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FIRST NAME: JAISON ROY

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Date submitted: .........10/11/2022......................

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 Department of Engineering
Module EG551Q

Well Testing: Analysis And Design Report

JAISON ROY
JOSEPH CALINS
Student ID-52105962
Degree Program: MSc in Petroleum Engineering
Introduction:
Hydrocarbon reservoirs are generally characterized qualitatively and quantitatively through well
testing, a subdivision of reservoir and production engineering. Well-testing generally examines the
pressure behaviour during shut-ins or production periods versus elapsed time. During testing, the
well pressure is evaluated over a short period of time in comparison with the entire reservoir life.
In the case of well evaluation, it takes a maximum of two days to conduct this test. While several
months are needed for pressure data recording to estimate the reservoir boundary [1]. The purpose
of well testing is typically to analyse a reservoir's properties and predict the reservoir's future
production based on the provided appropriate data and circumstances

There are several types of well tests, based on the method and objective of carrying them out.
There are six types of tests: drawdowns, build-ups, injections, falloffs, interferences, and pulses.
In the drawdown test, the reservoir pressure is stabilized at initial pressure, and then the well is
opened to flow at a constant rate, whereas the built-up test, involves closing the well that was
flowing at a constant rate to record the response to the pressure builds. In interference tests, wells
are tested for their ability to communicate, whereas pulse tests identify whether two reservoir zones
exist. A fall-off test or short injection test is conducted before oil production to evaluate well
injectivity. There are some other tests called deliverability test and transient test, where the
deliverability test measures the flow rate of the well, which is used to estimate inflow performance,
whereas the transients test measures changes in reservoir pressure as a result of changes in well
rates to determine reservoir structure and flow performance [2,3].

Furthermore, multi-well tests and single-well tests have different applicability. During the multi-
well test, an observation well measures pressure response because the current flow rate is not
constant at the active well. Multi-well tests provide important information about the well's
communication. The method and objectives of the single-well test are different, where it records
the response at the same well. By means of this method, the average pressure is estimated, the
extent of damage or stimulation is identified, in-situ permeability is calculated, and the drainage
zone of reservoir fluids is calculated.

During well testing. It is recommended to use dual-flow and dual shut-in for better analysis of well
and reservoir properties. The first has a short flow period followed by a shut-in, while the second
has a long flow period followed by a shutdown. To reach pressure stabilization, the initial flow
period should be as short as possible, and the initial shut-in period should be at least four times the
initial flow period. Initial flow and shut-in periods are used to estimate communication with the
formation and measure the initial pressure. It is important to perform a second flow and shut-in
test to estimate the representative volume of the formation and estimate productivity.
Consequently, it is recommended to run the flow for six hours to estimate stable production, and
the shut-in period is 1.5 to 2 times of flow period. Pressure gauges are used to measure pressure,
and it is recommended that high-precision gauges be used. It is also important to run more than
one gauge in addition to checking the sensitivity of the pressure gauge.
In order to obtain a better estimation of a reservoir's and well's properties, the quality of the
equipment to be used for testing should be checked in advance, as well as the quality of the data
gathered. It is essential to inspect, calibrate, and maintain the equipment used, such as pressure
gauges, flow meters, and thermometers. To analyze the pressure loss, it is expected to have stable
production as soon as possible. It is recommended that all data and events be documented. Before
the shut-in process, all essential data should be noted to calculate reservoir and well properties [4].

Objective:
The objective of this exercise is to compare the quality of the data generated using various
methods and to select the most reliable technique for calculating reservoir properties.

Methodology:
A manual method and the Kappa-Ecrin software were used for calculating the well and
reservoir properties based on well test data and reservoir properties that had already been
determined. Manual methods are too simple, and they do not account for the impact of multi-phase
fluid flow, multi-well interference, production history, multi-layering, multi-geological factors and
development factors, where the software includes all these factors for computation.
Manual Approach:
The reservoir properties were estimated using three different methods in this section. They are
• Agrawal method (equivalent time),
• Miller Dyes-Hutchinson (MDH) method and
• Grigarten-Bourdet type curve method

Equivalent Time Method (Agrawal)

For the data given of 1st build-up test, the Agarwal method is chosen since the data deals with
build-up and tp almost equal to ∆𝑡, which lasted for 3 hours, we calculated the reservoir properties;
permeability skin factor and initial reservoir pressure using the Agrawal method. Spivey and Lee
describe the procedure for conducting this method as follows [4],

• Calculating the equivalent time using the Eq.1, after the start of the shut-in period by
identifying the producing time and shut period.

