TAREA 2 - ANALISIS DE PRESIONES Fecha de asignación: Martes 26 de Marzo de 2014 Fecha de entrega: Viernes 5 de Septiembre de 2014

Instructor: Dr. Freddy Humberto Escobar 1. A well is producing at a rate of 400 STB/D from a reservoir which has the following rock and fluid characteristics: k = 50 md = 3 cp h = 30 ft co = 8x10-6 psi-1 = 0.30 B = 1.25 bbl/STB rw = 6 in cf = 2x10-6 psi-1 a) After what value of the flowing time is the approximation Ei(-x) ln (1.781 X) valid

for this reservoir? What does this suggest? b) What is the pressure drop at the well after flowing for 3 hours? c) Calculate the pressure gradient at a point 150 ft away from the well after 3 hours of

production. 2. The following data correspond to a reservoir which has only two producer wells. The distance between the two wells is 1000 ft. = 20 % h = 80 ft cf = 2x10-6

/psi co = 3x10-6

/psi k = 100 md = 3 cp Pi = 2500 psia B = 1.2 bbl/STB rw = 6 in re = 4000 ft s well A = 5 s well B = 0 An interference test was run in this system. At the beginning both wells were closed and stabilized. A pressure recorder with a precision of 0.001 psi was run in well B. Then well A was opened to produce 100 BOPD. What is the required time for the perturbation generated in well A to be reached well B? 3. It is desired to estimate the current pressure of a point N located 500 ft north from another well lying 500 ft east of a north-south flow barrier. The well has produced 230000 STB during one year at a constant rate. Reservoir an fluid properties are: s = -3 Pi = 3000 psi B = 1.1 bbl/STB = 2.3 cp h = 50 ft ct = 2x10-5 /psi = 8 % rw = 4 in k = 2 Darcies 4. If the wells depicted by Fig. 1 are placed on production at the same time, compute the flowing pressure for the three wells after 72 hours of production. q1 = 80 STB/D =16 % rw1 = rw2 = rw3 = 0.33 ft q2 = 150 STB/D ct = 24.6x10-6 psi-1 B = 1.35 RB/ STB

q3 = 210 STB/D h = 24 ft = 2.5 cp r12 = 800 ft k = 56 md Pi = 4735 psia r13 =500 ft r23 = 600 ft

What assumption is made in these calculations concerning the location of reservoir boundaries?

Well 1

Well 2

Well 3

r13

r23

r12

Fig. 1. Well position for problem 4

=90°

Fault

r 2r = 500 ft1

Well 1

Well 2

Image welld d

Fig. 2. Two-well system for problem 5

5. Consider a two- well system in a homogeneous reservoir with infinite radius of drainage away from a fault as is indicated in Fig. 1.20. These two new wells where

completed at the same time and both closed in until the pressure in the reservoir is stabilized throughout the reservoir, then well #1 is produced for 100 hours, at which time the pressure in well #2 is measured and found to be 987 psia. Additional data are:

q1 = 200 STB/D k = 200 md h = 30 ft = 3 cp ct = 1.5x10-5 /psi = 15 % Pi = 1017 psia B = 1.3 rb/STB

a) Determine the distance d. b) Does the log-approximation to the Ei function apply? If not, when is this

approximation possible? c) Derive the equation giving the pressure gradient at any point N at a radius d from

well 1. Calculate the maximum and minimum values of the pressure gradient on this circle.

Well 1

Well 2 Well 3

800 ft

400 ft

390 ft

400 ft

410 ft10 ft 10 ft

390 ftP2r r

LEASE A LEASE B

P1

Fig. 3. Infinite reservoir containing three wells and a lease line, problem 6

6. Compute the flow rate per foot of lease for point P on the lease line which is on a line joining well 2 and 3 as shown in Fig. 3. The lease line is 2640 ft long. Wells 1, 2 and 3 have been producing for 300, 200 and 250 hours at a constant flow rate of 100, 250 and 200 STB/D, respectively. Other information is given as follows:

= 20 % B = 1.30 rb/STB ct = 11.6x10–6 psi-1

h = 300 ft = 3 cp k = 200 md Pi = 1525 psia

7. Two wells A and B located 1000 ft apart in a 125 md formation are put into production at the same time at constant rates of 550 and 1100 STB/D, respectively. The average properties of the formation and fluid are as follows:

h = 57 ft = 12 % = 2.4 cp Pi = 3500 psia ct = 3x10-6 psi-1 B = 1.10 br/STB

a) Determine the location of the interference point N, after 60 days of production and the pressure at point N.

b) Derive an equation relating a1, b1 and the pressure point M, if well B was an injector (qi = 550 BPD) during 60 days. Calculate PM for b1 = 2a1.

Well AWell B

N

r A r B

a1b1

M

Fig. 4. Well system for problem 7