Post shut-in arrest and recession solutions for a deflating hydraulic fracture in a permeable elastic medium

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