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 $\text{tubing}^{1}$ .

$^1$ 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, $\text{TVD}_{\text{RKB}}$ .

   2. The wellhead/BOP interface, $\text{TVD}_{\text{WH/BOP}}$ .

   3. The TVD from rotary table to mud line, $\text{TVD}_{\text{RT}}$ to $_{ML}$.

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

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

3. Length below mud line to use seawater gradient, $l_m$, default is $l_m = 1000 ft (\simeq 300 m)$

4. Pressure drop, $p_n$ , default to $p_n = 500 psi (\simeq 3.4 MPa)$

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 $p_{\text{ml}+l_{m}}$ is the hydrostatic salt water pressure at the wellhead plus $l_m$ including the pressure drop, i.e.

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