𝑡𝑝 ×∆𝑡
te= ……………………………….Eq.1
𝑡𝑝+∆𝑡

• Using Ms-Excel, a graph has been plotted for calculated equivalent time (𝑡𝑒) for
respective bottom hole pressure (Pws).
• The best-fit line has been drawn through the infinite-acting radial flow region (IARF) and
the slope of that line has been calculated using the trendline option in Excel.
• The permeability of the reservoir has been calculated by substituting the slope found in
the Eq.2
 162.6×𝑄𝐵µ
K= ……………………………………… Eq.(2)
𝑀ℎ

• Using the best-fit line, calculate (te at 1hr) and read (Pws at 1hr).
• The skin is calculated by substituting the values found in previous steps in Eq.3
𝑃𝑤(Δ𝑡 = 1ℎ𝑟 )−𝑃𝑤(Δ𝑡 = 0ℎ𝑟
) 𝐾
S=1.151[ 𝑚
− 𝑙𝑜𝑔10 (𝜑µ𝑐 𝑟2 ) + 3.23…….…………... Eq. (3)
𝑡 𝑤

• The initial reservoir pressure is determined by extrapolating the semi-log plot for (te)
equal to the producing time (tp).

MDH Method (Draw Down)

From the second production data given the MDH method is chosen since that data are related to
production and tp >> ∆𝑡, which lasted for 24 hours, the reservoir and well properties like
permeability, skin factor, and wellbore storage can be calculated by the Miller Dyes-Hutchinson
(MDH) method by following the procedure described by Spivey and Lee [4],

• Calculate the elapsed time (𝛥𝑡) from the start of the second production period.
• Using MS Excel, a graph has been plotted for the log of calculated elapsed time (𝛥𝑡) for
respective bottom hole flowing pressure (Pwf).
• Draw the best-fit line through the infinite-acting radial flow region (IARF) and the slope
of that line has been calculated using the trendline option in Excel.
• The permeability of the reservoir has been by calculated substituting the calculated slope
in using the Eq.4

162.6×𝑄𝐵µ
K= …………………………………. Eq. (4)
𝑀ℎ

• The skin is calculated by substituting the values found in previous steps in Eq.5
𝑃𝑤(Δ𝑡 = 1ℎ𝑟 )− 𝑃𝑤(Δ𝑡 = 0ℎ𝑟
) 𝐾
S=1.151[ − 𝑙𝑜𝑔10 (𝜑µ𝑐 𝑟 2 ) + 3.23…………... Eq. (5)
𝑚 𝑡 𝑤

• A graph of log-log plot has been plotted for elapsed time (𝛥𝑡) with respective pressure
difference (𝛥𝑃) to calculate the slope of wellbore storage region (mwbs) using the Eq .(6)
𝑞𝐵
C = 24𝑚 ………………………………………….. Eq. (6)
𝑤𝑏𝑠

Gringarten-Bourdet method:

In the second build-up test, which lasted for 48 hours, the well and reservoir properties as well
as the boundary of the reservoir were evaluated using the Gringarten-Bourdet method by
following the procedure described by Spivey and Lee [4],
 • With the given data, the log-log graph has been plotted for pressure and pressure
derivative as a function of time using Kappa software.
• Regression was done for various parameters like skin, permeability and well storage to
match accurately.
• Export the plotted graph to the power point and match it with a transparent bourdet curve,
to find the change in pressure and equivalent time.
• The permeability has been calculated using the following Eq (7),
141.2×𝑞×𝐵×𝜇 𝑃𝐷
K= × ……………….………… Eq. (7)
ℎ ∆ 𝑝
• The dimensionless wellbore storage has been calculated using the Eq. (8)
0.0002637×𝑘 𝑡𝑒𝑞
CD = 2 (𝑡 𝐷 ) …………………….… Eq. (8)
∅×𝜇×𝐶𝑡 ×𝑟𝑤 ⁄𝐶
𝐷
• The wellbore storage coefficient (c) using Eq. (9)
2
∅×𝐶𝑡 ×ℎ×𝑟𝑤
C= × 𝐶𝐷…………………….…. Eq. (9)
0.894

• The Skin factor has been calculated using the Eq.10

1 𝐶𝐷 ×𝑒 2𝑆
S=2 ln ( 𝐶𝐷
)……………………………...….Eq.10

Software:
The KAPPA software was used to estimate reservoir and well properties. To estimate these
properties, the given reservoir, fluid properties and pressure and data have been entered and
infinite. Then, the log-log graph has been plotted for pressure difference and pressure derivative
as a function of time. The permeability, Skin factor and wellbore storage has been calculated using
the software. Finally, sensitive analysis has been done for permeability, skin factor and wellbore
storage for +-20% of each parameter to examine the effect of each parameter.

