# Lost Returns with Water

## In this section, we describe the load case "Lost returns with water", available in Oliasoft WellDesign.#

Lost returns with water is a burst load case, where the unknown is the internal 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#

This load case reflects that water is pumped from the surface down the tubing due to lost returns, and the pressure profile is given by the hydrostatic pressure from the fracture pressure at the shoe.

### Printable Version#

Oliasoft Technical Documentation - Lost Returns with Water

## Inputs#

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 hanger of the tubing, $TVD_{hanger}$
2. The shoe of the tubing, $TVD_{shoe}$
3. The mud-water interface, $TVD_{MW}$
3. The fracture pressure profile from hanger to shoe.
4. The mud weight/density, $\rho_{mud}$
5. The density of water, with default value $\rho_{water} = 998\ kg/m^3$
6. A fracture margin of eroor, added to the fracture pressure.

Scenario Illustration

## Calculation#

1. Calculate the fracture pressure at the shoe, $p_{f,shoe}$

2. Calculate the hydrostatic pressure from shoe to hanger, taking the mud-water interface into account. Explicitly, if the mud-water interface is below the shoe, i.e. $TVD_{MW} \geq TVD_{shoe}$ , then the internal pressure in the tubing, parametrised by TVD, is given by

$p_i = p_\text{f, shoe} - \rho_\text{water}\, g\left(\text{TVD}_{\text{shoe}} - \text{TVD} \right) \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (1)$

where $g$ is the gravitational constant. If, on the other hand, the mud-water interface is between the hanger and the shoe, i.e. $TVD_{hanger} \leq TVD_{MW} \leq TVD_{shoe}$ , then calculate the pressure at the mud-water interface

$p_\text{MW} = p_\text{f, shoe} - \rho_\text{mud}\, g\left(\text{TVD}_{\text{shoe}} - \text{TVD}_\text{MW} \right) \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (2)$

and the internal pressure in the tubing is

$p_i = \begin{cases} p_\text{MW} - \rho_\text{water}\, g\left(\text{TVD}_{\text{MW}} - \text{TVD} \right), \qquad \text{TVD} \leq \text{TVD}_{\text{MW}}, \\ p_\text{f, shoe} - \rho_\text{mud}\, g\left(\text{TVD}_{\text{shoe}} - \text{TVD} \right), \qquad \text{else}.\end{cases} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (3)$