TABLE 9.8—DATA FOR EXAMPLE 9

Mode IV. The injection well has been shut in before the test For the first step, the injection rate is constant and low enough that part-

Time (hours) pwf (psi) Pressure Derivative Dte nR (hours) (psi/STB-DDp/Dq ) Step 1 0.0000 3,059.000 0.0812 2,982.254 46.705 0.0812 0.0959 0.1625 2,949.867 51.832 0.1623 0.1364 0.2437 2,927.678 58.752 0.2434 0.1642 0.3250 2,910.036 64.779 0.3244 0.1862 0.4062 2,895.195 69.662 0.4052 0.2048 0.4874 2,882.139 74.016 0.4860 0.2211 0.5687 2,870.504 78.039 0.5668 0.2356 0.6499 2,859.946 81.417 0.6474 0.2488 0.7312 2,850.199 84.258 0.7280 0.2610 0.8124 2,841.110 87.034 0.8085 0.2724 0.8936 2,832.811 89.678 0.8889 0.2827 0.9749 2,825.024 91.862 0.9693 0.2925 1.0561 2,817.653 93.696 1.0495 0.3017 1.1374 2,810.641 95.251 1.1297 0.3104 1.2186 2,803.943 97.007 1.2098 0.3188 1.2998 2,797.561 98.446 1.2898 0.3268 1.3811 2,791.668 100.27 1.3698 0.3342 1.4623 2,786.044 101.79 1.4497 0.3412 1.5436 2,780.634 103.09 1.5296 0.3480 1.6248 2,775.416 104.54 1.6092 0.3545 1.7060 2,770.370 105.83 1.6888 0.3608 1.7873 2,765.482 107.18 1.7685 0.3669 1.8685 2,760.741 108.75 1.8480 0.3728 1.9498 2,756.135 110.25 1.9274 0.3786 2.0310 2,751.656 2.0067 0.3842 Step 2 2.0710 2,879.148 0.0397 0.0637 2.1110 2,941.543 0.0788 0.0949 2.1510 2,984.976 0.1173 0.1167 2.1910 3,019.437 0.1553 0.1339 2.2310 3,048.677 0.1927 0.1485 2.2710 3,074.148 0.2296 0.1612 2.3110 3,095.010 0.2661 0.1717 2.3510 3,113.920 0.3020 0.1811 2.3910 3,131.085 0.3375 0.1897 2.4310 3,148.915 0.3726 0.1986 2.4710 3,161.659 0.4072 0.2050 2.5110 3,175.486 0.4414 0.2119 2.5510 3,188.486 0.4753 0.2184 2.5910 3,200.615 0.5087 0.2245 2.6310 3,206.091 0.5417 0.2272 2.6710 3,213.005 0.5744 0.2307 2.7110 3,219.421 0.6068 0.2339 2.7510 3,225.389 0.6388 0.2369 2.7910 3,230.950 0.6705 0.2396 2.8310 3,236.139 0.7018 0.2422 2.8710 3,240.813 0.7328 0.2446 2.9110 3,245.045 0.7636 0.2467 2.9510 3,248.951 0.7940 0.2486 2.9910 3,252.575 0.8242 0.2505 3.0310 3,255.941 0.8540 0.2521

ǒ

168* 0 1.7060* 0 ) 168 * 0

Ǔ

(*800*0)ń(*800*0) + 1.6889 hours and the pressure function is

Dp Dq + pwfn(Dt) * pwfn*1ǒtn*1Ǔ qn*1* qn + pwf₂* pref q1* q2

0.4

�S'�1

0 _0.3 in f- � Step 2 'iii 0.2 e .41 0- €J � • Q, 0.1 � <:i 0.0 0.01 0.1 10

Radial·Flow Equivalent Time (hours)

Fig. 9.3O-Radial-flow equivalent-time plot, Example 9.5.

= = 0.3608 psi/STB-D.

Similarly, the equivalent time at Pwj= 3,095.01 psi in Step 2

(n = 3) is = (2.3110 - 2.03100)

(

)(-800-0)/[0-(-2000)]

(

l70.031 - 168

)[-0(-800l]/[0-(-2000)]

x _{2.3110 - 2.0310 + 170.031 - 168} =0.2661 hour

and the pressure function is

!'!P

Pwh - PlVh

!'!q

q2 q3

3095.01 - 275l.656 0 - (- 2000) = 0.1717psi/STB-D.

Rates are negative for injection. In the expressions for equivalent time, !'!t represents the elapsed time from the beginning of the test. In the pressure function,

!'!P

is the difference between measured Pwj

and

_Pwj

at the beginning of the step.

Fig. 9.30 shows a radial-flow multirate equivalent-time plot of the two-step-rate-test data. Data for the two steps coincide up until an equivalent time of 0.51 hour, after which the Step 2 data deviate from the baseline data of Step l. From Table 9.8, the pressure that corresponds to the equivalent time of 0.51 hour in Step 2 is 3,201

psi, which is interpreted to be the fracture-parting pressure.

9.7 Chapter Summary

In Chap. 9, we present an overview of pressure transient testing of injection wells.

In Sec. 9.2, we discuss methods for analyzing injectivity tests un der unit-mobility-ratio reservoir conditions. Injectivity tests are conducted by injecting into the reservoir at a constant rate and mea-

186

suring the resulting pressure response. Thus, injectivity tests corre spond directly to drawdown tests in producing wells.

Unit-mobility-ratio conditions occur when the pressure transients established during a test encounter only fluid having a single value of mobility. This can occur (1) when the injected fluid and the dis placed fluid have the same mobility, as in a brine-disposal well; (2)

when the injection period before the test is long enough so that the pressure transients during the test encounter only that region of the reservoir that has been swept by the injection fluid; or (3) when the injection period before the test is short enough so that the region swept by the injected fluid can be modeled by a zone of altered permeability, or skin.

