practical considerations in estimating test duration … · practical considerations in estimating...

October 2009, Volume 48, No. 10 13

Practical Considerations in Estimating Test Duration for Perforation Inflow Tests

S. THEYS*, F. BRUNNER, L. maTTaR Fekete associates Inc.

N.m.a. RaHmaN Schlumberger

* Now with Bureau Veritas

Peer reviewed PaPer (“review and Publication Process” can be found on our website)

IntroductionPerforation inflow tests are short and therefore increasingly

popular in the industry. They can deliver valuable reservoir in-formation, such as the initial reservoir pressure, the reservoir per-meability and the skin effect. The data obtained from perforation inflow tests can be divided into two parts: (a) the early-time data is wellbore storage dominated, and (b) the late-time data is reser-voir-dominated.

Perforation inflow tests are not likely to exceed approximately 24 hours, and should be designed so that reservoir-dominated flow occurs during that period. For cases where wellbore storage does not excessively affect the early time data and when reservoir per-meability is high enough, the duration of the perforation inflow test is likely sufficient to reach radial flow. However, for large well-bore storage and low reservoir permeability, the time to reach res-ervoir-dominated flow will be prohibitively long. In such cases, one option is to reduce wellbore storage by running a bridge plug, thus reducing the effects that initially masked the true reservoir performance.

The objective of this paper is threefold:

AbstractPerforation inflow tests are short, cost-effective and envi-

ronmentally-friendly solutions to estimate the initial reservoir pressure, permeability and skin, immediately after perforating the well. The reservoir-dominated (radial) flow regime must be reached before terminating the test in order to obtain reason-able estimates of these parameters. These reservoir parameters and chamber (or wellbore) volume directly influence the rate of build-up of pressure and the test duration. In the field, it is not easy to ascertain whether or not sufficient data has been obtained so that the test can be terminated, especially when the data is not analyzed in real time. If the rate of build-up is closely monitored, it is possible to predict whether (i) the minimum required data will be obtained within the stipulated test time, (ii) the test has to be run longer, or (iii) a downhole shut-in is required.

In this paper, analytical simulation is used to run a sensitivity study on reservoir and well parameters and see how these affect the onset of the reservoir-dominated flow regime. The impulse derivative is used to identify the presence of reservoir-dominated flow. The rate of pressure build-up at I hour is used to determine if sufficient data will be collected within the test duration.

The outcome is a practical field guide to help the operator de-cide whether the test should be continued, modified or stopped.

• To review the behaviour of early- and late-time data of per-foration inflow tests with various reservoir and wellbore parameters.

• To suggest a practical method for determining, early on in the test, whether the required reservoir-dominated flow regime will be reached within the allocated test time.

• To identify if running a downhole plug within the first few hours of the test will allow us to reach reservoir-dominated flow.

These objectives have been achieved by relating the rate of pres-sure buildup at 1 hour with the time required to reach reservoir-dominated flow.

Easy-to-use graphs have been prepared. Also, a field example is given to illustrate the method.

Theoretical DevelopmentThe focus of this paper is the application of PITA (perfora-

tion inflow test analysis) to tight gas. Accordingly, the equations are written using pseudo-pressure and pseudo-time, and assume a single-phase gas flow.

In this section, the early and late time approximations for PITA will be reviewed. The intent is to identify which parameters affect these analyses, and to what extent.

The solution of the closed-chamber test (slug test) is the basis of PITA equations, and was first introduced by Ramey et al.(1). Sub-sequent studies(1 – 4) have concentrated on the analysis of the late-time data to determine initial pressure and permeability.

Rahman et al.(4) derived the solutions of PITA, and provided early and late time approximations that lead to working equations. They showed that not only can late time data provide information on permeability and initial pressure, but early time data can give an estimate of skin.

The early-time (dominated by wellbore storage) equation, as de-rived by Rahman et al.(4), is given by:

ψ ψψ ψ

w woi wo

w

a

kh

V st= −

−( )( ) ×( )24 1 842 103.

∆

....................................................(1)

Differentiating Equation (1) gives:

d

d t

kh

V sw

a

i wo

w

ψ ψ ψ

∆=

−( )( ) ×( )24 1 842 103.

