# Fault Controls on Hydrocarbon Migration--An Example from the Southwestern Pearl River Mouth Basin
## 3 Data and Methods
### Methods
#### 3.2.1 Evaluation of Fault Rock Seals  
To assess the lateral sealing capacity of faults in sand-shale sequences, the focus was on the low-permeability of the fault going within the fault zones. The Shale Gouge Ratio (SGR) algorithm is commonly used to predict the type and distribution of the fault gouge along the fault surface [27; 36; 45]. Note that the composition of shale or mudstone sequences is difficult to predict, and different clay minerals usually present a similar physical property compared to sandstones, so this algorithm only considers the content of clay within the fault zone. The SGR value was calculated using Equation (1):  
\[\text{SGR}=\frac{\Sigma(\text{shale bed thickness})}{\text{throw}}\times 100\% \tag{1}\]  
The SGR value serves as a proxy for the fault sealing capacity, but it needs to be calibrated to establish a link with the actual sealing capacity. There are two common calibration methods. The first involves conducting laboratory experiments to determine the capillary threshold pressure of fault rock samples [38]. But this method needs a large number of fault rock samples, which is difficult to implement especially in offshore explorations. The second empirical method utilizes empirical pressure data from the strata on both the hanging wall and footwall of the sealing fault from a worldwide filed dataset to calculate the across-fault pressure difference (AFDP) or capillary threshold pressure (Pc) and relate it to the SGR [39; 61]:  
\[\text{AFPD}=10^{\text{(SGR-C)}} \tag{2}\]  
where the unit of AFPD is bar; when the burial depth is less than 3.0 km, C is 0.5; when the burial depth between 3.0 and 3.5 km, C is 0.25; when the burial depth is greater than 3.5 km, C is 0.  
\[\text{Pc}=0.3\times\text{SGR}-6 \tag{3}\]  
when the burial depth is less than 3 km.  
\[\text{Pc}=0.15\times\text{SGR}+1.9 \tag{4}\]  
when the burial depth is more than 3.5 km.  
It is important to note that when using this method, it is necessary to define the lower limit of the SGR, which indicates the threshold at which hydrocarbons can be sealed. Otherwise, even if the SGR value is very low, it could still be calculated as a positive value, leading to the sealing of a certain column height of hydrocarbons. The buoyancy pressure generated by the hydrocarbon column can be treated as equivalent to the AFPD or capillary threshold pressure. However, further charging will result in the buoyancy pressure exceeding the capillary threshold pressure, leading to leakage. The height of the supported hydrocarbon column can be calculated using Equation (5):  
\[\mathrm{H}=\frac{\mathrm{P_{c}}}{(\mathrm{\rho_{w}}-\mathrm{\rho_{h}})\mathrm{ g}} \tag{5}\]  
where H represents the height of the hydrocarbon column (m), Pc is the capillary threshold pressure of the fault rock (MPa), \(\mathrm{\rho_{w}}\) is the density of pore water (kg/m\({}^{3}\)), \(\mathrm{\rho_{h}}\) is the density of hydrocarbons (kg/m\({}^{3}\)), and g is the acceleration due to gravity (m/s\({}^{2}\)). We assume an oil density between 750 kg/m\({}^{3}\)[62], a gas density of 150 kg/m\({}^{3}\), and a formation water density of 1035 kg/m\({}^{3}\).