## Friday, July 9, 2010

### Charles Bukowski and volumetric flow rates

Mass flow rate...now that we have the analysis of the crude...and the specific API gravity...we can all know the density and therefore....

Mass flow rate is the mass of substance which passes through a given surface per unit time. Its unit is mass divided by time, so kilogram per second in SI units, and slug per second or pound per second in US customary units. It is usually represented by the symbol $\dot m$.

Mass flow rate can be calculated from the density of the substance, the cross sectional area through which the substance is flowing, and its velocity relative to the area of interest.
$\dot m = \rho \, v \, A$
where:
${\dot m}$ is the mass flow rate
ρ is the density
v is the velocity
A is the flow area
This is equivalent to multiplying the volumetric flow rate by the density.
${\dot m} = {\rho \cdot Q}$
where:
ρ is the density
Q is the volumetric flow rate
The symbol for mass flow rate is Newton's notation for a derivative:
$\dot m = \frac{dm}{dt}$

....ok, ...so , consider the size of the intersecting bores

The continuity equation is a statement of the conservation of mass in a system. Consider a pipe that is uniform in diameter at both ends but has a constriction between the ends, called a Venturi tube. Furthermore, assume that fluid is flowing through the pipe from one end through the narrow throat of the tube with cross-sectional areas A1 and A2, respectively. Let V1 and V2 be the average flow speeds at these cross sections. Assume also that there are no leaks in the pipe nor is fluid being pumped in through the sides. The continuity equation states that the fluid “mass flow rate”—the amount of fluid per unit time—must be the same at any cross section of the pipe or else there is an accumulation of mass—"mass creation"—and the steady flow assumption is violated. Simply stated,

 (Mass rate)1 = (Mass rate)2 (1)
where

 Mass rate = Density x Area x Velocity (2)
This equation reduces to

 p1A1V1 = p2A2V2 (3)
Since the fluid is assumed to be incompressible, p is a constant and equation (3) reduces to

 A1V1 = A2V2 (4)
This is the simple continuity equation for inviscid, incompressible, steady, one-dimensional flow with no leaks. If the flow were viscous, the statement would still be valid as long as average values of V1 and V2 across the cross section were used.

By rearranging equation (4), one obtains

 V2 = (A1/A2)V1 (5)
Since cross-section A1 is greater than cross-section A2, it can be concluded that V2 is greater than V1. This is a most important result. It states that the flow speed increases where the area decreases and the flow speed decreases where the area increases. In fact, by the continuity equation, the highest speed is reached where the area is the smallest. This is at the narrowest part of the constriction, commonly called the throat of the Venturi tube.

I'm going to have to substitute the letters

M ....for the symbol of mass flow rate, (instead of trying to copy and paste the symbol)

p......for the density

v......velocity

A.....for flow area.

....ok so ultimately....

$\dot m = \rho \, v \, A$

Below is a link to the graphic of a Venturi tube , so you understand what I mean by the mention of the diameters of the intersecting bores, ie: the shape of the intersection. Although the gradient of the angle of the inner diameter of the intersecting bore is not sharply observable in something like a 10' section , but rather expressed very gradually by the concentrically larger pipes leading away from the intersect, and away to the surface, just like the shape of the first bore, ....small to large casing from bottom to top, respectively....but also, since a oil trap is a larger space than the well casing, the casing diameter gets bigger bottom to top,.... Venturi

http://www.centennialofflight.gov/essay/Theories_of_Flight/Conservation/TH8G1.htm

the density of the crude is obtained with the knowledge of the specific API gravity.

Here is the site I used, it's a free converter....an. API to density converter.....how cool is that..?

http://www.ior.com.au/ecfdensity.html
........so the API gravity is 23.5         =         0.9129 grams per ml.   ....that's the density...

v...or velocity , The on-site team continued to refine its estimate and has concluded that the best estimate for the average flow rate was in the range of 12,600 to 21,500 barrels of oil per day.That's a link in the text below. I am looking forward to the new analysis.