.................................................................(2)

14 Journal of Canadian Petroleum Technology

The late-time (reservoir-dominated flow) equation, Rahman et al.(4) is:

ψ ψψ ψ

w i

w i wo

a

V

kh t= −

( ) ×( ) −( )24 1 842 10

2

3.

∆.............................................(3)

Differentiating Equation (3) gives:

d

d t

V

kh t

w

a

w i wo

a

ψ ψ ψ

∆ ∆=

( ) ×( ) −( )( )

24 1 842 10

2

3

2

.

................................................. (4)

Equations (2) and (4) identify the variables that affect the rate of pressure build-up (dp/dt ↔ dΨ/dt). These are: the permeability-thickness (kh), skin s, initial pressure pi, wellbore volume Vw and cushion pressure pw0. Accordingly, these are the variables that have been investigated in this study. The range of these variables is given in Table 1.

Pseudo-Time to Reservoir-Dominated Flow

Equation (4) describes the behaviour of reservoir-dominated flow, but it does not give any information on when this flow re-gime starts. One of the objectives of this paper is to predict when reservoir-dominated flow will start, for any given test. For this purpose, one requires a relationship between the time-to-start-of reservoir-dominated flow (tRF) and various wellbore / reservoir parameters.

In traditional well testing, Agarwal et al.(5) proposed the empir-ical 1-1/2 log-cycle rule to determine the time to reservoir-domi-nated flow (tRF). On a log-log plot of pressure change (ΔΨ) versus pseudotime, (tRF) will occur approximately one and a half log-cy-cles after the end of the wellbore storage unit slope. This rule is equivalent to Equation (5) below:

t s CD RF D, .= +( )60 3 5............................................................................. (5)

where tD,RF and CD are dimensionless time to reservoir-domin-ated flow and wellbore storage, defined in Equations (6) and (7), respectively:

tkt

rD

a

w

=λ

φ 2

................................................................................................ (6)

and

Cc V

hc rD

g w

t w

=η

φ 2

.......................................................................................... (7)

Analysis of synthetic PITA data generated for the different reservoir and wellbore parameters given in Table 1, gives an empirical correlation, Equation (8) below, of the same form as Equation (5):

t s CD RF D, = +( )56 8 ................................................................................ (8)

Inspection of this data shows that the 1-1/2 log-cycle rule is also applicable to PITA. This means that if the pressure change (ΔΨ) is plotted on log-log paper versus pseudotime, the time of departure from the unit slope, multiplied by 30, (approximately 1-1/2 log-cy-cles) corresponds to (tRF).

A log-log unit slope is consistent with Equation (1). Inspection of Equation (1) clearly shows that a Cartesian plot of Ψw versus pseudotime yields a straight line. Departure from this Cartesian straight line is also equivalent to departure from the log-log unit slope.

It can be concluded from these observations that during a PITA test, if the rate of pressure buildup at 1 hour is such that the log-log plot has not deviated from the unit slope (or the Cartesian plot is still a straight line), then it is likely that reservoir-dominated flow will NOT occur within a 30-hour time frame (1-1/2 log-cycles).

Our experience indicates that, while these procedures are rela-tively simple to apply, they are too subjective and are therefore not recommended. In the field, pressure and time are more readily available than pseudopressure and pseudotime, and it is tempting to reduce these relationships to Cartesian plots of pressure (instead of pseudopressure) versus time (instead of pseudotime). This too, is not recommended because of the potentially significant devia-tions caused by gas properties.

Methodology for Identifying tRFA new approach to identifying reservoir-dominated flow, based

on the PITA derivative, was developed by Rahman et al.(6). The PITA derivative is defined as:

PDER ttaa

= ∂∂

2 ψ

........................................................................................ (9)

It is illustrated in the three parts of Figure 1. These figures show that the PDER becomes a constant, at late times, when reservoir flow becomes dominant. This is consistent with Equation (4). It is evident from Equation (4) that PDER is a function of kh and Vw. Figures 1a and 1b show this dependence. Figure 1c shows the ef-fect of skin.

Also shown in Figure 1 is the start of reservoir-dominated flow (tRF). This was determined by visual inspection of the point where the derivative becomes constant. This determination is approximate, but every attempt was made to be consistent in se-lecting this point, for all the cases studied.

