TABLE 4.4—DRAWDOWN DATA TABULATED FOR PLOTTING

t (h ) pi*pwf ( i) t (h ) pi*pwf ( i) t (h ) pi*pwf ( i) (hours) (psi) (hours) (psi) (hours) (psi)

0.0109 24 0.164 307 2.18 1,232 0.0164 36 0.218 389 2.73 1,266 0.0218 47 0.273 464 3.28 1,288 0.0273 58 0.328 531 3.82 1,304 0.0328 70 0.382 592 4.37 1,316 0.0382 81 0.437 648 4.91 1,326 0.0437 92 0.491 698 5.46 1,335 0.0491 103 0.546 744 6.55 1,349 0.0546 114 1.09 1,048 8.74 1,370 0.109 215 1.64 1,172 10.9 1,386 16.4 1,413 k+ 141.2qBm h

ǒ

pD pi* pwfǓ MP +(141.2)(500)(1.2)(0.8)₍₅₆₎

ǒ

0.85₁₀₀

Ǔ

+10.3 md.

From the time match point, fct+ 0.000264k mr2 w

ǒ

t tD

Ǔ

_MP +(0.000264)(10.3) (0.8)(0.3)2

ǒ

1 1.93 104

Ǔ

82 PRESSURE TRANSIENT TESTING

Fig. 4.5—Drawdown-test analysis with Ramey’s type curve. FLOW TIME, hours

p p

CD

CD

+1.96 10–6 _psi–1_.

Compare these with the values used to determine CD from C:

fct+(0.2)(1 10–5)

+2 10–6_.

This is the same value we used to calculate CD. As noted previously,

the time match point does not provide an independent estimate of fc_t.

4.3.2 McKinley Type Curve. McKinley1 _{developed type curves}

with the primary objective of characterizing damage or stimulation in a drawdown or buildup test in which wellbore storage distorts most of or all the data, thus making this characterization possible with rela- tively short-term tests. In constructing his type curves, McKinley ob- served that the ratio of pressure change, Dp, to the flow rate causing the change, qB, is a function of several dimensionless quantities:

Dp qB +f

ǒ

khDt mC , fmckDttr2w , _rre w, D t tp

Ǔ

. . . (4.22)

Type curves with so many parameters would be difficult, if not im- possible, to use. Accordingly, McKinley simplified the problem with the following assumptions.

1. The first is that the well has produced long enough (essentially to stabilization) so that the last group, Dt /tp, is not important. In oth-

er words, he assumed that the producing time, tp, is much greater

than the test duration, Dt. Consequently, the type curves may not give accurate results for pressure-buildup tests with short producing periods before shut-in.

2. He ignored boundary effects, thus eliminating the variable

r_e/r_w in the logic used to construct the type curves (see, however, As- sumption 6).

3. His analysis of simulated buildup and drawdown curves showed that, during the wellbore-storage-dominated portion of a test, the parameter khDt/mC was much more important in determin- ing Dp/qB than was kDtńfmctr2w. Accordingly, he let kńfmctr2w

+10 106 _{md-psi/cp-ft2 (an average value) for all his type curves.}

Even when kńfmctr2w varies from this average value by one or two

orders of magnitude, the shape of the type curves is not affected sig- nificantly. The reason for this approximation was McKinley’s judg- ment that the loss of accuracy is more than compensated for by the

WELL-TEST ANALYSIS USING TYPE CURVES 83

Fig. 4.7—Early-time data fit on McKinley’s1 _{type curve.} gain in sensitivity in the type curves (i.e., the shape of each curve is distinctly different at earliest times).

4. To account for the remaining parameters that do have a signifi- cant influence on test results, McKinley plotted his type curves as Dt (ordinate) vs. 5.615CDp/qB (abscissa) with the single correlating parameter kh/5.615Cm. Fig. 4.6 shows a small-scale version of McKinley’s curves.

5. The skin factor, s, does not appear as a parameter in his curves. Instead, they assess damage or stimulation by noting that the earliest wellbore-storage-distorted data are dominated by the effective near- well transmissibility, (kh/m)wb. Thus, (kh/m)wb can be calculated

from a type-curve match of the earliest test data. After wellbore- storage distortion has diminished, pressure/time behavior is gov- erned by the transmissibility in the formation, (kh/m)_f, which can be estimated from a type-curve match of later data.

