# 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 as casing or tubing. All calculations however encompass any tubular, such as tubings, casings, liners, tie-backs etc.

## Summary#

The 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.

### Printable Version#

Oliasoft Technical Documentation - Fluid Gradient with APB

## Inputs#

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

1. 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.

2. 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, $\text{TVD}_{\text{HID}}$

3. The mud weight / density, $\rho_m$

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

## Calculation#

The 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.