## 3 Materials and Methods
### Pore Pressure Prediction Methods
#### 3.1.1 [PERSON]'s Resistivity Method with Depth-Dependent Normal Compaction Trend (NCT) Line  
[PERSON]'s method is an experimental technique that uses resistivity, sonic, and density logs calibrated to reflect pore pressure using drill stem tests (DST) and repeat formation tests (RFT) to envisage pore pressure (RFT) [50]. The [PERSON] model [50] was established by observing that a well log can predict pore pressure at depth based on deep resistivity measurement. The following equation was used to predict pore pressure gradients in shales using a resistivity log:  
\[\mathrm{Pp}\;=\;\mathrm{OBG}\;-\;\mathrm{(OBG}-\;\mathrm{Png)}\;\times\;\mathrm{( Ro/Rn)} \tag{1}\]  
where  
\(\mathrm{Pp}\) = pore pressure gradient;  
\(\mathrm{OBG}\) = overburden stress gradient (ppg), (psi/ft);  
\(\mathrm{Png}\) = hydrostatic pore pressure gradient, normally 0.45 psi/ft/1.03 MPa/km based on the water salinity of the region;  
\(\mathrm{Ro}\) = observed shale resistivity (ohm/m);  
\(\mathrm{Rn}\) = normal shale resistivity (hydrostatic pressure).  
Finding the state of hydrostatic pore pressure for the shale resistivity when using Equation (1) is challenging; the best solution is to obtain the Normal Compaction Trend line for the prediction of pore pressure. Normal resistivity, or \"Rn,\" depends on the burial  
\begin{table}
\begin{tabular}{l l l l l} \hline
**Method** & **Primary Log(s) Used** & **Strengths** & **Limitations** \\ \hline \multirow{4}{*}{Eaton (resistivity)} & & - & More stable in shale & - & Less sensitive to \\  & & - & More stable in shale & & mechanical compaction \\  & & - & zones & changes \\  & & - & Simple to apply & - & May misidentify \\  & & & - & Improved accuracy over & \\  & & & original Eaton & - & Still does not account for \\ Modified Eaton & Resistivity (adjusted & - & More tailored to & unloading \\  & formula) & - & & Requires calibration \\  & & & formation type & - & \\  & & - & Incorporates mechanical & \\  & & & rock properties & - & Requires multiple logs \\ Mathews andKelly & Sonic + density & - & Can be adapted for & - & Sensitive to data quality \\  & & & resistivity & & \\  & & - & Versatile method with & \\  & & & adaptability & - & Complex calculation \\ Baker \& Wood & Sonic + density (adaptable & - & Depends on accurate \\  & to resistivity) & - & Suitable for varying & NCT definition \\  & & & lithologies & - & Requires unloading path \\  & & - & Most precise under & estimation \\ Bowers & Sonic (velocity) & - & unloading conditions & - & May be complex to \\  & & - & Based on effective stress & implement in real-time \\  & & & & drilling \\ \hline \end{tabular}
\end{table}
Table 1: _Cont._depth, and the most effective method for determining the resistivity of shale conditions of the pore pressure (hydrostatic) is to set up the NCT for pore pressure prediction using the following equation:  
\[\text{InRn = InRo + bZ} \tag{2}\]  
where  
R\(\mu\) = shale resistivity in the normal compaction condition;  
Ro = shale resistivity in a mudline;  
b = constant number;  
Z = profundity of mud line below.  
The resultant formula from Equations (1) and (2) is called the Eaton resistivity equation and can be presented as follows:  
\[\text{Ppg = OBG - (OBG - Prg) \left(\text{R/Roe}^{\text{bz}}\right)^{n}} \tag{3}\]  
where  
\(R\) = shale resistivity measured at depth Z;  
b = logarithmic resistivity normal compaction line slope;  
Ro = mudline normal compaction shale resistivity.