Tubing Leak

In this section, we describe the load case Tubing leak, available in Oliasoft WellDesign.

Tubing leak is a burst load case, where the unknown is the internal pressure profile of the casing / 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

This load case is used in connection with production- and injection- operations, and represents a surface pressure on top of a completion fluid due to a tubing leak.

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Oliasoft Technical Documentation - Load cases - Tubing Leak.pdf

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Oliasoft Technical Docs - Tubing Leak

Inputs

The following inputs define the tubing leak 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 and inclination.

2. The true vertical depth / TVD of

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

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

   3. The packer depth, $\text{TVD}_\text{packer}$.

   4. The perforation depth, $\text{TVD}_{\text{perforation}}$.

3. The pore pressure profile from hanger to influx depth.

4. The packer fluid density, $\rho_\text{packer}$ .

5. The temperature at the perforation depth, $T_\text{perforation}$ .

6. The gas gravity, $\text{sg}_\text{gas}$ .

Scenario Illustration

Calculation

The internal pressure profile of the casing / tubing is calculated as follows

1. Calculate the pore pressure at perforation depth, $p_\text{p, perforation}$.

2. Calculate the gas density at perforation depth from gas gravity, using Sutton correlations, $\rho_\text{gas, perforation}$ .

3. Calculate the pressure at the hanger

$$\begin{equation} p_\text{hanger} = p_\text{p, perforation} - \rho_\text{gas, perforation}\, g\, (\text{TVD}_{\text{perforation}} - \text{TVD}_{\text{hanger}}) \end{equation} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (1)$$

where $g$ is the gravitational constant.

4. The internal pressure of the tubing depends on where the packer- and perforation- depth are related to each other and the shoe of the tubing. Explicitly, parametrize the tubing by TVD

a) If $\text{TVD}_\text{shoe} \leq \text{TVD}_\text{packer} \leq \text{TVD}_\text{perforation}$ , or if $\text{TVD}_\text{shoe} \leq \text{TVD}_\text{perforation} \leq \text{TVD}_\text{packer}$ , then

$$\begin{equation} p_i = p_\text{hanger} + \rho_\text{packer}\, g\, (\text{TVD} - \text{TVD}_{\text{hanger}}) \end{equation} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (2)$$

b. If $\text{TVD}_\text{packer} \leq \text{TVD}_\text{shoe} \leq \text{TVD}_\text{perforation}$ , then from hanger to packer

$$\begin{equation} p_i = p_\text{hanger} + \rho_\text{packer}\, g\, (\text{TVD} - \text{TVD}_{\text{hanger}}), \end{equation} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (3)$$

and from packer to shoe

$$\begin{equation} p_i = p_\text{perforation} - \rho_\text{gas, perforation}\, g\, (\text{TVD}_\text{perforation} - \text{TVD}). \end{equation} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (4)$$

c. If $\text{TVD}_\text{packer} \leq \text{TVD}_\text{perforation} \leq \text{TVD}_\text{shoe}$ , then from hanger to packer

$$\begin{equation} p_i = p_\text{hanger} + \rho_\text{packer}\, g\, (\text{TVD} - \text{TVD}_{\text{hanger}}) \end{equation} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (5)$$

from packer to perforation

$$\begin{equation} p_i = p_\text{perforation} - \rho_\text{gas, perforation}\, g\, (\text{TVD}_\text{perforation} - \text{TVD})\end{equation} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (6)$$

and finally, from perforation to shoe

$$\begin{equation} p_i = p_\text{perforation} + \rho_\text{packer}\, g\, (\text{TVD} - \text{TVD}_\text{perforation}) \end{equation} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (7)$$

d. If $a = b$ , then from hanger to perforation

$$p_i = p_\text{hanger} + \rho_\text{packer}\, g\, (\text{TVD} - \text{TVD}_{\text{hanger}}) \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(8)$$

and from perforation to shoe

$$p_i = p_\text{perforation} + \rho_\text{packer}\, g\, (\text{TVD} - \text{TVD}_\text{perforation}). \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (9)$$

e. The last scenario, $\text{TVD}_\text{perforation} \leq \text{TVD}_\text{packer} \leq \text{TVD}_\text{shoe}$ , is physically impossible.

References

[1] Curtis H. Whitson and Michael R. Brule ́. Phase behavior, volume 20 of Henry L. Doherty series. SPE Monograph series, 2000.

[2] Sutton, R.P.: “Compressibility Factors for High-Molecular Weight Reservoir Gases,” paper SPE 14265 presented at the 1985 SPE Annual, Technical Conference and Exhibition, Las Vegas, Nevada, 22–25 September.