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# Mud and Cement Slurry

Fluid gradients with pore pressure 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 the pore pressure from 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 mud and cement 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. Top of lead cement, $\text{TVD}_{\text{lead}}$

d. Top of tail cement, $\text{TVD}_{\text{tail}}$

e. The shoe of the casing / tubing $\text{TVD}_{\text{shoe}}$

3. The fluid density of mud in annulus, $\rho_m$

4. The fluid density of lead cement, $\rho_{l}$

5. The fluid density of tail cement, $\rho_{t}$

## Calculation#

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

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

where $g$ is the gravitational constant, and $p_{\text{TOC}}$ is the hydrostatic fluid pressure at top of cement. The pressure below TOC down to top of tail cement is:

$p_{\text{TOCtail}} = \rho_{l}\, g\, \left(\text{TVD}_{tail} - \text{TVD}_{TOC} \right)+ p_{TOC}$

and the pressure below any potential tail cement is :

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