From these observations, and from inspection of Equation (4), it is possible to identify the variables that affect reservoir domi-nated flow. These are shown in Table 1, along with the range in-vestigated. Using this range, a large number of synthetic PITA derivatives (PDER) were generated and examined to ascertain the start of reservoir-dominated flow (tRF).

Relationship Between tRF and Rate of Pressure Buildup

The synthetic data gave not only the PITA derivative, but also the synthetic pressure buildup observable during the test. It is in-tuitive that a high permeability will result in a short duration of wellbore storage (small tRF) and a high rate of pressure buildup, and vice versa. Accordingly, we hypothesized that the rate of

TABle 1: Range of variables investigated.

Permeability, k, mD 0.0001 to 100Initial reservoir pressure, pi, kPa 1,000 to 20,000Cushion pressure, pw0, kPa 100 to 1,000Skin, s, dimensionless 0 to 20Wellbore volume, Vw, m3 0.1 to 100Net pay thickness, h, m 1 to 10Wellbore radius, rw , m 0.0914Porosity, φ, fraction 0.2Gas saturation, Sg, fraction 0.8


pressure buildup is a good indicator of how “fast” reservoir domi-nated flow will occur.

Because time and pressure are continuously monitored during a test, the rate of pressure buildup is readily available. Thus, it was decided to correlate the rate of buildup with the tRF. The time of 1 hour into the test was selected arbitrarily, with the following considerations: it is late enough into the test to allow initial insta-bilities to dissipate, and early enough to decide on an operational change if necessary.

Accordingly, all the synthetic data were plotted in the format of Figure 1. The tRF was selected visually from these graphs as pre-viously described, and the rate of pressure buildup at 1 hour (dp/dt–1) was also noted.

tRF vs. dp/dt–1Figure 2 represents the time to start of reservoir-dominated flow

(tRF) versus the rate of pressure build-up at 1 hour (dp/dt–1), for permeability-thickness products varying from 0.0001 to 1,000 mD.m, while all other reservoir and wellbore conditions are kept

fixed. It is evident that the higher the permeability, the faster the pressure increases (high dp/dt-1), and tRF decreases. Conversely, the smaller the permeability, the smaller dp/dt–1, and the later the time to reservoir-dominated flow.

Figure 3 represents the behaviour of time to reservoir-domi-nated flow (tRF) versus rate of pressure buildup at one hour (dp/dt–1), when skin and cushion pressure are changed along with the permeability-thickness: the two cases of (a) skin of 0 and cushion pressure of 1,000 kPa and (b) skin of 20 and cushion pressure of 100 kPa are the limits of the range investigated. As skin increases, tRF increases [see Equation (8)] and dp/dt-1 decreases. The cushion pressure affects tRF to a much lesser extent – the smaller the cushion pressure, the greater tRF. The variation in skin (and to a lesser ex-tent, the cushion pressure) creates an envelope of solutions. Note that if the permeability-thickness product and the cushion pressure are fixed, the rate of pressure build-up at 1 hour will be greater for a skin of 0 than that for a skin of 20, assuming all other param-eters remain unchanged. This is to be expected, because the time to reservoir-dominated flow is not a strong function of skin, but the rate of pressure buildup is (skin impedes influx into the well-bore and diminishes rate of pressure build-p, dp/dt–1). Negative skins have not been investigated. This is not restrictive, because in most situations of PITA (before well completion) the skin is usu-ally positive.

Figure 4 shows the time to reservoir-dominated flow versus rate of pressure build-up for two cases of reservoir pressure when all other parameters (excluding kh) are fixed. Both the 20,000 kPa and the 10,000 kPa cases will have the same time to reservoir-dominated flow but the rate of build-up at 1 hour for the 20,000 kPa reservoir pressure case will be twice the rate of buildup for the 10,000 kPa reservoir pressure case. This illustrates that the rate of pressure buildup is directly proportional to (Ψi–Ψw0), which is consistent with Equation (2), and it follows that the two curves in Figure 4 would collapse to a single curve if the X-axis were nor-malized by using dp/dt-1 divided by (Ψi–Ψw0) instead of dp/dt–1

1.E+02

1.E+01

1.E+00

1.E-01

1.E-02

1.E-03

1.E-04

1.E-05

1.E-06

1.E-07

PIT

A D

eriv

ativ

e

Time0.001 0.01 0.1 1 10 100 1,000

tRF = 300

tRF = 30

Vw = 100

Vw = 10

FIGURE 1b: Variation of the PITA derivative due to wellbore volume Vw.

