THEORY & FORMULA

Transient Pressure BuildUp Analysis (Oilwell)
Pressure buildup (PBU) survey involves measuring the changes in wellbore pressure with time after a well has been shut in. PBU requires that the well produce at a stabilized rate before shut-in. The PBU equation introduced by Horner is given by:

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where pws = sandface pressure, psig pi = initial reservoir pressure, psig Qo = stabilized oil rate, STB/day μo = oil viscosity, cp Bo = formation volume factor, rB/STB k = permeability of formation rock, mD h = formation thickness, ft tp = flowing time before shut-in, hr Δt = shut-in time, hr.
A plot of pws versus (tp+Δt)/Δt would ideally produce a straight line with an intercept at pi (or p*) and a slope of ,strong>-m. This plot is known as the Horner plot, a semi-log plot. In practice, there is a deviation from a straight line in the initial section of the plot due to skin and wellbore storage effects. The straightline portion of the plot can be graphically identified by interactively ignoring a number of early plot points and performing a straightline fit on the rest.
When a satisfactory straight line is obtained, the initial reservoir pressure pi is estimated by extrapolation to the pressure corresponding to (tp+Δt)/Δt = 1. That is, the extrapolated pressure (p*) = (pi) for an infinite reservoir or for wells tested early in the life of the reservoir.
Another pressure point of importance on the fitted straightline is the pressure corresponding to Δt = 1 hour. Also computed is the slope (m) of the straight line in units of psi/log cycle.
Finally, the permeability of the formation (k) and the skin factor (s) can be calculated according to the relationships:

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where m = slope of semi-log straight line, psi/log10cycle p1hr = pressure at time 1-hour on semi-log straight line, psig pwf(Δt=0) = sandface pressure immediately prior to shut-in, psig ct = total compressibility coefficient, 1/psi

Tips:

◊ Use link

EXAMPLE Of Input/Output to demo data entry expectations and results; you may edit & use it as starting point

◊ Between 15 to 30 measurements points may be entered

◊ Up to 11 points may be ingored in the staright-line fitting process

◊ If the required Java plug-in not installed on your computer, an auto-download of this plug-in will be initiated before the plot is displayed.

BIBLIOGRAPHY
Dake L.P.; Fundamentals Of Reservoir Engineering; Elsevier Scientific Publ. Co., Amsterdam, Netherlands, 1978.
Horne R.N.; Modern Well Test Analysis - A Computer-Aided Approach; Petroway Inc., Palo Alto, California, 1995.
Earlougher R; Advanced Well Test Analysis; Monograph Series Vol 5, SPE, Dallas, 1977.
Kansas Geological Survey, Oil & Gas Information, Gemini Project, Lawrence, Kansas, 2002.

Recreated by @Abrar2009

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* Effect of Oil Production Rate

* Science Direct Journal

* Haliburton Public Data

* Petroleum Engineering Calculator

GEOMETRY/STRUCTURE:

A motor and gearbox supply power to turn the power shaft. There is a counterweight at the end of the crank. A pitman arm is attached to the crank and it moves upward when the crank moves counterclockwise. The Samson arms support the walking beam. The walking beam pivots and lowers or raises the plunger. The rod attaches the plunger to the horsehead. The horsehead (not rigidly attached) allows the joint (where rod is attached) to move in a vertical path instead of following an arc. Every time the plunger rises, oil is pumped out through a spout. The pump consits of a four bar linkage is comprised of the crank, the pitman arm, the walking beam, and the ground.

EXPLANATION OF HOW IT WORKS/ IS USED:

Here the plunger is shown at its lowest position. The pitman arm and the crank are in-line. The maximum pumping angle, denoted as theta in the calculations, is shown. L is the stroke length. After one stroke, the plunger moves upward by one stroke length and the walking beam pivots. The crank also rotates counterclockwise. At the end of the upstroke the pitman arm, the crank, and the walking beam are in-line.

For name and location of parts, see Figure A.
A motor supplies power to a gear box. A gearbox reduces the angular velocity and increases the torque relative to this input.
As shown in Figure B, (the crank turns counterclockwise) and lifts the counterweight. Since the crank is connected to the walking beam via the pitman arm, the beam pivots and submerges the plunger. Figure B also shows the horsehead at its lowest position. This marks the end of the down stroke. Note that the crank and the pitman arm are in-line at this position.
The upstroke raises the horsehead and the plunger, along with the fluid being pumped. The upstroke begins at the point shown in Figure B. At the end of the upstroke, all joints are in-line. This geometric constraint determines the length of the pitman arn.
Figures C(a) and C(b) show the plunger and ball valves in more detail. These valves are opened by fluid flow alone. On the upstroke, the riding valve is closed and the standing valve is open. Fluid above and within the plunger is lifted out of the casing while more fluid is pumped into the well. On the down stroke, the riding valve is opened and the standing valve is closed. Fluid flows into the plunger and no fluid is allowed to leave the well. [More Detail..]

Use link:
* Animate Softwere
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* Pump Accessories