Fluid Gradient with APB

Fluid gradient with APB (annular pressure buildup) is an external profile, where the unknown is the external pressure profile of the tubing.

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.

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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, $\rho_m$ .

Calculation

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

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Inputs

The following inputs define the fluid gradient with APB load case

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

\begin{equation} 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} \end{equation}

where

g

is the gravitational constant.