1.E+02

1.E+01

1.E+00

1.E-01

1.E-02

1.E-03

1.E-04

1.E-05

1.E-06

1.E-07

PIT

A D

eriv

ativ

e

Time

0.001 0.01 0.1 1 10 100 1,000

tRF = 150

tRF = 30

s = 5

s = 0

FIGURE 1c: Variation of the PITA derivative due to skin s.

dp/dt-1 (kPa/hr)

t RF

(hr)

100,000

10,000

1,000

100

10

1Vw = 7 m3, pi = 10,000 kPa, s = 20, pw0 = 300 kPa - kh varies

Increasing kh

kh = 0.001 mD.m

1 10 100 1,000 10,000

FIGURE 2: tRF versus dp/dt-1: Effect of varying the flow capacity (kh).

dp/dt-1 (kPa/hr)

t RF

(hr)

100,000

10,000

1,000

100

10

1

Vw = 7 m3, pi = 10,000 kPa - kh varies

1 10 100 1,000 10,000

s = 20pw0 = 100 kPa

s = 0pw0 = 1,000 kPa

FIGURE 3: tRF versus dp/dt-1: Effect of varying skin s and cushion pressure pw0.

1.E+02

1.E+01

1.E+00

1.E-01

1.E-02

1.E-03

1.E-04

1.E-05

1.E-06

1.E-07

PIT

A D

eriv

ativ

e

Time0.001 0.01 0.1 1 10 100 1,000

tRF = 0.7

tRF = 30(kh) = 150

(kh) = 1.5

FIGURE 1a: Variation of the PITA derivative due to flow capacity (kh).


on its own. Figure 5 has been generated by dividing the X-axis of Figure 4 by (pi –pw0), and applies to a wellbore volume of 10 m3.

Of all the parameters that significantly influence tRF, the only ones over which the operator has any control are the wellbore volume and the cushion pressure. As can be noted from Equations (4) and (8), the wellbore volume, Vw, affects tRF directly. If the wellbore volume is reduced by 100 times, the time to reservoir-dominated flow will correspondingly reduce by 100. This knowl-edge gives us an opportunity to manage the test procedure, so that reservoir-dominated flow can be obtained earlier, if desired. This is often easily achievable by decreasing the wellbore volume, using down-hole shut-in (packer, tubing plug, and the like).

However, Figures 2 – 5 raise two issues: (a) tRF is not single-valued at the high rates of pressure build-up; and (b) skin creates a wide spread in the curves (Figure 3).

multiple Values of tRF

Looking at a typical graph of tRF vs dp/dt–1, as shown in Figure 6, it can be seen that at large values of dp/dt–1, tRF can have two values. As the permeability increases, the time to reservoir-dom-inated flow decreases and the rate of build-up reaches a peak in value. Then this rate of build-up decreases again while time to res-ervoir-dominated flow continues to decrease. In other words, for one value of dp/dt–1, there are two possible values of tRF. How do we differentiate between these two solutions?

To differentiate between the two solutions, the pressure reading itself is monitored in comparison to the reservoir pressure. From the synthetic data studied, it has been observed empirically that, if the “pressure” (not dp/dt–1) measured at one hour is higher than 65% of the reservoir pressure, then the lower of the two tRF values is the correct one. If, on the other hand, the pressure reading at 1 hour is below 65% of the reservoir pressure, then the higher value of tRF applies. Figure 6 illustrates the issue.

Effect of SkinAs can be seen in Figure 3, at any specified value dp/dt–1,

the value of tRF depends on skin. While all parameters affect the curves, the skin is the biggest factor in causing the separation of the two curves. To reduce this range, a few guidelines can be presented as a result of the analysis of the synthetic data:

• If high skin is suspected (often associated with high perme-ability), the lower value of tRF should be selected;

• When the pressure stabilizes quickly to the estimated reser-voir pressure, or dp/dt–1 is high, the operator can be confi-dent that reservoir-dominated flow will be reached within the time allocated for the test, and skin has little effect.

