## 3 Materials and Methods
### Coupled Seepage Field-Stress Field Modeling  
A multi-field fully coupled simulation method is developed based on porous elasticity theory, the finite element method, and the consideration of the microscopic seepage mechanism of shale oil by combining the seepage equations in the porous medium with the equilibrium equations of the rock and the eigen equations. This approach is intended to address the issues of dredging and the stress reorientation of residual oil following initial fracture recovery. According to the notion, the rock skeleton is elastic, linear, and conforms to the [PERSON] porous elasticity theory [32]. Shale oil has an adsorption impact, and the combined effects of pore pressure and effective stress, as well as the combined effects of fracture opening and closing, affect permeability [33]. The 3D constitutive equation based on [PERSON]'s effective stress concept has the following component form:  
\[\begin{cases}\sigma_{xx}=C_{11}\epsilon_{xx}+C_{12}\epsilon_{yy}+C_{13} \epsilon_{zz}+C_{14}\gamma_{xy}+C_{15}\epsilon_{yz}+C_{16}\epsilon_{xy}\\ \sigma_{yy}=C_{21}\epsilon_{xx}+C_{22}\epsilon_{yy}+C_{23}\epsilon_{zz}+C_{24} \gamma_{xy}+C_{25}\epsilon_{yz  
where \(\sigma\) is the stress tensor; \(C\) is the elastic stiffness matrix; and \(\epsilon\) is the strain tensor. The stress field's equilibrium equation, which takes the seepage volume force into account, is provided by  
\[ \begin{cases}\frac{\partial\sigma_{xx}}{\sigma_{x}}+\frac{\partial\tau_{xy}}{ \partial\sigma}+\frac{\partial\tau_{xz}}{\sigma_{z}}-\alpha\frac{\partial p}{ \sigma_{x}}=0\\ \frac{\partial\sigma_{xx}}{\sigma_{x}}+\frac{\partial\tau_{xy}}{\partial \sigma}+\frac{\partial\tau_{xz}}{\sigma_{z}}-\alpha\frac{\partial p}{\sigma_{y }}=0\\ \frac{\partial\tau_{xx}}{\sigma_{x}}+\frac{\partial\tau_{xy}}{\partial \sigma}+\frac{\partial\tau_{yz}}{\sigma_{z}}-\alpha\frac{\partial p}{\sigma_{z }}=0\end{cases}  \tag{8}\]  
The compatibility equation, or the relationship between the displacement field and the strain tensor, is [34]:  
\[\text{Displacement field }\mathbf{U}=(u,v,w) \tag{9}\]  
\[\text{Strain-displacement relationship }\mathbf{\varepsilon}=\frac{1}{2}\Big{(}\
abla\mathbf{U}+( \
abla\mathbf{U})^{\text{T}}\Big{)} \tag{10}\]  
Component form of the compatibility equation:  
\[ \begin{cases}\begin{aligned} \varepsilon_{xx}=\frac{\partial u}{ \partial x},\varepsilon_{yy}=\frac{\partial u}{\partial y},\ \varepsilon_{zz}=\frac{\partial u}{ \partial z}\\ \gamma_{xy}=\frac{\partial u}{\partial y}+\frac{\partial p}{\partial x},\ \gamma_{yz}=\frac{ \partial p}{\partial z}+\frac{\partial u}{\partial y},\ \gamma_{zx}=\frac{ \partial w}{\partial x}+\frac{\partial u}{\partial z}\end{aligned}\end{cases}  \tag{11}\]  
The microscopic seepage mechanism of shale oil in combination with [PERSON]'s law, the impact of pore changes on permeability, and the response of stress variations on fluid flow must all be taken into account when discussing seepage. [PERSON]'s seepage law governs how pore fluids leak through porous media:  
\[\{v\}=-[K]\{\
abla h\} \tag{12}\]  
Continuity equations for pore fluids:  
\[\
abla^{\text{T}}\{v\}-Q=\{m\}^{\text{T}}\alpha\frac{\partial\epsilon}{ \partial t}+\Bigg{[}\frac{(n-1)}{K_{s}}+\frac{n}{K_{w}}-\frac{k_{T}}{(K_{s})^{ 2}}\Bigg{]}\frac{\partial p}{\partial t} \tag{13}\]  
Ordinary differential equation form:  
\[ \begin{bmatrix}0&0\\ 0&[Kp]\end{bmatrix}\begin{Bmatrix}\{u\}\\ P\end{Bmatrix} + \begin{bmatrix}[K]&[C]\\ [C]^{T}&CP\end{bmatrix} \frac{d}{dt} \begin{Bmatrix}\{u\}\\ P\end{Bmatrix} = \begin{Bmatrix}\{dF/dt\}\\ \{Q\}+\{G\}\end{Bmatrix}  \tag{14}\]  
The updated porosity and permeability equations are [35]:  
\[\varnothing=\frac{\varnothing_{0}-\Delta\varnothing}{1-\Delta\varnothing}\qquad[K ]=[K_{0}]\frac{\varnothing^{3}/(1-\varnothing)^{2}}{\varnothing_{0}^{3}/(1- \varnothing_{0})^{2}} \tag{15}\]  
The equations for the seepage field and stress field are completely coupled.