Page 174 - Petroleum Production Engineering, A Computer-Assisted Approach

Guo, Boyun / Computer Assited Petroleum Production Engg 0750682701_chap12 Final Proof page 170 4.1.2007 2:43pm Compositor Name: SJoearun

12/170 ARTIFICIAL LIFT METHODS
Tapered rod strings are designed for static (quasi-static) PRL max ¼ W f S f (62:4) W r þ W r þ W r F 1
lads with a sufficient factor of safety to allow for random g s
low level dynamic loads. Two criteria are used in the ¼ 5,770 (0:9042)(62:4)(6,138)=(490) :
design of tapered rod strings:
þ 6,138 þ (6,138)(0:794)
1. Stress at the top rod of each rod size is the same ¼ 16,076 lbs < 21,300 lb
throughout the string.
2. Stress in the top rod of the smallest (deepest) set of rods c. The peak torque is calculated by Eq. (12.30):
should be the highest ( 30,000 psi) and the stress pro-
gressively decreases in the top rods of the higher sets of 1 2SN W r
2
rods. T ¼ SW f þ
4 70,471:2
!
The reason for the second criterion is that it is preferable 1 2(85:52)(22) (6,138)
2
that any rod breaks occur near the bottom of the string ¼ (85:52) 5,770 þ 70,471:2
4
(otherwise macaroni).
¼ 280,056 lb-in:< 320,000 lb-in:
Example Problem 12.1 The following geometric dim- d. Accurate calculation of counterbalance load requires
ensions are for the pumping unit C–320D–213–86:
the minimum PRL:
d 1 ¼ 96:05 in.
c
2
2
d 2 ¼ 111 in. SN (1 ) (85:52)(22) (1 0:33)
h
c ¼ 37 in. F 2 ¼ 70,471:2 ¼ 70,471:2 ¼ 0:4
c/h ¼ 0.33.
W r
PRL min ¼ S f (62:4) þ W r W r F 2
7
1
If this unit is used with a 2 ⁄ 2 -in. plunger and ⁄ 8 -in. rods g s
to lift 25 8API gravity crude (formation volume factor 6,138
1.2 rb/stb) at depth of 3,000 ft, answer the following ¼ (0:9042)(62:4) 490 þ 6,138 (6,138)(0:4)
questions: ¼ 2,976 lb
a. What is the maximum allowable pumping speed if 1 1
L ¼ 0.4 is used? C ¼ (PRL max þ PRL min ) ¼ (16,076 þ 2,976) ¼ 9,526 lb:
2
2
b. What is the expected maximum polished rod load?
c. What is the expected peak torque? A product catalog of LUFKIN Industries indicates that
d. What is the desired counterbalance weight to be placed the structure unbalance is 450 lb and 4 No. 5ARO coun-
at the maximum position on the crank? terweights placed at the maximum position (c in this case)
on the crank will produce an effective counterbalance load
of 10,160 lb, that is,
Solution The pumping unit C–320D–213–86 has a peak
torque of gearbox rating of 320,000 in.-lb, a polished rod (37) (96:05)
W c þ 450 ¼ 10,160,
rating of 21,300 lb, and a maximum polished rod stroke of (37) (111)
86 in.
which gives W c ¼ 11,221 lb. To generate the ideal counter-
balance load of C ¼ 9,526 lb, the counterweights should be
a. Based on the configuration for conventional unit placed on the crank at
shown in Fig. 12.5a and Table 12.1, the polished rod
stroke length can be estimated as r ¼ (9,526)(111) (37) ¼ 36:30 in:
(11,221)(96:05)
d 2 111 The computer program SuckerRodPumpingLoad.xls can
S ¼ 2c ¼ (2)(37) ¼ 85:52 in: be used for quickly seeking solutions to similar problems.
d 1 96:05
It is available from the publisher with this book. The
The maximum allowable pumping speed is solution is shown in Table 12.2.
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
70,471:2L (70,471:2)(0:4)
N ¼ ¼ ¼ 22 SPM: 12.5 Pump Deliverability and Power Requirements
c
S(1 ) (85:52)(1 0:33)
h Liquid flow rate delivered by the plunger pump can be
expressed as
b. The maximum PRL can be calculated with Eq. (12.17). S p E v (24)(60)
The 25 8API gravity has an S f ¼ 0:9042. The area of the q ¼ A p N (bbl=day)
7
1
2
2 ⁄ 2 -in. plunger is A p ¼ 4:91 in: . The area of the ⁄ 8 -in. 144 12 B o 5:615
2
rod is A r ¼ 0:60 in: . Then or
A p NS p E v
q ¼ 0:1484 (stb=day),
B o
DA p (3,000)(4:91)
W f ¼ S f (62:4) ¼ (0:9042)(62:4) where S p is the effective plunger stroke length (in.), E v is
144 144
the volumetric efficiency of the plunger, and B o formation
¼ 5,770 lbs
volume factor of the fluid.
g s DA r (490)(3,000)(0:60)
W r ¼ ¼ ¼ 6,138 lbs 12.5.1 Effective Plunger Stroke Length
144 144 The motion of the plunger at the pump-setting depth and
the motion of the polished rod do not coincide in time and
2
2
SN 1 þ c (85:52)(22) (1 þ 0:33)
F 1 ¼ h ¼ ¼ 0:7940: in magnitude because sucker rods and tubing strings are
70,471:2 70,471:2 elastic. Plunger motion depends on a number of factors
Then the expected maximum PRL is including polished rod motion, sucker rod stretch, and