6. McKinley approximated boundary effects by plotting the simu- lator-generated type curves for approximately one-fifth log cycle beyond the end of wellbore-storage distortion and then making the curves vertical. This step roughly simulates drainage conditions of 40-acre spacing. Note that this gives the curves early-, middle-, and late-time regions, but the curves were designed to be used primarily to analyze early-time data. Hence, when the curves are applied to drawdown tests, they must be applied to data not affected by bound- aries because they do not simulate boundary effects in drawdown tests properly.

McKinley prepared three different type curves: one for 0.01 to 10 minutes, one for 1 to 1,000 minutes, and one for 103 _{to 10}6 _minutes.

The curve for 1 to 1,000 minutes is by far the most useful and, ac- cordingly, is the only one shown here. Earlougher3 provides the oth- er curves. The following steps outline a recommended procedure for using McKinley’s type curves.

1. Plot Dt (minutes) as the ordinate vs. Dp+(p*pwf) for a draw-

down test or (pws*pwf) for a buildup test as the abscissa either on

tracing paper or on 3 5 cycle log-log paper the same size as McKin- ley’s type curve. The time range on the axis should correspond exact- ly to one of the type curves; i.e., it should span 0.01 to 10, 1 to 1,000, or 103 _{to 10}6 _minutes.

2. Match the time axis of the test-data plot with that of the ap- propriate McKinley type curve. Move the data horizontally only un- til the earliest data match one of the type curves (Fig. 4.7).

3. Record the correlating parameter value [(kh/m)/5.615C]wb for

the matched type curve.

4. Choose a match point, any Dp from the test data plot and the corresponding value of 5.615DpC /qB from the type curve, or (Dp, 5.615DpC/qB)MP.

5. Determine the wellbore-storage coefficient, C, from the match point:

C+

ǒ

5.615DpCńqB

Dp

Ǔ

_MP

ǒ

qB

5.615

Ǔ

. . . (4.23) 6. Calculate near-well transmissibility, (kh/m)wb, from the param-

eter value recorded in Step 3 and the wellbore-storage coefficient determined in Step 5: ǒkhńmǓwb+ 5.615C

ǒ

khńm 5.615C

Ǔ

wb . . . (4.24)

Fig. 4.8—Later-time data fit on McKinley’s1 _{type curve.} 7. If the data trend away from the type curve matching the earliest data, then shift the data plot horizontally to find another type curve that better fits the later data. A shift to a higher value of (kh/m)/5.615C indicates damage, while a shift to a lower value indi- cates stimulation (Fig. 4.8).

8. Calculate formation transmissibility: ǒkhńmǓf+ 5.615C

ǒ

khńm

5.615C

Ǔ

7

(C)5, . . . (4.25)

where 7 and 5+Steps 7 and 5, respectively. Note that we do not find a new pressure match point to determine C again. The storage coef- ficient, C, is found ultimately in Step 5. In fact, if only data reflecting formation transmissivity (after wellbore-storage distortion has dis- appeared) are analyzed, error will result with the McKinley method. However, in such a case, other methods, such as semilog analysis, are accurate. The match point must be found with early wellbore- storage-distorted data.

9. Flow efficiency also can be estimated with McKinley’s type curves.2 _{A working definition of flow efficiency, E, is}

E[p ** pwf* Dps

p ** pwf +

Dp * * Dps

Dp * . . . (4.26) The quantities Dp* _{and Dp}

s are estimated from the McKinley type

curves. In Eq. 4.26, Dp*_{+the vertical asymptote approached by Dp}

in the McKinley plot (Fig. 4.9), while Dps is calculated from Dpd,

the pressure change at the intersection of the early-fit type curve and the late-fit type curve. Dps is calculated from

Dps+

ǒ

1*

kwb

k_f

Ǔ

Dpd. . . (4.27)

Example 4.2—Drawdown Test Analysis With McKinley’s Type Curve. Problem. A drawdown test was run on an oil well. Table 4.5

summarizes known data. Estimate near-well permeability, forma-

Fig. 4.9—Flow efficiency calculation from McKinley’s2 _type curve.

84 PRESSURE TRANSIENT TESTING

ÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁ ÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁ

TABLE 4.5—PRESSURE-DRAWDOWN-TEST DATA,

In document Pressure Transient Testing (Page 90-93)