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# Water Injection Well - Pressure Drop

## Water Injection Well - Pressure Drop

(OP)
Hello to All,

I would like to discuss some doubts that I have about the way to calculate the pressure drop in a water injection well during fracture operation.

Here is my escenario, I have a 2D well path (vertical 9000 ft; horizontal 8000 ft), the fluid injected is slickwater (density 1300 km/m3) with propant. The pump pressure in the wellhead is 65000 kpa.

My first approach was to use Bernoulli with the addicional term of Head Loss for the horizontal path. This is a turbulent fluid so I calculated the friction factor in the head loss term using colebrook eq. When I try to do the same calcuations using WellFlo I can´t achieve the same results for high flow rate (up to 3 m3/min). In WellFlo I set the Begg & Brill (modified) correlation.

Does anyone know why the difference?. Is it ok to use bernoulli for solving this type of problem (I think it is..). I would appreciate any help on this issue!.

### RE: Water Injection Well - Pressure Drop

The FIRST, NUMBER ONE, INITIAL assumption in the development of the Bernoulli Equation was that there is ZERO friction. So do you really think that adding a friction term after the equation is developed will actually give you a reasonable result in a 10 km pipe? You have to be kidding. Go back to Navier-Stokes and don't set friction (and swirl, and body forces) to zero and see if you can develop a closed-form equation. If you do, make sure your calendar is clear for that trip to Sweden for your Nobel Prize. That is kind of the Holy Grail in fluid mechanics that tens of thousands of researchers have spent tens of millions of hours trying to solve with exactly zero success.

Every so often, in very small dP cases, that STUPID modification of Bernoulli to tack on a meaningless headloss term matches actual data within a couple of dozen percentage points and everyone sings Hosannas to its vast usefulness. Nonsense.

No, Bernoulli is not appropriate. You can try to use D'Arcy-Weisbach, but it assumes an absolutely incompressible fluid and your hydrostatic plus dynamic pressure is high enough (around 130 MPa minus friction) that you are probably compressing the liquid 20% or so. If you use that, be really careful how you calculate your friction factor, you are going to be way outside the horizontal straight line portion of the Moody Diagram.

David Simpson, PE
MuleShoe Engineering

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

### RE: Water Injection Well - Pressure Drop

(OP)
What abaut the pressure drop correlations like beggs and brill amongst others?.

### RE: Water Injection Well - Pressure Drop

I've used the Beggs and Brill equations of state with decent results. I've seen their flow stuff, but never used it in anger. Normally I see it talked about in the same context as Hagedorn-Brown, Duns Rooss, Duckler, etc. so I'm thinking that its strength would be multi-phase flow, not continuous phase liquid.

For an injection stream of single-phase water (even if it does have a specific gravity of 1.3, it should still be mostly Newtonian) I'd tend to calculate a friction drop using D'Arcy-Weisbach (ignoring elevation change) and then determine injection pressure as Surface Pressure + Hydrostatic Pressure - Friction Drop. Compressibility of the water is going to add significantly to your uncertainty, but it probably is not big enough to lead you to a different decision.

David Simpson, PE
MuleShoe Engineering

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

### RE: Water Injection Well - Pressure Drop

(OP)
Hi, thanks again for your help on this issue.
Is it possible to apply the Fanning-Liquid Correlation for single phase liquid with good results?. Do you have experience using this one?.

I´m having problem in estimating the friction factor with D'Arcy.

Furthermore, I´m a little confuse about the effect of the hydrostatic colum on the comprensibility of the water, the height of the vertical section is about 3 km and the horizontal section is about 4 km of lenght. How can I check this?

Thanks again!

### RE: Water Injection Well - Pressure Drop

(OP)
Sorry it´s compressibility

### RE: Water Injection Well - Pressure Drop

You can get friction factor from the ubiquitous Moody Diagram or generate your own using Colebrook. It really isn't that hard.

You can look at any of the closed form equations, but all of them have a rigid set of assumptions that allow them to estimate friction factor in a single step.

I'm not familiar with Fanning Liquid Correlation, but I did find a site that indicated that vertical flow violated one (or more) of Fanning's underlying assumptions.

No I don't have a bibliography.

David Simpson, PE
MuleShoe Engineering

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

### RE: Water Injection Well - Pressure Drop

Better you quick run OLGA model to calculate the pressure drop across the well as Here

### RE: Water Injection Well - Pressure Drop

Why would you point a single-phase problem to a VERY EXPENSIVE multi-phase program? I think you could do better on this problem with an Ouija Board than with Olga.

David Simpson, PE
MuleShoe Engineering

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

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