# NMR Evaluation of Shale Oil Mobility: Combined Pyrolysis and CO\({}_{2}\) [PERSON]
## 2 Materials and Methods
### Theory of 2D NMR Component Analysis  
NMR occurs when a brief, periodic radiofrequency pulse is applied perpendicularly to the main magnetic field. If the pulse matches the precession frequency of protons, it causes them to absorb energy and transition to a higher energy state. This leads to a directional change in the macroscopic magnetization vector. Following the pulse, longitudinal (\(T_{1}\)) and transverse (\(T_{2}\)) relaxation processes take place. \(T_{1}\) relaxation is the gradual return of the magnetization vector to its original equilibrium position under the main magnetic field, with the \(T_{1}\) time defined as the time needed for the vector to recover to approximately 63% of its maximum value. Conversely, \(T_{2}\) relaxation is attributed to the decay in the transverse magnetization vector due to microenvironmental magnetic field fluctuations around proton groups. The \(T_{2}\) value is the time for the transverse magnetization vector to decay to 37% of its maximum value under ideal homogeneous external magnetic field conditions. In shale NMR testing, \(T_{1}\) and \(T_{2}\) relaxation are the main factors affecting the results [32]. For low-viscosity fluids within pores, relaxation times are primarily related to the size of the pores, expressed as follows:  
\[\frac{1}{T_{1}}=\frac{1}{T_{1B}}+\rho_{1}\frac{S}{V} \tag{1}\]  
\[\frac{1}{T_{2}}=\frac{1}{T_{2B}}+\rho_{2}\frac{S}{V}+\frac{D(\gamma GT_{E})^{ 2}}{12} \tag{2}\]  
where \(T_{1B}\) represents the longitudinal relaxation time; \(T_{2B}\) represents the transverse relaxation time; \(\rho_{1}\) is the longitudinal surface relaxation rate; \(\rho_{2}\) is the transverse surface relaxation rate; \(S/V\) is the ratio of the pore surface area to volume; \(D\) is the diffusion coefficient; \(\gamma\) is the gyromagnetic ratio; \(G\) is the magnetic field gradient; and \(T_{E}\) is the echo time interval.  
In high viscosity fluids or quasi-solids, relaxation characteristics are affected by intramolecular dipole-dipole interactions. In the kerogen and clay structures of shale samples, there are also \({}^{1}\)H nuclei. The Bloembergen-Purcell-Pound (BPP) model, crucial for clarifying this mechanism, includes and explains the rotational correlation time (\(\tau_{c}\)) and the system's resonant frequency (\(\omega_{0}\)) within molecular dynamics. The processes of spin-lattice relaxation and spin-spin relaxation can be described as follows [33]:  
\[\frac{1}{T_{1}}=\left(\frac{6}{20}\right)\left(\frac{\hbar\gamma_{1}^{2}\gamma _{S}^{2}}{r^{6}}\right)\left(\frac{\tau_{c}}{1+\omega_{0}^{2}\tau_{c}^{2}}+ \frac{4\tau_{c}}{1+4\omega_{0}^{2}\tau_{c}^{2}}\right) \tag{3}\]  
\[\frac{1}{T_{2}}=\left(\frac{3}{20}\right)\left(\frac{\hbar\gamma_{1}^{2}\gamma _{S}^{2}}{r^{6}}\right)\left(3\tau_{c}+\frac{5\tau_{c}}{1+\omega_{0}^{2}\tau_ {c}^{2}}+\frac{2\tau_{c}}{1+4\omega_{0}^{2}\tau_{c}^{2}}\right) \tag{4}\]  
where \(\hbar\) represents the Planck constant; \(\gamma_{1}\) and \(\gamma_{S}\) are the magnetogyric ratios for the hydrogen atom and the electron, respectively; and \(r\) is the distance between the interacting spins.  
Equations (3) and (4) together reveal that \(T_{1}\) and \(T_{2}\) are dependent on the size and viscosity of fluid molecules. An increase in molecular size and fluid viscosity corresponds to a longer rotational correlation time, resulting in an increase in \(T_{1}\) and a decrease in \(T_{2}\). Consequently, when these equations are applied to analyze fluid components in shale pores, the \(T_{1}/T_{2}\) ratio is approximately 1 for low fluid viscosity. This ratio increases as both fluid viscosity and molecular size rise. Thus, \(T_{1}\)-\(T_{2}\) measurements are sensitive to the molecular size of different hydrogen-containing components and can be used to distinguish different components within the shale.