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# Calculating Backpressure on Formation from Fluid Column in Tubing4

## Calculating Backpressure on Formation from Fluid Column in Tubing

(OP)
I have what I believe to be a fairly simple fluid dynamics question, but I’m struggling to understand the mechanics at play in the wellbore.

Assume you have a well producing up tubing only (Casing Shut-In, No Packer). As depletion occurs, the well begins to load resulting in an increase in surface casing pressure and an unbalanced fluid column in the tubing (fluid column in tubing is higher than fluid column in casing).

My question is how do you calculate the backpressure exerted on the formation as a result of the standing fluid column in the tubing? Can the hydrostatic backpressure from the fluid column be calculated as follows:

Height of fluid column in tubing relative to casing fluid height [ft TVD] * Weight of wellbore fluid [psig/ft] = Hydrostatic Backpressure on Formation [psig]

My confusion lies in the fact that the casing and tubing fluid heights are not equal. Does the casing pressure increase that occurs due to loading equal the hydrostatic exerted from the fluid column in the tubing?

Thank you

### RE: Calculating Backpressure on Formation from Fluid Column in Tubing

You are not considering friction in the flowing tubing.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. ùGalileo Galilei, Italian Physicist

### RE: Calculating Backpressure on Formation from Fluid Column in Tubing

(OP)
With fluid friction added to the equation, does the rest of the logic appear correct in calculating the backpressure on the formation due to the tubing load?

I appreciate the help.

### RE: Calculating Backpressure on Formation from Fluid Column in Tubing

4
The only things you ever know for certain are:
1. The tubing and casing pressure at the end of the tubing must be equal to each other because they are the same parameter being measured
2. The flowing tubing pressure can be measured accurately
3. The shut-in casing pressure can be measured accurately
4. The mass flow rate of the fluids flowing in the tubing can be determined accurately (but rarely is).
Flowing tubing pressure = Flowing bottomhole pressure - hydrostatic head of the fluids in the tubing - friction

Flowing casing pressure = Flowing bottomhole pressure - hydrostatic head of the fluids in the casing

The rub is that you never know with any certainty what the hydrostatic head of either the tubing or casing is (and it never stays the same for more than a few miliseconds). So the difference between flowing tubing and shut-in casing pressure is tubing friction ± difference in hydrostatic gradients between tubing and casing. We usually assume that gas will enter the casing and displace liquids until the liquid column is insignificant so the tubing/casing differential is friction plus tubing hydrostatic. There are equations to calculate the friction loss in the tubing for a given mass flow rate of reservoir fluids--if your tubing/casing differential is significantly higher than calculated friction then it is likely that you have liquid build up in the tubing. Not certain, but likely.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. ùGalileo Galilei, Italian Physicist

### RE: Calculating Backpressure on Formation from Fluid Column in Tubing

(OP)
Thank you for the very thorough explanation. That helps immensely.

### RE: Calculating Backpressure on Formation from Fluid Column in Tubing

Great post?
Star it!

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