# Research Status and Development Direction of Formation Damage Prediction and Diagnosis Technologies
## 3 Laboratory Tests and Numerical Approach Method
### Mathematical Modeling Method
Although this method can achieve a quantitative diagnosis of each damage factor, it has many disadvantages, such as difficulties in obtaining representative experimental cores, significant differences between the core properties used in the experiments and the formation rock properties after the field has been developed for a period of time, time-consuming experiments and large workload, lack of universality of mathematical models for each damage factor, and large errors when comparing diagnostic  
Figure 5: Cumulative pore space variation in cores measured by NMR [74]. results and real damage. In 2010, [PERSON] et al. [84] considered a low-permeability gas formation in the Ordos Basin as an example, and manually selected 12 parameters reflecting four types of properties: formation lithology, physical properties, cement type, and microscopic pore structure. This was done to constitute a set of factors for the second-level fuzzy multi-objective comprehensive judgment (different degrees of water-lock damage constitute the judgment set). They used the fuzzy complementary judgment matrix to determine the weights of each factor and utilized the ridge-shaped function to obtain a comprehensive judgment matrix, thus constructing a second-level multi-objective comprehensive judgment to substantially reduce the experimental workload of gas-water two-phase seepage and save costs. In 2011, [PERSON] et al. [85] used hierarchical analysis to assign weights to the influencing factors of formation sensitivity damage in order to improve the accuracy of the rapid formation damage prediction method. With the development of 2D and 3D imaging techniques, an increasing number of scholars started to combine imaging techniques with mathematical models for formation damage description. [PERSON] and [PERSON] [86], [PERSON] et al. [87], [PERSON] [88], [PERSON] et al. [89], [PERSON] [90], [PERSON] et al. [91], and [PERSON] et al. [92] combined petrographic analysis techniques (cast thin section, scanning electron microscopy, X-ray diffraction, X-ray fluorescence spectroscopy, etc.) with dynamic and static filtration loss experiments in drilling fluids to study the variation pattern and its influence of mud-cake properties (thickness, porosity, permeability, compressibility, etc.) and to develop a model for calculating mud-cake parameters. In 2015, [PERSON] et al. [93] also used a combination of mathematical simulations and special experiments to develop a dynamic characteristic model describing the changes in formation properties in the near-well zone due to the intrusion or removal of drilling fluid components. Moreover, they simulated the effects of drilling fluid intrusion-induced sensitivity and rock surface wettability changes on the near-well zone skin coefficient. Although these scholars adopted advanced experimental equipment and observational means (NMR technique, tracer technique, X-ray scanning, mass spectrometry, scattering neutron source, etc.) to study the damage mechanism of different formations from the pore scale (or small-scale, i.e., mesoscopic and microscopic scale) with great advantages, which can reflect the damage mechanism and kinetic characteristics more clearly, they were unable to isolate the proportion of formation damage by drilling fluids from the many damage factors, the proportion of damage caused by sensitivity and wettability changes, etc. In a recent study, [PERSON] et al. [94] incorporated geomechanics into a flow model, where they considered the roles played by overburden stress, oil flow, deviation factor, and Biot coefficient in formation permeability variation. Moreover, they derived a new deviation factor by comparing the nonlinear effects of the classical solution for constant permeability with the decoupling available in the literature. [PERSON] et al. [95] carried out spontaneous seepage experiments and used the Lucas-Washburn model to describe seepage behavior.