The lower the cushion pressure, the higher the wellbore storage, and the later the time to reservoir-dominated flow. However, the effect of cushion pressure is minimal compared to that of skin.

Application of Methodology Once graphs similar to Figure 5 have been generated for a par-

ticular wellbore volume and range of skin, these graphs can be used to determine if reservoir-dominated flow will be reached during the expected duration of the test. If the indication is that this will occur, then the test can proceed as planned. If the tRF estimated from these graphs is too long, then a decision can be made whether to abort the test or to reduce the wellbore volume by using some sort of downhole shut-in. From Equation (8), it is clear that the tRF is directly proportional to the wellbore volume. Therefore, re-ducing the wellbore volume by a factor of 100 (easily achieved by downhole shut-in) will reduce the tRF correspondingly by a factor of 100.

Figures 7 – 10 have been prepared as the “working graphs” to be used in the field for estimating tRF . They are applicable to well-bore volumes of 0.5, 7, 10 and 20 m3 respectively. For other values of Vw, interpolation between the values from these graphs is con-sidered to be valid.

Practical Method for the FieldAs mentioned earlier, the simplest and most practical way to

hasten the time to reservoir-dominated flow during a test is to re-duce the wellbore volume. For example, a 139.7-mm-(5.5-in.)-di-ameter, 1,000-m deep well has a 9.1 m3 wellbore volume. Reducing the wellbore length from 1000 m to a 10-m isolated interval, the wellbore volume gets reduced to 0.091 m3. Correspondingly, the time to reservoir-dominated flow reduces by 100 times. This can be accomplished by running a plug (with downhole gauges below the plug). Thus, if dp/dt–1 indicates tRF to be excessive, the recommendation is to run the plug immediately after the diagnosis is made at one hour.

Based on the observations made in this paper, the following is a practical method of how to proceed with a perforation inflow test and thus decide on the fly whether to run a plug or not:

dp/dt-1 (kPa/hr)

t RF

(hr)

100,000

10,000

1,000

100

10

1

Vw = 20 m3, s = 20, pw0 = 300 kPa - kh varies

1 10 100 1,000 10,000

pi = 10,000 kPapi = 20,000 kPa

FIGURE 4: tRF versus dp/dt-1: Effect of varying initial reservoir pressure pi.

dp/dt-1 (pi - pw0) (1/hr)

t RF

(hr)

100,000

10,000

1,000

100

10

1Vw = 20 m3, s = 20, pw0 = 300 kPa - kh varies

0.01 0.10 1.00 10.00

pi = 10,000 kPa

pi = 20,000 kPa

FIGURE 5: tRF versus dp/dt-1 / (pi – pw0) for s = 20, Vw = 20 m3.

dp/dt-1 (kPa/hr)

t RF

(hr)

10,000

1,000

100

10

1100 1,000 10,000

Double value of tRF

Max (dp/dt) occurs at 65% pi

Below 65% pi

Above 65% pi

FIGURE 6: tRF versus dp/dt-1: Differentiating the double value of tRF at high (dp/dt-1).


• Measure both the pressure and the rate of pressure build-up immediately after the start of the perforation inflow test, and continue this until the end of the test.

• At 1 hour into the test, verify whether the pressure reading is above 65% of the estimated reservoir pressure.

• At 1 hour, determine the rate of pressure build-up (dp/dt–1).

• Read the time to reservoir-dominated flow, tRF, corresponding to the measured dp/dt–1, from Figures 7 to 10, as appropriate (Estimate the skin, or interpolate between the two values as appropriate). If you are on the right side of the graph, two values of tRF may exist. If the pressure at 1 hour is higher than 65% of the reservoir pressure, use the lower value; otherwise, use the higher value of tRF;

• The tRF as determined previously can fit into three categories:

1. tRF is less than the planned test time limit: In this case, sufficient data will be collected with the current operating conditions. No changes are necessary to the conduct of the test.

2. tRF falls between the planned test duration and 100 times the planned test duration: In this case, if it is economical to do so, run a plug with downhole gauges. This will shorten the required time in proportion to the volume of wellbore reduced.

3. tRF is beyond 100 times the planned test duration: In this situation, it is unlikely that any change in operating con-ditions will provide the necessary pressure data. The op-erator may consider reducing the wellbore volume as well as running the test for an extended period of time.