If unit-mobility-ratio reservoir conditions are present, injectivity tests may be analyzed with techniques that are analogous to those used in analyzing drawdown tests. We illustrate the application of both semilog and type-curve analysis methods to injectivity tests through an example.

Just as injectivity tests correspond to drawdown tests in produc ing wells, injection-well falloff tests correspond to buildup tests in producing wells. In Sec. 9.3, we discuss analysis of falloff tests un der unit-mobility-ratio conditions. Again, we can use both Horner semilog-analysis and type-curve-analysis methods that have been developed for producing wells. We illustrate these techniques with an example.

In Sec. 9.4, we briefly discuss the application of the Matthews et at. method for estimating average drainage-area pressure to injec tion wells. In addition to the assumption of unit-mobility-ratio reser voir conditions, application of the Matthews et al. method to injec tion wells requires that the injected and displaced fluids have comparable values of </JeTh.

In Sec. 9.5, we turn our attention to composite systems (that is, sys tems where the assumption of unit-mobility-ratio conditions is not valid). In this situation, there are at least two and possibly three differ ent zones with different fluid saturations and mobility ratios.

In Sec. 9.5.1, we discuss the Hazebroek et ai. method for analyz ing falloff tests in injection wells before fillup. This method assumes that (1) a significant gas saturation exists in the reservoir outside the oil bank, (2) the pressure at the outer edge of the oil bank is constant, and (3) wellbore-storage effects are negligible.

The Hazebroek et ai. method requires the following information: the mobility ratio, the ratio of the total compressibilities in the oil and water banks, and the ratio of the inner and outer radii of the oil bank. The size of the oil bank can be estimated if the fluid saturations in the three zones and the water-injection volume are known.

The first step in applying the Hazebroek et at. method is to deter mine the pressure at the outer edge of the oil bank by a trial-and-er ror process with a semilog plot of log(pws -

Pe)

vs. !'!t. The perme ability thickness product kwh is then determined from the y intercept of the plot with correlations that Hazebroek et al. developed. After

kwh is determined, the effective permeability-thickness product for oil in the oil bank, k"h, is estimated from the mobility ratio and the viscosities of the oil and water.

We present an example analysis of a falloff test using the Haze broek et al. method.

In Sec. 9.5.2, we discuss the Merrill et al. method for analyzing falloff tests in liquid-filled reservoirs. This method allows the engi neer to estimate both the location of the front of the injected-fluid bank and the perrneabilities of the two fluid banks. The Merrill et al.

method is developed for situations where the oil bank is much larger than the water bank, 1f21'fl > _50.However, it provides acceptable re sults when 1f2I'fl> _10.Unlike the Hazebroek et al. method, the Merrill et ai. method does not require prior knowledge of the mobil ity ratio.

A conventional Horner plot is used as the basis for the Merrill et at. method. When this method is applicable, two semi log straight lines are present, reflecting responses from the two fluid banks. The distance to the front of the injected-fluid bank may be estimated from the time of intersection of the two straight lines or from the time when the observed pressure data deviate from the first straight line. The permeability in the injected-fluid bank and the skin factor may be obtained from the slope of the flfSt semilog straight line. Al though the permeability in the oil bank is related to the slope of the

INJECTION-WELL TESTING 187 second semilog straight line, it may not be computed directly from

the slope. Instead, the permeability in the oil bank must be estimated from the permeability in the water bank by use of correlations that Merrill et al. developed. We illustrate the use of the Merrill et al. method with an example.

In Sec. 9.6, we discuss step-rate testing. The objective of step-rate testing is to determine the parting pressure, which is the pressure at which fractures are created or extended. Care must be taken to avoid injecting at pressures higher than the parting pressure to prevent pre- mature breakthrough, poor sweep efficiency, reduced oil recovery, and loss of expensive injection fluids.

In Secs. 9.6.1 through 9.6.3, we discuss step-rate-test analysis with conventional and multirate analysis methods. The conventional analysis method, discussed in Sec. 9.6.1, requires either steady- state flow be achieved during the test or that equal-length timesteps be used. The parting pressure is determined from the intersection of two straight lines on a plot of injection BHP vs. injection rate. The conventional analysis method uses only a single pressure point at each rate.

In Sec. 9.6.2, we discuss the multirate analysis method. This method requires pressures to be recorded continuously, rather than at the end of each injection period as in the conventional method. The multirate method assumes transient radial flow into the reservoir during each constant-rate-flow period. In Sec. 9.6.3, we extend the multirate method to apply to linear flow to a vertical fracture.

In Sec. 9.6.4, we present a special case of multirate testing, the two-step rate test. In this test, the first rate is selected to be low enough so that the parting pressure is not exceeded during the first injection period, while the second rate is selected so ensure that the parting pressure is exceeded during the second period. The two tests are plotted as pressure difference divided by flow rate vs. the Agar- wal multirate equivalent-time function. If the parting pressure is not exceeded in either test, the data from the two tests lie along a single trend. Departure from the trend established by the first injection period indicates that the parting pressure was exceeded during the second injection period. The parting pressure is then obtained directly from the pressure corresponding to the point of departure from the trend. We present an example application of the two-step-rate-test method to determine parting pressure.

Exercises

1. An injection test was conducted in a salt water disposal well. Given the following rock and fluid properties, estimate permeability and skin factor from the injection test data. qw+450 STB/D; h+54

ft; Bw+1.028 RB/STB; pi+3430 psia; f+20.8%; ct+6.16 10–6

psi–1; rw+0.46 ft; m+0.65 cp.

In document Pressure Transient Testing (Page 194-196)