# Fluid Gradient with APB

Fluid gradients with pore pressure is an **external profile**, where the unknown is the external pressure profile of the tubing. The pressure profile consists of the hydrostatic pressure from a fluid above and a the pore pressure from top of cement (TOC).

NOTE!

In this documentation we denote any tubular ascasingortubing. All calculations however encompass any tubular, such as tubings, casings, liners, tie-backs etc.

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SummaryThe scenario is an APB in an external annuli relative to the tubing. Somewhere in the string there is also a **hydrostatic isolation depth** (HID), where the excess pressure from APB is bled off.

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Printable VersionOliasoft Technical Documentation - Fluid Gradient with APB

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InputsThe following inputs define the fluid gradient with APB load case:

The true vertical depth (TVD) along the wellbore as a function of measured depth. Alternatively, the wellbore described by a set of survey stations, with complete information about measured depth, inclination, and azimuth.

The true vertical depth/TVD of:

a. The hanger of the tubing, $\text{TVD}_{\text{hanger}}$

b. The shoe of the tubing, $\text{TVD}_{\text{shoe}}$

c. The hydrostatic isolation depth, $\text{TVD}_{\text{HID}}$

The mud weight / density, $\rho_m$

The APB pressure, $p_\text{APB}$

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CalculationThe external pressure profile, parametrized by TVD, of the tubing is then given by:

$p_e = \begin{cases} \rho_m \,g\,\text{TVD} + p_\text{APB}, \quad &\text{TVD} \leq \text{TVD}_{\text{HID}}, \\ \rho_m \,g\,\text{TVD}, \quad &\text{else}, \end{cases}$

where $g$ is the gravitational constant.