# Negative Pressure Test

## In this document we describe the load case Negative pressure test available in the Oliasoft application.#

Negative pressure test is a collapse load case, where the unknown is the internal pressure profile of the tubing$^1$.

NOTE!
$^1$ We denote any tubular by tubing. All calculations encompass both tubings and casings.

## Summary#

The pressure profile consists of the hydrostatic salt water pressure to $l$ meters below the mud line, plus an additional pressure drop, and the hydrostatic mud pressure below.

## Inputs#

The following inputs define the negative pressure test 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
1. The rig RKB, TVD$_{RKB}$.
2. The wellhead/BOP interface, TVD$_{WH/BOP}$.
3. The TVD from rotary table to mud line, TVD$_{RT}\ to\ _{ML}$.
4. The hanger of the tubing, TVD$_{hanger}$.
5. The shoe of the tubing, TVD$_{shoe}$.
3. Length below mud line to use seawater gradient, $l_m$, default is $l_m$ = 1000ft ($\approxeq$ 300m)
4. Pressure drop, $p_n$, default to $p_n$ = 500 psi ($\approxeq$ 3.4 MPa)
5. The mud weight/density, $\rho_m$
6. The salt water density, $\rho_{sw}$

## Calculation#

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

$p_i = \begin{cases} \rho_{sw}\, g\, \text{TVD} - p_n, \quad &\text{TVD} \leq \text{TVD}_{\text{RT to ML}} + l_m, \\ p_{\text{ml+l}_m} + \rho_m\, g\, \left(\text{TVD} - (\text{TVD}_{\text{RT to ML}} + l_m) \right), \quad &\text{else}, \end{cases}$

where $g$ is the gravitational constant, and $p_{ml+l_m}$ is the hydrostatic salt water pressure at the wellhead plus $l_m$ including the pressure drop, i.e.

$p_{\text{ml+l}_m} = \rho_{sw}\, g\, (\text{TVD}_{\text{RT to ML}} + l_m) - p_n$