5. HY HYDR DRA AUL ULIC IC FR FRA ACTU CTURI RING NG 2
TUNIO, May' 2011,,, Courtesy AP Aung
1
FRACTURING HYDRA HYDRAULICS ULICS
•
The hydraulic power required to pump qt barrels of fluid per minute into a well with a surface injection pressure of or,, con conve verti rting ng to ps psi is given by the product ps qt or hydraulic horsepower,
TUNIO, May' 2011,,, Courtesy AP Aung
2
Surface Injection Pressure
•
The pump pressure or surf surface ace inje injection ction pre pressur ssure e, ps, is bottom tom-hol -hole e fra fractur cture e trea treating ting equal to the sum of the bot pressure pt , the frictional pressure drop in the pipe ∆p f , press essur ure e dr drop op thr throug ough h the per perfo forrat ation ionss ∆ p , and an d th the e pr minus the hydrostatic pressure ∆ ps, (4.20)
•
If, du If, duri ring ng th the e tr trea eatm tmen ent, t, th the e pu pump mpss ar are e sto topp pped ed,, th the e surface pressure will drop, as there is no flow. TUNIO, May' 2011,,, Courtesy AP Aung
3
Surface Injection Pressure
•
In the momentary absence of frictional pressure losses, the bottom-h -ho ole fractu turre tr tre eating pressure can be calculated with greater precision from the expression .
•
inst stan anta tane neou ouss su surf rfac ace e sh shut ut-d -dow own n Where pi is the in pressure.
•
In addition, the frictional pressure losses in the system (∆ pt + ∆ p p) can be me meas asur ured ed in indi dirrec ectl tly y, by us use e of th the e equation TUNIO, May' 2011,,, Courtesy AP Aung
(4.22)
4
Surface Injection Pressure
•
Since the pressure drop across the perforations is usually small in comparison with the other pressure terms, one can ca n as assu sume me th that at it is ne negl glig igib ible le an and d ob obttai ain n th the e su surf rfac ace e injection pressure as (4.23)
•
Since ∆ p f and ∆ p p in Eq (4.20) are influenced by the flow rate, the surface injection pressure will also be dependent upon rate.
TUNIO, May' 2011,,, Courtesy AP Aung
5
Bottom-hole Treating Pressure
•
The bottom-hole treating pressure pt is determined from the fracture gradient G f and the depth D to the fracture, since (4.24)
(4.25)
TUNIO, May' 2011,,, Courtesy AP Aung
6
Hydrostatic Hydrosta tic Pressure •
The hydrostatic pressure ∆ ps is obtained from the density of the fluid including the propping agent.
(4.26)
where gravity ity of the fracture fracture fluid, is the specific grav x is the conce concentr ntratio ation n of sand in pounds per gal gallon lon of fluid, specific ific gra gravity vity of sand. 2.63 2. 63 is th the e spec
TUNIO, May' 2011,,, Courtesy AP Aung
7
Hydrostatic Hydrosta tic Pressure
•
If th the e sp spec ecif ific ic gr grav avit ity y of th the e fr frac actu turi ring ng fl flui uid d is given at 60oF, the specific gravity at the average well temperature T is calculated from
(4.27)
TUNIO, May' 2011,,, Courtesy AP Aung
8
Hydrostatic Hydrosta tic Pressure
•
Where β is the thermal coefficient of expansion of the fluid.
•
If th crud ude e oi oill, the value of β is the e fr frac actu turre flu luid id is a cr obtained from volume correction tables.
•
The hydrostatic pressure ∆ ps is equal to the hydrostatic gradient times the depth,
(4.28) TUNIO, May' 2011,,, Courtesy AP Aung
9
Pressure Drop Across Perforations
•
Pressure drop across the perforations is obtained directly from Bernoulli’s equation and converting necessary units.
.
•
Where ρ in pounds per gallon, q in gallons per minute, A in square inches, and pressure in pounds per square inch.
TUNIO, May' 2011,,, Courtesy AP Aung
10
FRACTURE DESIGN CALCULATION
•
The objective of any type of fracture design calculation is to plan the most economical treatment that will in the
There Ther e are are 2 desi design gn cases. cases.
