# Numerical Heat Transfer Simulation of Oil Shale Large-Size Downhole Heater
## 2 Materials and Methods  
Jilin University implemented two types of heaters, namely a segmental baffle and a helical baffle, in field applications through the establishment of pilot project bases in Nong'an and Fuyu. Both types have operated successfully. The deployment of heaters in the subsurface has indirectly enhanced the efficiency of in situ oil shale conversion, as shown in Figures 1 and 2. To enhance the efficiency of in situ oil shale heating, this paper introduces the design of a large-size helical baffle downhole heater. The heater's physical model (Figure 3) is composed mostly of the heater shell, continuous helical baffle, center tube, and heating rods. Given the vertical orientation of the heater in the borehole, the z-axis was chosen as  
The computational domain in this study adopted no-permeability, no-slip, and adiabatic boundary conditions. Meshing was used to define the heater's mesh, and localized, appropriate refinement was applied in the vicinity of the heating rods and shells. The mesh used was a hexahedral mesh with a quantity of 2,502,315 and a mesh-independent validation grid was utilized to ensure the model converged accurately to meet the accuracy requirements. The air inlet temperature was 283 K and the outlet was a pressure outlet boundary, which followed the constant temperature boundary condition \(T_{w}\) = 873 K.  
In this paper, the following assumptions for numerical simulations were made:  
1. The shell-side fluid was a fully developed turbulent flow in a steady state;
2. The fluid in the helical channel was incompressible;
3. The heat dissipation on the external wall of the shell cylinder was ignored;
4. The heating rods were regarded as walls with a constant heat flux density;
5. The specific heat capacity of air, thermal conductivity, and dynamic viscosity with temperature were fitted by segmented polynomials, and density was considered a constant. The heater shell process gas follows the following equations during flow:  
The mass conservation equation:  
\[\frac{\partial\overline{u}_{i}}{\partial x_{i}}=0 \tag{1}\]  
The momentum conservation equation:  
\[\frac{\partial(\rho\overline{u}_{i})}{\partial t}+\frac{\partial\big{(}\rho \overline{u}_{i}\overline{u}_{j}\big{)}}{\partial x_{j}}=-\frac{\partial \overline{p}}{\partial x_{i}}+\frac{\partial}{\partial X_{j}}\Bigg{(}u_{eff} \frac{\partial\overline{u}_{i}}{\partial x_{j}}-\rho\overline{u}_{i}^{\prime }\cdot\overline{u}_{i}^{\prime}\overline{u}_{j}^{\prime}\Bigg{)} \tag{2}\]  
The energy conservation equation:  
\[\frac{\partial}{\partial t}(\rho E)+\frac{\partial}{\partial x_{i}}(u_{i}( \rho E+p))=\frac{\partial}{\partial x_{i}}\bigg{(}k_{eff}\frac{\partial T}{ \partial x_{i}}\bigg{)}-\sum_{j^{\prime}}h_{j^{\prime}}J_{j^{\prime}}+u_{j} \big{(}\tau_{ij}\big{)}_{eff}+S_{h} \tag{3}\]  
The renormalization group (RNG) \(k\)-\(\epsilon\) model was used to provide fully developed flows with high streamline curvature for the model, and the options 'enhanced wall treatment' and 'thermal effects' were selected. The universal governing equation of the mass, energy, momentum, and RNG \(k\)-\(\epsilon\) turbulent viscosity is expressed as follows:  
\[div(\rho U\Phi)=div(\Gamma_{\Phi}grad\Phi)+S_{\Phi} \tag{4}\]  
where \(U\) is the velocity vector, \(\Phi\) is a universal variable representing, \(u_{i}\), \(T\), \(k\), \(\epsilon\) or another variable, \(\Gamma_{\Phi}\) is a generalised diffusion coefficient, and \(S_{\Phi}\) is a generalised source term. The commercial computational fluid dynamics (CFD) software FLUENT 2020 R2 was used to calculate the shell-side flow and heat transfer. The SIMPLE algorithm was adopted to address the coupling between the velocity and pressure, while the momentum, energy, and turbulence parameters were solved using the second-order upwind scheme. The  
Figure 3: Heater physical model. default values of the under-relaxation factors were used for the pressure, momentum, and turbulent kinetics.