Illustration of the Method

Figures 11 – 13 illustrate the procedure. The initial wellbore volume is 10 m3, and estimated reservoir pressure is 10,000 kPa.

Suppose that the operator wants to limit the perforation inflow test to 24 hours. To signify this, a straight line indicating a 24-hour test time limit has been drawn on the plot. Another straight line, indicating a 2,400-hour (or 100 times the test duration) has been added. Test conditions exhibiting a time to reservoir-dominated flow of 2,400 hours or less can be altered by reducing the well-bore volume by 100 times. The new conditions should then exhibit

t RF

(hr)

10,000

1,000

100

10

1

0

pw0 = 300 kPa - kh, pi varies

0.0010 0.0100 0.1000 1.0000

s = 20

s = 0

VW = 0.5 m3

[dp/dt-1 (pi - pw0)] (1/hr)

FIGURE 7: Working graph of tRF versus dp/dt-1 / (pi – pw0) for Vw = 0.5 m3.

t RF

(hr)

10,000

1,000

100

10

1


0.010 0.100 1.000

s = 20

s = 0

VW = 7 m3

[dp/dt-1 (pi - pw0)] (1/hr)

FIGURE 8: Working graph of tRF versus dp/dt-1 / (pi – pw0) for Vw = 7 m3.

t RF

(hr)

10,000

1,000

100

10

1


0.010 0.100 1.000

s = 20

s = 0 VW = 10 m3

[dp/dt-1 (pi - pw0)] (1/hr)


[dp/dt-1 (pi - pw0)] (1/hr)

t RF

(hr)

10,000

1,000

100

10

1


0.00001 0.00010 0.00100 0.01000

s = 20

s = 0 VW = 20 m3


t RF

(hr)

10,000

1,000

100

10

1


0.010 0.100 1.000

VW = 10 m3

s = 0s = 2024-hr Test2400-hr Limit

p-1 = 9,000 kPa = 90% pi

dp/dt-1 = 2,000 kPa/hr dp/dt / (pi - pw0) = 0.2

[dp/dt-1 (pi - pw0)] (1/hr)

FIGURE 11: Case where tRF falls within the planned test time limit (24 hours).


a time to reservoir-dominated flow within the desired 24-hour test duration. As an example:

• If the pressure reading is 9,000 kPa and dp/dt–1 is 2,000 kPa/hr (Figure 11): the measured pressure is above 65% of the estimated reservoir pressure. tRF is then in the lower part of the envelope plot. It also indicates an estimated time to reservoir-dominated flow below 24 hours. No operating changes are necessary.

• If the pressure is 5,000 kPa and dp/dt–1 is 2,000 kPa/hr (Figure 12): the measured pressure is below 65% of the estimated reservoir pressure. The estimated time to reservoir-dominated flow falls between 24 and 2,400 hours. The recommendation is then to reduce the wellbore volume, which will reduce the minimum test time from 200 hr to 2 hr.

• If the measured pressure is 750 kPa and dp/dt-1 is 200 kPa/hr (Figure 13): the measured pressure is below 65% of the estimated reservoir pressure. The estimated time to reser-voir-dominated flow is above 2,400 hours. The test should be stopped.

Figure 14 summarizes the steps for the proposed practical field method in the form of an algorithm.

Field exampleA field example is presented below to illustrate the method-

ology described earlier. It highlights the value of a reduced well-bore volume.

Figures 15 (which is derived from Figure 7) and 16 illustrate the calculations of tRF during a perforation inflow test performed on a tight gas well. The operator – having already a fair idea of the reservoir pressure – wanted a quick test, and thus immediately chose to reduce the wellbore volume to 0.45 m3 and run downhole gauges. The estimated reservoir pressure is 30,000 kPa. Reading at 1 hour gives a pressure of 10,800 kPa and rate of pressure build-up of 6,050 kPa/h. Applying this to the Vw = 0.5 m3 envelope plot, tRF is estimated at 3.5 hours, well below the 24 hour test limit. Later, the analysis of the full test confirmed that reservoir-domi-nated flow was met at 3.8 hours, giving a skin of 1, permeability of 0.003 mD and reservoir pressure of 30,774 kPa.

