###### Contents:

- 1 introduction
- 2 Literature Review
- 3 Discussion

## introduction

Addressing pore pressure before drilling stage in hydrocarbon exploration started to play a vital role in risk analysis specially in deep offshore wells. Hence, the deeper the target, the more challenging it would be to explore and drill. Recent publication stated that 40% of offshore exploration and production budget is allocated to drilling. In drilling, overpressure zones are considered a drilling hazard and potentially cost more to drill. In fact, drilling problems attributed to geopressure such as formation collapse, stuck pipe, well kicks and blowouts account for 30% of the deep water drilling budget (citation not found: dutta2002geopressure).

In absence of direct pressure measurement, we can predict pressure at the borehole using indirect methods. Acceptable indirect pressure prediction methods at the borehole involve analyzing normal compaction trends (NCT) \shortcitegutierrez2006calibration, Vp/Vs \shortciteDvorkin:1999aa, empirical relations \shortcitedoi:10.1190/1.1442580, bowers1995pore or vertical seismic profile \shortcitestone1983predicting, shapiro1985seismic.

This paper will revisit two common practice and techniques to predict pressure using borehole acoustic measurement. Acoustic-based pressure prediction methods assume velocity decreases when pressure increases; hence, we can correlate velocity to pressure. In this paper, we will focus on application of using compressional velocities to predict pressure.
Below I first present a review of relevant literature to provide the context for this work, followed by a discussion of the two methods with examples from the Gulf of Mexico before before conclusion.

## Literature Review

\citeA
hubbert1959role employed Terzaghi’s principle (Terzaghi, 1943) in subsurface pressure as the total pressure exerted on a rock is supported by the rock matrix and the pore fluid could be expressed as:

\begin{equation}
\sigma_{ij}=\ \sigma^{\prime}_{ij}+\ \alpha\ P_{P}\ \delta_{ij}\\
\end{equation}
where:
\(\sigma\) is total stress tensor,
\(\sigma^{\prime}\) is the effective stress tensor,
\(\delta_{ij}\) is the kronecker delta, and
\(P_{P}\) is fluid pore pressure. Since \(\alpha=1\) for soft sediments and \(i=j\), then:

\begin{equation}
\sigma=\ \sigma^{\prime}+\ P_{P}\\
\end{equation}

Adaptation of the effective-stress principle provided a basis to transform velocities to pressure. \citeAtodd1972effect showed that pore pressure could be presented as a function of compressional velocity.

(citation not found: brown1975dependence) introduced an equation to relate the dependence of the elastic properties of a porous material to the compressibility of the pore fluid proving that relationship is dependent on the fluid compressibility and the porosity of the medium using lab measurement on the Berea sandstone.

\citeA
doi:10.1190/1.1442580 formulated an empirical relation between seismic velocity, effective pressure, porosity and clay content in sandstone using offshore data from the Gulf of Mexcio. (citation not found: prasad1997effects) continued ultra-sonic measurements on the Berea and Michigan sandstones and concluded a relationship between differential pressure and quality factor.

\citeA
doi:10.1190/1.1441910 pointed that poisson’s ratio could use to infer pore pressure. They measured velocity as a function of effective pressure in the Berra sandstone and showed that velocity decrease as pore pressure approach confining pressure. \citeADvorkin:1999aa followed similar method to predict pore pressure using (\(V_{p}/V_{s}\)).

Most papers studied on modeling pressure as a function of a specific parameter as pressure can not be attributed to a single parameters.Modeling pressure is a multi-disciplinary problem that required parameters like thermal gradient, porosity, permeability, lithology, elastic properties, burial history, weight of the the compacted material, total organic content and burial geochemical processes.

## Discussion