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# Mud and Cement Slurry

Mud and cement slurry is an **external profile**, where the unknown is the external pressure profile of the tubing. The pressure profile consists of the hydrostatic pressure from mud and cement in annulus.

{% hint style="info" %}
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.
{% endhint %}

## 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 

$$
p\_{\text{shoe}} = \rho\_{t}, g, \left(\text{TVD}*{shoe} - \text{TVD}*{TOCtail} \right)+ p\_{TOCtail}
$$