Fracture at Prior Shoe with Gas Gradient Above

In this section we describe the load case "Fracture at Prior Shoe with Gas Gradient Above" available in Oliasoft WellDesign™.

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The Fracture at Prior Shoe with Gas Gradient Above is a collapse load case, where the unknown is the external pressure profile of the tubing.

NOTE!
Note: In this documentation we denote any tubular as tubing. All calculations however encompass any tubular, such as tubings, casings, liners, tie-backs etc.

Summary

The Fracture at Prior Shoe with Gas Gradient Above is an external collapse load case. The profile is based on the fracture pressure at previous shoe, with a gas gradient from previous casing shoe to the wellhead, and fluid gradients from previous casing shoe to the casing shoe.

Below the previous casing shoe, two fluid gradients can be defined: one above top of cement (TOC) and one below TOC. If TOC is below the previous casing shoe, the fluid gradient above TOC is used from the previous casing shoe to TOC, and the fluid gradient below TOC is used from TOC to the casing shoe. The pressure profile is continuous at TOC. If TOC is above the previous casing shoe, only the fluid gradient below TOC is used, and the Fluid gradient above top of cement input is hidden.

The gas can be defined either by gas density or by gas gravity.

Illustrating Pressure Profile Graph

TOC below previous casing shoe

TOC above previous casing shoe

Printable Version

Oliasoft Technical Documentation - Fracture at Prior Shoe with Gas Gradient Above

Inputs

The following inputs define the Fracture at Prior Shoe with Gas Gradient Above 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, TVD$_{hanger}$.
   2. The shoe of the tubing, TVD$_{shoe}$.
   3. The shoe of the prior tubing, TVD$_{prior\;shoe}$.
   4. The top of cement, TVD$_{TOC}$.
3. The temperature profile of the wellbore, $T$.
4. The fracture pressure at prior shoe, P$_{f@ps}$, from the selected Fracture Pressure estimate.
5. The gas definition, selected in the Gas density / gas gravity drop down:
   1. Gas Density: the gas gradient, $\rho_{g}$ (sg).
   2. Gas Gravity: the gas specific gravity, $\text{sg}_{gas}$.
6. The fluid gradient above top of cement, $\rho_{aTOC}$. Only used and shown when TVD$_{TOC}$ > TVD$_{prior\;shoe}$.
7. The fluid gradient below top of cement, $\rho_{bTOC}$.
8. The gravitational constant, $g$.
9. Fracture margin of error, $\varepsilon_{FEM}$.

NOTE!
Before this change, the input was called Gas Gravity, but the value was used as a gas gradient in sg. Existing load cases are migrated with Gas Density selected and the same value, so existing results do not change.

Calculation

The external pressure profile is given by the hydrostatic gas profile from the prior shoe to the hanger, and hydrostatic fluid profiles from the prior shoe to the shoe, with fracture pressure at the prior shoe as fix point. If Gas Gravity is selected, a gas gradient, $\rho_{g}$, is calculated from the gas specific gravity, $\text{sg}_{gas}$, using z-factor and Sutton correlations [1], using the temperature and fracture pressure at the prior shoe as input. If Gas Density is selected, the gas gradient, $\rho_{g}$, is used directly.

If TOC is below the prior shoe, TVD$_{TOC}$ > TVD$_{prior\;shoe}$, the external pressure profile is:

$$P_{e} = \begin{cases} P_{f@ps} - g \rho_{g} (TVD_{prior\;shoe} - TVD), & \epsilon \; [TVD_{hanger}, TVD_{prior\;shoe}], \\ P_{f@ps} + g \rho_{aTOC} (TVD - TVD_{prior\;shoe}), & \epsilon \; [TVD_{prior\;shoe}, TVD_{TOC}], \\ P_{TOC} + g \rho_{bTOC} (TVD - TVD_{TOC}), & \epsilon \; [TVD_{TOC}, TVD_{shoe}], \end{cases} \qquad (1)$$

where $P_{TOC}$ is the pressure at TOC, which makes the profile continuous at TOC:

$$P_{TOC} = P_{f@ps} + g \rho_{aTOC} (TVD_{TOC} - TVD_{prior\;shoe}) \qquad (2)$$

If TOC is above the prior shoe, TVD$_{TOC}$ ≤ TVD$_{prior\;shoe}$, only the fluid gradient below TOC is used below the prior shoe:

$$P_{e} = \begin{cases} P_{f@ps} - g \rho_{g} (TVD_{prior\;shoe} - TVD), & \epsilon \; [TVD_{hanger}, TVD_{prior\;shoe}], \\ P_{f@ps} + g \rho_{bTOC} (TVD - TVD_{prior\;shoe}), & \epsilon \; [TVD_{prior\;shoe}, TVD_{shoe}], \end{cases} \qquad (3)$$

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References

[1] Curtis H. Whitson and Michael R. Brul$\acute{\text{e}}$. Phase behavior, volume 20 of Henry L. Doherty series. SPE Monograph series, 2000.