" The nodal analysis team is continuing to work on independent estimates that will be completed later this month   "

12,600 to 21,500 barrels of oil per day was the estimate, I'm going to actually calculate from the middle of the estimate.....21,500 - 12,600 = 8900/2=4450 , 12,600 + 4450 = 17,050 Bpd.

.....A...... is the flow area in this function, in this case, it's a 2 dimensional area, the cross section of the riser pipe. The casing at the seafloor level ,  at the outer diameter is 21", the wall is 2"....so that gives an inner diameter of 19" .

............The area of a circle is obtained in the following

Figure out the length of the radius. This may be as simple as dividing the diameter by 2.
Note the formula. The formula for finding the area of a circle is:
....that's ...area equals pi times the radius squared....in literary format.

......so the radius is half the diameter, ..or....8.5"

......times itself.....8.5" x 8.5" equals 283.385"

......so that is....    A

.....A = 283.385"

.......so far, ..that's

M =
p (  density )  = 0.9129 grams per ml.
v ( volume ) = 17,050 bpd
a (area)       = 283.385"

.....again for the sake of reiteration..
${\dot m}$ is the mass flow rate
ρ is the density
v is the velocity
A is the flow area
This is equivalent to multiplying the volumetric flow rate by the density.

The volumetric flow rate in fluid dynamics and hydrometry, (also known as volume flow rate or rate of fluid flow) is the volume of fluid which passes through a given surface per unit time (for example cubic meters per second [m3 s-1] in SI units, or cubic feet per second [cu ft/s]). It is usually represented by the symbol Q.

Given an area A, and a fluid flowing through it with uniform velocity C with an angle θ away from the perpendicular direction to A, the flow rate is:

$Q = A \cdot C \cdot \cos \theta$
....so ultimately, ...lol.....17,050bpd...or Q x the density of the fluid...0.9129 grams per ml gives the volumetric flow rate .

.......ok......

........17 050 barrel [US, petroleum] = 2 710 733 378.6 milliliters

........1 barrel [US, petroleum] = 158 987.294 93 milliliters

........Q times v = 15, 564.945 Bpd.

(edit)...ahaha..sorry...Q x p.....>facepalm<

So what I am saying is that I learned to carefully observe just not my own actions, but especially the actions of everything around me. You can learn much more by watching somebody else screw something up. I might fall flat on my face, but we can laugh together.

also, ...lets say 2 people are having a conversation about a topic.

a 3rd person enters....observes the conversation between the first 2 and states.." You guys are idiots "

at the same time, ....a 4th person is also observing the conversation and resulting reactions between the 3.

If the 4th person was originally listening to the debate before the 3rd person came along, than the 4th was also rationally,.. with the open mind of someone who wants to learn ,...was considering each side of the debate equally....50/50....but not engaging with the 2 original people directly.

So if the 3rd person says something...it's either fact or opinion. ... in the case of this guy , he said " You guys are idiots. " So all of a sudden, the 4th person's bias becomes further diluted...no longer 50/50.

All by the selfish actions of a rude interjection into a mature scientific discussion, 3 possibly prevents 4 from learning, just by being an asshole.

.........That's not cool.

If classically , the truth is reached by the quantification of facts under peer review, than the more that join the conversation, the more facts can be reviewed by the collective minds engaged in the debate, and the faster the bullshit can be disregarded, the faster the solution is reached. The Final solution or " truth " is really just a super-critical thought explosion.  Nowhere to go but out into the collective consciousness.where it becomes accepted fact, .....same thing as a nuclear super-critical reaction....it's why I say things like " molecules or mentalities, they follow the same laws."

Goodnight, ....or good-day......good..

tomorrow, I'll do the same maths, but will look at eroded wellbores, stratigraphic pressures, diameters of the intersection point ( Venturi ), flow rates of the two different fluids at the intersection, how 2 liquids of different densities react when they meet, what the densities are, ...tired ...umm......probably I will have some other things to add, on my mind when I wake up.

(edit) "tomorrow"......well, here I am again. .........I'm bored with it, I see that postulating outcomes based on speculative numerical modeling is........pointless ? It was fun teaching myself last night how to do it , and it has definitely opened my eyes once again to something wonderful. Moving on..

http://en.wikipedia.org/wiki/Volumetric_flow_rate