Result:
5050
5000
Presuure (psia)

4950
4900
4850
4800
4750
4700
0 10 20 30 40 50 60 70 80 90
Time (hr)

cleaning period 1st buil-up Production period 2nd build up

Figure 1 Scheduled Built-up and production for a function of time

Figure describes the graph that is plotted for the pressure as a function of time, where region the
orange line describes the first build-up period, the grey line describes the production period, and
the yellow line describes the second build-up period.

Equivalent Time Method (Agrawal):

5010
5000 y = 20.067x + 4994.6
R² = 0.9984
4990
4980
Pws (psia)

4970
4960
4950
4940
4930
4920
4910
-2.5 -2 -1.5 -1 -0.5 0 0.5
te (hr)

Figure 2 Semi-log plot Pws as function of equivalent time (te)

Figure describes the semi-log plot that was plotted bottom hole pressure as a function of calculated
equivalent time. The blue line describes the wellbore storage, and the orange line describes the
IARF region. The slope of the IARF region was estimated.

Table 1 Reservoir Properties obtained using Agrawal Method

Permeability Skin Factor Initial pressure

113.31 mD 4.38 4916.53 psia
MDH Method (Draw Down):

4860 y = -21.438x + 4754.8

4840 R² = 0.9999

4820
Pws (psia)

4800
4780
4760
4740
4720
4700
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

log (Delta t) (hr)

Figure 3 Flowing bottom hole pressure (Pwf) as function of elapsed time (∆ t)

Figure describes the semi-log plot that was plotted bottom hole pressure as a function of calculated
equivalent time. The blue line describes the wellbore storage, and the orange line describes the
IARF region. The slope of the IARF region was estimated at about.

Table 2 Reservoir and well Properties obtained using MDH method

Permeability Skin Factor Wellbore Storage

130.07 6.88 0.106 bbl/psi

Gringarrten-Bourdet Type-curve Match:

Figure 4 Gringarten-Bourdet Type_curve Match

Figure describes the log-log plot of pressure and pressure derivative as a function of time, and it
was matched with Gringarrten-Bourdet to estimate reservoir and well properties using the
dimensionless parameter.

Table 3 Reservoir and Well properties obtained from Gringarten-Bourdet

Permeability Skin Factor Wellbore Storage

134.476 3.36 0.07787
 (a) (b)

(c)

Figure 5 Sensitivity Analysis

In Figure 5 (a) Shows the sensitivity analysis of skin, (b) shows the sensitivity analysis for
permeability and (c) shows the sensitivity analysis of wellbore storage.

Kappa Result:
The reservoir and well properties have been estimated for 1st build-up, production and 2nd
build-up using the Kappa software and tabled in Table 4

Table 4 Results obtained from Kappa

Period Pi, psia K, md Skin Wellbore Storage Boundary

(bbl/psi)
1st Build-Up 4999.9 120.160 5.51 0.00999 Infinite
Production 4999.9 120.160 5.51 0.00999 Infinite
2nd Build-Up 4999.9 120.160 5.51 0.00999 Infinite

The reservoir and well properties obtained from a manual method such as the Agrawal method
(equivalent time), Miller Dyes-Hutchinson (MDH) method and Grigarten-Bourdet type curve
method have been tabled in Table 1,Table 2,Table 3 respectively and reservoir and well properties
obtained from the Kappa software has been tabled in Table 4. The magnitude of each parameter
obtained from each method has been graphically represented in the bar diagram Figure 6 to
describe the percentage of error. These variations might be due to regression on data which is
automatically done by Kappa and also due to manual error which includes shifting the pressure
data for respective time and improper identification of IARF region which have significant
uncertainty.
Software and manual Computation Comparison:
(a) (b) (c)

10 140 0.15

5 120 0.1

0.05
0 100
skin Variation Permability Variation 0
Wellbore Storage variation
Build-up 1 Skin prodution Built-up1 Production
Built-Up-2 Kappa Built-up 2 Kappa prodution Built-up-2 Kappa

Figure 6 Result comparison of manual and software approach

In figure 6 (a) shows the variation of skin ,(b) shows the variation of permeability and (c) the
variation of wellbore storage and legend in each figure shows the respective period

Uncertainty:

In well-test analysis, there are four main sources of uncertainty, with varying degrees of
importance and resolvability. These include data errors caused by noise, drift, temperature
changes, and time shifts, errors in flow rate measurements, ambiguity in response interpretations
(matching different models with an apparent equal level of verisimilitude), and uncertainty about
rock and fluid properties and especially when manually calculating, a significant error is caused
by the incorrect identification of IARF regions, which vary greatly [5].

