reservoirs using induced seismicity and numerical modeling. PhD diss.