# Experimental Study of Imbibition Characteristics of Silica Sol in Coal-Measure Mudstone Matrix
## 5 Pressureless Imbibition Experiment
### Experimental Principle and Process  
NMR is a physical phenomenon of nuclei in a static magnetic field under the action of another alternating magnetic field. It is a newly emerged testing technique specified by rapid and nondestructive properties, simultaneously. The main parameters include longitudinal relaxation time (\(T_{1}\)) and transverse relaxation time (\(T_{2}\)). Based on the difference of relaxation time, the characteristics of hydrogen proton can be measured quickly and accurately. The measure of \(T_{1}\) is time-consuming,  
Figure 6: Time-varying curves of viscosity with different ratios between silica sol and accelerator (volume).  
so \(T_{2}\) is usually used to reflect the physical properties and fluid characteristics of the sample. Based on NMR diffusion with a surface relaxation model [17], nuclear relaxation in a single pore of a sample can be described by relaxation time.  
\[\frac{1}{T_{2}}=\frac{1}{T_{2B}}+\rho_{2}\frac{S}{V}+\gamma^{2}G^{2}D\tau^{2}/3 \tag{10}\]  
where \(T_{2B}\) is volume (free) relaxation time of liquid; \(\rho_{2}\) is the surface relaxation strength, a parameter to characterize fluid properties in rocks depending on the pore surface properties and mineral composition; \(\frac{S}{V}\) is the specific surface area of a single pore, inversely proportional to the pore radius; \(D\) is the diffusion coefficient; \(G\) is the internal magnetic field gradients; \(\tau\) is echo spacing; and \(\gamma\) is the gyromagnetic ratio.  
The first item on the right side of the formula can be ignored for \(T_{2B}>>T_{2}\). The third item is the diffusion relaxation term, and the experiment used the uniform magnetic field to eliminate the influence of diffusion relaxation. Therefore, it can be simplified into:  
\[\frac{1}{T_{2}}\approx\rho_{2}\frac{S}{V} \tag{11}\]  
Thus, the \(T_{2}\) distribution reflects the distribution of the inner surface of rock and the strength of the fluid force on the surface [18]. Research shows that when \(T_{2}\) is inferior to 10 ms, the fluid in the pores has difficulty flowing because of the larger flow resistance, appearing as bound fluid and containing an adsorption bound state and a capillary bound state. When \(T_{2}\) exceeds 10 ms, the fluid in the pores is movable.  
The apparatus used in the pressureless imbibition experiment is a MesoMR23-060H-I (Figure 7a), produced by Niumag Electronics and Technology Corporation Limited, with a resonance frequency of 23.423 MHz, a magnet temperature of 32.00 \(\pm\) 0.02 \({}^{\circ}\)C, a probe coil diameter of 25 mm, and a lab climate humidity of 68%.  
As shown in Figure 7b, the sample was placed on the porous stone. The sample was then removed for the \(T_{2}\) test after short intervals (a few seconds) early during the testing, then at long intervals (hours) later in the testing. The sample was returned to the porous stone after testing to continue to absorb grout. When the sample became saturated, NMR imaging and SEM imaging were carried out. The total duration was 9 days.  
Figure 7: Spontaneous imbibition device. (**a**) Schematic plot of MesoMR23-060H-I; (**b**) schematic diagram of experiment.