# Sand Production Characteristics of Hydrate Reservoirs in the South China Sea
## 4 Numerical Simulation of Sand Production Based on Logging Data  
To understand the mechanism and risk of sand release from hydrate reservoirs in the South China Sea, it is implemented numerical simulations of sand production based on logging data of three hydrate reservoir drilling wells in the sea area. Our method is based on the acoustic time difference method, combined modulus method, sand emergence index method and Schlumberger's ratio method [43]. The data of reservoir density, acoustic time difference and Poisson's ratio are substituted into the calculation formula to carry out the simulation of sand emergence from the reservoir, qualitatively determine the risk of sand emergence from the reservoir and solve the problem of determining sand emergence before the exploitation of hydrate. The acoustic time difference method can be described by:  
\[ \begin{cases}\Delta t_{\text{$\
u$}}<312\ \text{\mu s/m},\text{ Stabilisation without sand}\\ 312\ \text{\mu s/m}\leq\Delta t_{\text{$\
u$}}\leq 345\ \text{\mu s/m},\text{ Possibility of sanding}\\ \Delta t_{\text{$\
u$}}>345\ \text{\mu s/m},\text{ Unstable, highly prone to sanding}\end{cases}  \tag{1}\]  
The combined modulus method is expressed by:  
\[E_{c}=\frac{9.94\times 10^{5}\times\rho_{r}}{\Delta t_{\text{$\
u$}}^{2}} \tag{2}\]  
where \(E_{c}\) is the Yung modulus of elasticity of the rock, MPa; \(\rho_{r}\) is the bulk density of the formation rock, kg/m\({}^{3}\); and \(\Delta t_{\text{$\
u$}}\) is the time difference of the acoustic longitudinal wave, \(\text{\mu s/m}\). \[ \begin{cases}E_{c}>2.0\times 10^{4}\ \text{MPa},\text{ normal production wellbore without sand}\\ 1.5\times 10^{4}\ \text{MPa}\leq E_{c}\leq 2.0\times 10^{4}\ \text{MPa},\text{ slight sand production}\\ E_{c}<1.5\times 10^{4}\ \text{MPa},\text{ serious sand release}\end{cases}  \tag{3}\]Sand out index method can be simplified by:  
\[B=\frac{\rho_{r}}{\Delta t_{v}^{2}}\times 10^{-10} \tag{4}\]  
where \(B\) is the sand out index, MPa; \(\rho_{r}\) is the bulk density of formation rock, kg/m\({}^{3}\); \(\Delta t_{v}\) is the time difference of acoustic longitudinal wave, \(\mu\)s/m. \[\left\{ \begin{aligned} & B\geq 2.0\times 10^{4}\;\text{MPa},\text{ No sand or little sand in normal production}\\ & 2.0\times 10^{4}\;\text{MPa}>B>1.4\times 10^{4}\;\text{MPa},\text{ medium level of sand production}\\ & B\leq 1.4\times 10^{4}\;\text{MPa},\text{ excessive sanding of stratum}\\ \end{aligned} \right. \tag{5}\]  
The Schlumberger ratio methodology is in the form of:  
\[R=\frac{(1-2\mu)(1+\mu)}{6(1-\mu)^{2}}\frac{\rho_{r}^{2}}{\Delta t_{v}^{4}} \times 10^{-20} \tag{6}\]  
where \(R\) is the Schlumberger ratio, MPa\({}^{2}\); \(\mu\) is the rock Poisson's ratio, dimensionless. \[R<5.9\times 10^{7}\;\text{MPa}^{2},\text{ No sand or little sand in normal production} \tag{7}\]  
The results of the simulations are shown in Figures 1-4. Figure 3: Simulated sand output results of sand output index for wells W05A (**a**), W10 (**b**) and W19 (**c**). Figure 2: Sand simulation results of combined modulus method for wells W05A (**a**), W10 (**b**) and W19 (**c**). The combined modulus method, which incorporates density logging data from hydrate formations into the calculation, provides more informative results than the acoustic time-difference method. Whereas the Schlumberger ratio method, which introduces [PERSON]'s ratio into the simulation, has a wider range of applications in the field of oil and gas in offshore sands and provides more reliable results. The results show that: 1 the combined modulus E\({}_{\text{C}}\) value of well W05A is \(\leq\)7.1 \(\times\) 10\({}^{3}\) MPa in the non-hydrate layer section, which is much lower than the cut-off line of 1.5 \(\times\) 10\({}^{4}\) MPa for severe sand production/slight sand production, indicating that the sand layer has a serious tendency to produce sand when there is no hydrate cementation.