# Research on Pore Pressure Detection While Drilling Based on Mechanical Specific Energy
## 1 Introduction
\[P_{\rm pg}=\frac{v_{\rm max}-v}{v_{\rm max}-v_{\rm min}}\mathrm{O}BG \tag{5}\]  
where \(v\) is the seismic interval velocity (ft/s); \(v_{\rm min}\) is the seismic interval velocity when rock rigidity is 0 (ft/s); and \(v_{\rm max}\) is the seismic interval velocity when formation porosity is 0 (ft/s). [PERSON] [8] derived the empirical equations between effective stress and sonic velocity based on the effective stress principle. In this way, the pore pressure can be estimated from the sonic velocity. He considered the relationship between effective stress and sonic velocity from soil mechanics for different overpressure genesis. When the overpressure is caused by uncompaction, the relationship follows the original curve (Equation (6)), while when it is caused by the expansion of the fluid, the relationship follows the unloading curve (Equation (7)). The values of parameters A and B can be calibrated with offset sonic velocity versus effective stress data. \[V=5000+\mathrm{A}\sigma_{\rm e}^{\rm B} \tag{6}\]  
\[V=5000+\mathrm{A}\left[\sigma_{\rm max}\left(\frac{\sigma_{\rm e}}{\sigma_{ \rm max}}\right)^{\frac{1}{6}}\right]^{\rm B} \tag{7}\]  
\[\sigma_{\rm max}=\left(\frac{V_{\rm max}-5000}{\mathrm{A}}\right)^{\frac{1}{6}} \tag{8}\]where \(V\) is the sonic velocity (ft/s); \(V_{\text{max}}\) is the velocity at the onset of unloading (ft/s); \(\sigma_{\text{e}}\) is the vertical effective stress (psi); and \(\sigma_{\text{max}}\) is the vertical effective stress at the onset of unloading (psi). Most current pore pressure prediction methods are applicable to shale intervals, where there is a strong relationship between porosity and pore pressure. In contrast, carbonate rocks are harder, and overpressure has a weak effect on porosity. [PERSON] and [PERSON] [9] and [PERSON] et al. [10] derived the relationship between the pore pressure and compressibility to estimate pore pressure in carbonate rocks (Equation (9)). By further studying the numerical empirical relationship between compressibility correlations and porosity, a simplified approximation of Equation (10) with only porosity and effective stress was obtained [11]. This new method requires sufficient logging and core data to obtain regional formation porosity and pore volume compressibility. \[P_{\text{P}}=\left(\frac{(1-\phi)C_{\text{b}}\sigma_{\text{eff}}}{(1-\phi)C_{ \text{b}}-\phi C_{\text{P}}}\right)^{\gamma} \tag{9}\]  
\[P_{\text{P}}=\left(\frac{(1-\phi)\sigma_{\text{eff}}}{(1-2\phi)}\right)^{\gamma} \tag{10}\]  
where \(\phi\) is the formation porosity (fraction); \(C_{\text{b}}\) is the bulk compressibility (psi\({}^{-1}\)); \(C_{\text{p}}\) is the pore compressibility (psi\({}^{-1}\)); and \(\sigma_{\text{eff}}\) is the effective overburden pressure (overburden pressure-hydrostatic pressure) (psi). Due to complicated geological factors and variable causes of overpressure, the development of deep and ultra-deep wells makes it difficult to accurately predict the pore pressure simply by pre-drill prediction. Therefore, during the drilling process of deep and complicated formations, it is inevitable to carry out the detection of pore pressure while drilling. Real-time detection of pore pressure usually uses LWD and drilling parameters. LWD generally offers more accurate results than methods based on drilling parameters. However, the real-time performance of the LWD is not ideal because the LWD tool is positioned before the drill collar, slightly far from the bit. Moreover, there is a time delay in bottom hole data transmission [12]. Conversely, drilling parameters are real-time field data that are easily obtained in the drilling process. This paper is concerned with drilling parameter-based pore pressure detection. [PERSON] and [PERSON] [13] proposed the concept of the d-exponent for pore pressure detection by normalizing the factors (WOB, rotary speed, bit diameter) affecting the rate of penetration (ROP). Making a normal compaction trend (NCT) in the shales, the d-exponent will increase linearly with depth in normal pressure intervals.