Conclusion:
The reservoir and well properties have been estimated using both manual and software method
and found that manual method has more uncertainty than software method. Source of these
uncertainty and sensitivity has been discussed briefly.
Reference:

1]Abdolhossein Hemmati Sarapardeh, Aydin Larestani, Nait Amar Menad and Sassan Hajirezaie
(2020). Applications of Artificial Intelligence Techniques in the Petroleum Industry. Gulf
Professional Publishing.

2] Barnum, R.S. and Vela, S., 1984, January. Testing Exploration Wells by Objectives. In SPE
Annual Technical Conference and Exhibition. Society of Petroleum Engineers.

3]Abdus Satter, Ghulam M. Iqbal, in Reservoir Engineering, 2016

4] Spivey, J.P. and Lee, W.J., 2013. Applied well test interpretation. Richardson, TX: Society of
Petroleum Engineers

5] Horne, R.N., 1994, January. Uncertainty in well test interpretation. In University of Tulsa
Centennial Petroleum Engineering Symposium. Society of Petroleum Engineers.
Appendix:
Appendix for Task-1:

162.6×𝑞𝐵µ 162.6×3980×1.35×0.8
K= = = 113.31 md
𝑀ℎ 19.58×315
𝑃𝑤(Δ𝑡 = 1ℎ𝑟 )− 𝑃𝑤(Δ𝑡 = 0ℎ𝑟
) 𝐾
S=1.151[ 𝑚
− 𝑙𝑜𝑔10 (𝜑µ𝑐 𝑟2 ) + 3.23]
𝑡 𝑤

4991−4801.7 113.31
S=1.151 [ 20.067
− 𝑙𝑜𝑔10 (0.15×0.8×1.35×10−5 ×0.31252 ) + 3.23] = 4.38

Initial pressure extrapolated from the plot at 𝛥𝑡𝑒 = 0.01, (Pi) = 4916.53 psi

Appendix for Task-2:

162.6×𝑄𝐵µ 162.6×5000×1.35×0.8
K= = =130.07 md
𝑚ℎ 21.43×315

𝑃𝑤(Δ𝑡 = 1ℎ𝑟 )− 𝑃𝑤(Δ𝑡 = 0ℎ𝑟

) 𝑘
S=1.151[ 𝑚
− 𝑙𝑜𝑔10 (𝜑µ𝑐 𝑟2 ) + 3.23]
𝑡 𝑤

4745.8−4995.88 130.07
S=1.151[ − 𝑙𝑜𝑔10 ( )+ 3.23] =6.88
21.43 0.15×0.8×1.35×10−5 ×0.31252

1000
y = 2646.5x + 120.59
Change in pressure

100

10

1
0.01 0.1 1 10 100
tp (hr)

𝑞𝐵 5000×1.35
C = 24𝑚 = 24×2646.5
=0.106 bbl/psi
𝑤𝑏𝑠
Appendix for Task-3:

141.2×𝑞×𝐵×𝜇 𝑃𝐷
K= ×
ℎ ∆𝑝

141.2×5000×1.35×0.8 10
K= × = 134.476
315 180

0.0002637×𝑘 𝑡𝑒𝑞
CD = 2 (𝑡 𝐷 )
∅×𝜇×𝐶𝑡 ×𝑟𝑤 ⁄𝐶
𝐷

0.0002637×134.476 0.085
CD =0.15×0.8×1.35×10−5 ×0.31252 ( 10
) = 1905.27

2
∅×𝐶𝑡 ×ℎ×𝑟𝑤
C= 0.894
× 𝐶𝐷

C = 0.4248 bbl/psi

1 𝐶𝐷 𝑒 2𝑆
S=2 ln ( 𝐶𝐷
)

1 1010
S= ln ( ) =3.36
2 1905.27