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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:

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

=

( )( ) ( )24 1 842 103.

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

14 Journal of Canadian Petroleum Technology

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

w i

w i wo

a

V

kh t=

( ) ( ) ( )24 1 842 102

3.

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

Differentiating Equation (3) gives:

d

d t

V

kh t

w

a

w i wo

a

=

( ) ( ) ( )( )

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 d/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 () 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

=

2................................................................................................ (6)

and

Cc V

hc rD

g w

t w

=

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 () 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 w 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 tta a

=

2

........................................................................................ (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