Post shut-in arrest and recession solutions for a deflating hydraulic fracture in a permeable elastic medium
Description
This data set provides the numerical solutions generated using an Implicit Moving Mesh Algorithm (IMMA) that has been adapted to include the k-g, r-g multiscale and k and r-vertex asymptotes to model the post-shut-in arrest and recession of a radial hydraulic fracture in a permeable elastic medium. The theory behind this work is described in the paper "The arrest and recession dynamics of a deflating radial hydraulic fracture in a permeable elastic medium" published in the JMPS (https://doi.org/10.1016/j.jmps.2022.104926). For the simulations I set the following parameters to unity: Ep = 1 mup = 1 Cp = 1 Q0 = 1 Since V0 = Q0*ts, from eq (39) in the paper you can vary omega = ts/tmm~ = ts (since all the material parameters in t_mm~ are 1) and choose the value of phi^V that you want by setting Kp as follows: Kp = (TS'*(phi).^(-65/9)).^(1/26); Recall: tmmt = (mup^4*Q0^6/Cp^18/Ep^4)^(1/7); omega = Ts/tmmt; phiV = (Ep^21*mup^5*Cp^10*Q0*Ts/Kp^26)^(9/65); Issue the command load(Extract_Radial_MKC1_Ts_1em3_phi_50); to access the structures Results, which contains the structure Input. The file names embed the two dimensionless parameters: omega=Ts/tmm~=Ts (since tmm~=1) and phiV. To avoid decimal points in the file name I have multiplied the phiV value by 100. So the above data file is for the case omega=10^{-3} and phiV=0.5. Input = struct('Ep',Ep,... % Pa plane strain modulus 'mup',mup,... % Pa*s, alternate fluid viscosity 'Cp',Cp,... % m/s^1/2, alternate Carter's leak-off coefficient 'Kp',Kp,... % Pa*m^1/2, alternate fracture toughness 'Q0',Q0,... % m/s, injection rate 'Ts',Ts,... % shut-in time 'omega',omega,... % dimensionless shut-in time 'phiV',phiV,... % arrest regime parameter 'Nr',Nr,... % number of grid points in r direction 'Nt',itcol); % number of time steps till collapse Results=struct('pt',P(1,1:itcol),... % wellbore pressure versus t 'Rt',R(1:itcol),... % fracture radius versus t 'wt',W(1,1:itcol),... % wellbore aperture versus t 'eta',eta(1:itcol),... % efficiency versus t 'pr',P(:,1:itcol),... % fluid pressure versus r at all times Nt 'wr',W(:,1:itcol),... % fracture width versus r at all times Nt (because of the moving mesh to plot in real space use plot(rho*R(it),wr(:,it))) 'rho',rho,... % lateral spatial coordinate 't',time(1:itcol),... % time 'keyindx',[its ita itd itcol],... % key indices keyindx(1)=its (shut-in index), keyindx(2)=ita (arrest), keyindx(3)=itr (recession), keyindx(4)=itc (collapse) 'Input',Input); % Input Structure
Files
Steps to reproduce
See the following article in the JMPS for a detailed description: https://doi.org/10.1016/j.jmps.2022.104926