•
(1) As (1) Assu sumi ming ng injec injecti tion on rate rate,, size size of tr trea eatm tmen ent, t, frac fractu ture re gradient
•
(2)
Assumi Ass uming ng Pr Produ oducti ctivi vity ty Rat Ratio io TUNIO, May' 2011,,, Courtesy AP Aung
11
FRACTURE DESIGN CALCULATION
•
This ty This type pe of ca calc lcul ulat atio ion n in invo volv lves es con onsi side derrat atio ion n of th the e following variables: •
Fracturing fluid coefficient C
•
Injection rate q
•
Total injection volume V
•
Area of the fracture A
•
Weight Wei ght of propping agent S
•
Surface injection pressur pressure e ps
•
Horsepower Horsepo wer required Hh
•
Productivity ratio of the well PR TUNIO, May' 2011,,, Courtesy AP Aung
12
Example (4.5)
•
Design a fracture treatment assuming an injection rate, size of treatment, and fracture gradient, given:
TUNIO, May' 2011,,, Courtesy AP Aung
13
Example (4.5) • the frictional pressure drop is 1826 psi • vo volu lume me per uni nitt are rea a of th the e fr frac actu ture re is 0.00833 cu ft/sq ft • po poro rosit sity y of mo most st fr frac actu turin ring g sa sand nd is of th the e order of 35 per cent • The specific gravity of sand is 2.63 and the density is 2.63 x 62.4 or 164 lb/cu ft • eq equi uival valen entt di diam amet eter er (d (de) e) of th the e ci circ rcul ular ar pipe is 3.62 in • Fracture pressure is 1826 psi
Solution
• A review of past treatm tme ents in th the e area shows that a treatment of 40,000 gal of lease oil at an injection rate of 30 bbl per minute has given effective results in this reservoir, also, it is noted that the fracture gradients have Courtesy 14 been approximately TUNIO, 1.0May' psi2011,,, per ft.AP Aung
Example (4.5)
bottom tom-hol -hole e trea treating ting • With th this is frac actu turre grad adiient, th the e bot pressure is
• Then the differential pressure across the fracture face is
• Since lease oil is to be used as the fracturing fluid, the fracturing fra cturing fluid coefficie coefficient nt is C c
TUNIO, May' 2011,,, Courtesy AP Aung
15
Example (4.5)
• The pumping time for 40,000 gal of fluid at a rate of 30 bbl/min is
• Solving for x
• And the efficiency from Fig (7.11) is 31 per cent. Then from Eq (4.18) the fracture area is
TUNIO, May' 2011,,, Courtesy AP Aung
16
Example (4.5)
• Then the weight of sand, S , necessary to pack one square foot of fracture is
• The maximum amount of sand needed is
TUNIO, May' 2011,,, Courtesy AP Aung
17
Example (4.5) • And the sand concentration in pounds per gallon of oil is 176,600/40,000 or 4.42 lb/gal.
• The actual flow rate (including sand) is the total volume (oil plus sand) divided by the total fracture time , or
TUNIO, May' 2011,,, Courtesy AP Aung
18
Example (4.5)
• The coefficient of thermal expansion for oil approximately specific ific gr gravi avity ty of the oil at the 0.0005 per degree. The spec average well temperature is
• And the density is
• The hydrostatic pressure developed at 2000 ft is TUNIO, May' 2011,,, Courtesy AP Aung
19
Example (4.5) • The average flow velocity in the equivalent pipe is
• The Reynolds number of the flow in the equivalent pipe is found from
TUNIO, May' 2011,,, Courtesy AP Aung
20 20
Example (4.5) surf rfac ace e in inje ject ctio ion n pr pres essu sure re, neglecting the • Then the su pressure drop across the perforations is
• Si Sinc nce e for 5 ½ in in,, JJ-55 55 casi casing ng 60 pe perr ce cen nt of the burs bursti ting ng pressure (5320 psi) is 3724 psi, the injection pressure used rau c orsepower s s w n e sa e m . e y ra calculated calcula ted as
• On the basis of 600 hydraulic horsepower per pump truck , five pumper pumperss are required for the job. producti ductivity vity ra ratio tio, sev • To ca calcu lcula late te the pro sever eral al ass assump umptio tions ns
must be made.
TUNIO, May' 2011,,, Courtesy AP Aung
21
Example (4.5)
• Since the gradient is 1.0 psi per ft and the well depth is 2000 ft, it is assumed that the fracture plane is horizontal.
•
2 = , , = ft. the ratio of fracture radius to external radius is r f /r e = 252/660 = 0.381.
TUNIO, May' 2011,,, Courtesy AP Aung
22
Example (4.5)
• From Fig (4.7) the permeability of 10-20 mesh sand for a fracture treating pressure of 2000 psig is 60,000 md, the value of k f W/ k h is
• From Fig (4.6) the PR is 5.0, so that, if the initial production was 10 bbl per day, the production after fracturing is 50 bbl per day.
TUNIO, May' 2011,,, Courtesy AP Aung
23
TUNIO, May' 2011,,, Courtesy AP Aung
24