Taller Mdh-horner 1.pdf

Before shut-in the well had produced 9075 STB at a stabilized rate of 220 STB/D. I. Horner Method – Find: 1. The formation permeability and transmissibility. 2. The skin factor and wellbore storage coefficient. 3. Find flow efficiency, damage ratio and damage factor 4. The afterflow duration from pressure buildup data.

Solution 1. Conventional Techniques Horner Method Using data given on Table 2.1, Pws vs. Horner time ratio is plotted in semi log (Fig. 2.1). Horner Semilog Plot 3400 P* 3300 3200 3100 P1hr=3105 3000 2900

Pws (psia)

2. Problem No. 2 The following pressure buildup data were obtained from an oil well located at the center of a constant pressure square reservoir.

2800

Known reservoir and pressure data are:

2700 2600

h = 32ft; ø = 10 %; µ = 0.85 cp; rw = 3 in Bo = 1.29 bbl/STB; ct = 12*10-6psi-1 Pwf(∆t=0)=2450 psig Table 2.1 ∆t, hours 0.00 0.10 0.15 0.20 0.25 0.40 0.80 1.00 1.50 2.00 3.00 4.00 5.00 6.50 8.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00 110.00

2500 2400 10,000

1,000

100 starting time

10

1

Horner Time Ratio

Figure 2.1. Horner Plot Pws, psig 2450 2565 2620 2750 2800 2840 2880 2930 3000 3050 3100 3130 3145 3152 3160 3165 3185 3196 3205 3213 3220 3222.5 3224 3225.2 3226 3226.5

From figure 2.1 m  65 psia / cycle

Permeability is computed from q k  162.6 mh k  162.6 *

220 *1.29 * 0.85  18.8md 65 * 32

Transmissibility is estimated from k *h T



T

(2.1)

(2.2)

18.8 * 32  707md * pie / cp 0.85

tp must be estimated from data tp=9075*24/220=990 hours, then Horner ratio for tp1hr=991 and p1hr from figure 2.1 is 3,105 psia. Skin factor is computed from

2

 p1hr  p wf   k    3.23 (2.3) s  1.1513  log 2  m     ct rw   3,105  2,464    18.8   3.23 s  1.1513  log 6 2   65 0 . 1 * . 85 * 12 * 10 * 0 . 25    

s  5.3

Wellbore Storage coefficient is

 t * K * h C   0.14s  170,000 *  * e

  

DF  1  0.65  0.35  35%

These values show that the area next to the wellbore is damaged S> 0, FE < 1, DR> 1, and DF > 0. The afterflow duration is calculated looking for the starting time in Horner Plot. The Horner time ratio is 200, t p =990 then the time is: tp  t  200 t

(2.4)

t  4.52 hours

∆t is the starting time. In Horner plot figure 2.1 the Horner time ratio for TSSL is 200 then ∆t =4.97 hours and C is:

Miller-Dyes-Hutchinson method MDH

  4.97 *18.8 * 32 C     0.0098bbl / psia 0.14*5.3   170,000 * 0.85 * e 

MDH method indicates that a plot of pws vs ∆t should be a straight line with slope m. Permeability can be estimated from:

Flow efficiency, damage radio and damage factor are estimated from:

k

p s FE  1  (2.5) p *  p wf (t  0) From figure 2.1 p*=3320 psia, pwf=2,464.7 psia and ∆ps is estimated from:

From figure 2.2

162.6 * q * B *  m*h

(2.9)

Miller Dyes Hutchinson (MDH) 3400

3200 m=64

(2.6) Pws (psi)

ps  0.87 * m * s

3000

ps  0.87 * 65 * 5.3  300.045

2800

2600

2400

Now it is possible to calculate FE

FE  1 

2200

300.045  0.65  65% 3,320  2,464.7

DR 

1 FE

DR 

1  1.54  154% 0.65

DF  1  FE

2000 0.01

0.10

1.00

10.00 Shut in time Hours strarting time=8

Figure 2.2 MDH plot (2.7)

m  64 psia / cycle

k  162.6 *

(2.8)

220 *1.29 * 0.85  19.1md 64 * 32

100.00 End time=60

1000.00

3

The skin factor can be estimated from  p1hr  p wf   k    3.23 s  1.1513  log 2  m     ct rw 

(2.10)  3,105  2,464    19.1   3.23 s  1.1513  log  6 2  0.1 * .85 *12 *10 * 0.25  64    

s  5.47

Of the semilog straight line (Figure 2.2) the starting time and end time are respectively: 8 and 60 hours. Table . Comparative analysis Method K s md Horner

18.8

5.3

MDH

19.1

5.47

The results are very similar. Horner and MDH methods are more reliable and the values are very close.