[dp/dt-1 (pi - pw0)] (1/hr)

t RF

(hr)

10,000

1,000

100

10

1


0.010 0.100 1.000

VW = 10 m3


p-1 = 5,000 kPa = 50% pi

dp/dt-1 = 2,000 kPa/hr dp/dt / (pi - pw0) = 0.2

Reduce WellboreVolume

FIGURE 12: Case where tRF falls between the planned test time limit (24 hours) and 100 times the test time limit (2400 hours).

t RF

(hr)

10,000

1,000

100

10

1pw0 = 300 kPa - kh, pi varies

0.010 0.100 1.000

VW = 10 m3


p-1 = 750 kPa = 7% pi

dp/dt-1 = 200 kPa/hr dp/dt / (pi - pw0) = 0.02

Stop Test

[dp/dt-1 (pi - pw0)] (1/hr)

FIGURE 13: Case where tRF falls above the 100 times of the test limit (2400 hours).

Measure (p, dp/dt) at 1 hour

Yes

tRF read < test limit

Continue Test

1Test limit < tRF read < 100 x test limit

Run Plug and Bottomhole Gauges

2tRF read > 100 x test limit

Stop Test

3

Read tRF by selecting Figures 7, 8, 9 or 10, closest to your Vw

Nop > 65 % pi tRF is the upper solution tRF is the lower solution

10,000

1,000

100

10

1Tim

e to

Rad

ial F

low

(hr)

1 10 100 1,000 10,000

dp/dt (1 hr)

FIGURE 14: Flow chart to estimate time to reservoir-dominated flow.


Time (hr)

Pre

ssur

e (k

Pa)

and

Rat

e o

fP

ress

ure

Bui

ld-u

p (k

Pa/

hr)

30,000

25,000

20,000

15,000

10,000

5,000

0

pi (estimate) = 30,000 kPa

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

VW = 0.45 m3Rate of Pressure Build-up

Data Pressure

p-1 = 10,800 kPa = 36% pi

dp/dt-1 = 6,050 kPa/hr

FIGURE 15: Field example: Estimation of tRF in a tight gas reservoir reading of p and dp/dt at 1 hour.

ConclusionsThe following conclusions can be drawn:1. A practical method for identifying the likelihood of attaining

the reservoir-dominated flow regime during a PITA test has been derived from synthetic data.

2. The start of reservoir-dominated flow, tRF, can be identified using PDER, the PITA derivative.

3. tRF can be estimated using the 1-1/2 log cycle rule of trad-itional well testing methods. However, identifying the end of the wellbore storage appears to be too subjective, and is not recommended except as a last resort.

4. Graphs have been developed relating tRF to dp/dt–1 for various wellbore volumes. These can be used to decide, at 1 hour into the test, whether (a) reservoir-dominated flow will occur, (b) if the test duration should be extended or (c) if a downhole shut-in is required.

AcknowledgementsThe authors wish to thank the management of Fekete Associates

Inc. for permission to publish this paper.

t RF

(hr)

10,000

1,000

100

10

1

0

pi-ref = 30,000 kPa, Vw = 0.5 m3

0.0010 0.0100 0.1000 1.0000

p-1 = 10,800 kPa = 36% pi dp/dt-1 = 6,050 kPa/hr dp/dt / (pi - pw0) = 0.24

tRF (estimate) = 3.5 h

s = 0

s = 20

[dp/dt-1 (pi - pw0)] (1/hr)

FIGURE 16: Field example: Identification of time to reservoir-dominated flow on Vw = 0.5 m3 graph.

NOmENCLaTUREcg = gas compressibility, kPa–1

ct = compressibility, kPa–1

CD = wellbore storage, dimensionlessdp/dt–1 = rate of pressure rise at 1 hour, kPa/hh = formation thickness, mk = absolute permeability, mDp = pressure, kPapi = initial pressure, kPapw0 = initial cushion pressure or wellbore pressure at

time t = 0, kPaPDER = PITA derivative, kPa2/cpPITA = perforation inflow test analysisrw = wellbore radius, ms = skin, dimensionlesst = time, hrtD,RF = dimensionless time to start of reservoir-dominated

flowtRF = time to start of reservoir-dominated flowVw = wellbore volume, m3

Δta = pseudotime, hr, 1µg gc

dt∫η = 1 / 2π, units conversion coefficient λ = 3.6 × 10–3, coefficient of dimensionless timeφ = porosity, fractionψi = initial pseudopressure, kPa/sψw = pseudopressure corresponding to measured wellbore

pressure, kPa/sψw0 = initial cushion pseudopressure, kPa/s

REFERENCES 1. Ramey, H.J., Agarwal, R. and Martin, I. 1975. Analysis of ‘Slug Test’

or DST Flow Period Data. J. Cdn. Pet. Tech. 14 (July–September): 37–47.

