# Research Status and Development Direction of Formation Damage Prediction and Diagnosis Technologies
## 3 Laboratory Tests and Numerical Approach Method
### Numerical Simulation Methods  
The basic principle of the numerical simulation method is based on Darcy's law, material balance theory, convection-diffusion equation, and other principles, used to derive the seepage partial differential equation. Numerical computational methods are used by combining the initial and boundary conditions to discretize the continuous mathematical model and replace the analytical solution of the original partial differential equation with the discrete distribution of field variables. The main numerical computational methods for solving seepage problems are the finite difference method, finite element method, and finite volume method. The finite difference method mainly employs the Taylor series expansion to construct the difference. By combining distinct difference formats in time and space, the difference calculation results can be obtained with different accuracies [96]. The finite element method uses the extreme value principle and division interpolation to select the approximation function and integrate the region in the variational calculation, which has wide adaptability. The discrete equations have a standardized form and are easy to program, but they cannot give a reasonable physical interpretation due to numerous errors encountered when dealing with the requirements of conservation, strong convection, and incompressibility of seepage problems [97; 98]. The finite volume method, on the other hand, allows each grid node in the computational region to be surrounded by a control volume that does not overlap with the other, and divides the control equations for each control volume to obtain the discrete equations [99]. Table 2 shows the pros and cons of common laboratories evaluation and numerical approach for seepage problems resolution. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  
[PERSON] et al. [100] combined a numerical model of gas-liquid two-phase flow velocity versus the average fluid density, dynamic viscosity, formation pressure, surface tension interval, and a numerical model of bacterial biofilm in porous media to study the effect of bacterial biofilm on gas flow in proppant-filled formations. [PERSON] [101] used a finite difference format to solve the formation pressure and fluid saturation profiles for water-based drilling fluid intrusion in the formation and analyzed the effect of formation properties (permeability, porosity, wettability, and fluid viscosity) and drilling conditions (mud-cake shear rate and drilling fluid immersion time) on drilling fluid intrusion by numerical simulations. [PERSON] et al. [102] used numerical simulations to give the characteristics of the variation of inductive logging response in thin sandstone formations during water-based drilling fluid intrusion and concluded that drilling fluid intrusion leads to higher water content saturation than the true value when the formation thickness is less than the longitudinal resolution of inductive logging. [PERSON] et al. [103,104] proposed a quantitative numerical model considering various effects of mud-cake dynamic growth, multiphase seepage, and drilling fluid filtrate intrusion. They combined experiments to determine model parameters and analyzed the effects of sensitive factors, such as mud-cake permeability, mud-cake porosity, drilling fluid solid phase content, relative permeability, capillary pressure, formation permeability, gravity partitioning, and interlayer fugitive flow on drilling fluid intrusion. They used a three-dimensional multiphase flow numerical simulation tool to simulate the array induction logging response characteristics of straight and large-slope wells under drilling fluid intrusion conditions.