Fluid Gradients (Dual)

Fluid gradients (dual) is an external profile, where the unknown is the external pressure profile of the tubing. The pressure profile consists of the hydrostatic pressure from a fluid above and a fluid below the top of cement (TOC)

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.

Inputs

The following inputs define the fluid gradients (dual) external profile

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

a. The rig RKB, $\text{TVD}_{\text{RKB}}$ b. The hanger of the casing / tubing, $\text{TVD}_{\text{hanger}}$ c. The shoe of the tubing, $\text{TVD}_{\text{shoe}}$

3. The fluid density above top of cement, $\rho_m$

4. The fluid density below top of cement, $\rho_{c}$

Calculation

The external pressure profile above and including TOC, parametrized by TVD, of the casing / tubing is then given by

$$p_{\text{TOC}} = \rho_{m}\, g\, \text{TVD}_{\text{TOC}}$$

where $g$ is the gravitational constant, and $p_{\text{TOC}}$ is the hydrostatic fluid pressure at top of cement. The pressure below TOC and including the casing / tubing shoe is thus

$$p_{\text{shoe}} = \rho_{c}\, g\, \left(\text{TVD}_{\text{shoe}} - \text{TVD}_{TOC} \right)+ p_{TOC}$$