2. Cinco-Ley, H., Kuchuk, F., Ayoub, J., Samaniego-V., F., and Ayes-taran, L. 1986. Analysis of Pressure Tests Through the Use of Instantaneous Source Response Concepts. Paper SPE 15476 pre-sented at the SPE Annual Technical Conference and Exhibition, New Orleans, 5–8 October. doi: 10.2118/15476-MS.

3. Rahman, N.M.A., Mattar, L., and Zaoral, K. 2006. A New Method for Computing Pseudo-Time for Real Gas Flow Using the Material Bal-ance Equation. J. Cdn. Pet. Tech. 45 (October): 36–44.

4. Rahman, N.M.A., Pooladi-Darvish, M., and Mattar, L. 2005. De-velopment of Equations and Procedure for Perforation Inflow Test Analysis (PITA). Paper SPE 95510 presented at the SPE Annual Technical Conference and Exhibition, Dallas, 9–12 October. doi: 10.2118/95510-MS.

5. Agarwal, R.G., Al-Hussainy, R., and Ramey, H.J. Jr. 1970. An In-vestigation of Wellbore Storage and Skin Effect in Unsteady Liquid Flow: I. Analytical Treatment. SPE J. 10 (3): 279–290; Trans., AIME, 249. SPE-2466-PA. doi: 10.2118/2466-PA.

6. Rahman, N.M.A., Pooladi-Darvish, M., and Mattar, L. 2005. Perfora-tion Inflow Test Analysis. Paper 2005-031 presented at the Canadian International Petroleum Conference, Calgary, 7–9 June.

7. Rahman, N.M.A., Pooladi-Darvish, M., Santo, M.S., and Mattar, L. 2006. Use of PITA for Estimating Key Reservoir Parameters. Paper 2006-172 presented at the Petroleum Society’s 7th Canadian Inter-national Petroleum Conference (57th Annual Technical Meeting), Calgary, 13–15 June.

Provenance—Original Petroleum Society manuscript, Practical Con-siderations in Estimating Test Duration for Perforation Inflow Tests (2007-160), first presented at the 8th Canadian International Petroleum Conference (the 58th Annual Technical Meeting of the Petroleum Society), June 12-14, 2007, in Calgary, Alberta. Abstract submitted for review De-cember 15, 2006; editorial comments sent to the author(s) May 19, 2009; revised manuscript received July 6, 2009; paper approved for pre-press July 10, 2009; final approval September 8, 2009 - SPE 130068-PA.


Authors’ BiographiesSophie Theys is currently an account man-ager for Bureau Veritas in its Oil and Gas Division. She has experience in energy and utilities management, as well as coiled tubing operations. She holds a diploma of engineering from Ecole Polytechnique Féminine and an MS degree in petroleum engineering from Texas A&M University. She is an active member of the Society of Petroleum Engineers.

Louis Mattar is the President of Fekete As-sociates, Inc. He specializes in well testing and production data analysis, and has au-thored 50 technical publications. He has received the Petroleum Society’s Distin-guished Author Award and the Outstanding Service Award. In 2003, Louis was the SPE Distinguished Lecturer in well testing.

Noor M. Anisur Rahman is currently working as a Reservoir Engineer with Schlumberger Testing Services. During his previous employment as an R&D En-gineer at Fekete Associates Inc., he was leading the efforts in developing analysis techniques for short tests. Dr. Rahman has a B.Sc. and an M.Sc. in mechanical engi-neering from the Bangladesh University of Engineering and Technology, and a Ph.D. in petroleum engineering from the Univer-sity of Alberta.

Frank Brunner is currently a Senior Tech-nical Advisor in the Well Test group at Fekete. Frank has over 30 years of industry experience, focusing on pressure transient analysis and production optimization.

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