University of Miskolc Faculty of Earth Science and ...midra.uni-miskolc.hu/document/29770/25645.pdf · The technique of well testing, especially pressure transient analysis (PTA)

University of Miskolc

Faculty of Earth Science and Engineering

Petroleum and Natural Gas Institute

Analysis of Hydraulic Fracturing Results in two

Hungarian Oil Wells.

Author`s name: Hernán Vicente Aguilar Torres

Department Supervisor: Prof. Gábor Takács

External Supervisor: Zsófia Sári

Miskolc, May 11th, 2018.

II

Statement of originality

I hereby certify that I am the sole author of this thesis and that no part of this thesis has been

published or submitted for publication.

I certify that, to the best of my knowledge, my thesis does not infringe upon anyone's copyright

nor violate any proprietary rights and that any ideas, techniques, quotations, or any other material

from the work of other people included in my thesis, published or otherwise, are fully

acknowledged in accordance with standard referencing practices.

May 11th, 2018.

Signature of the student

III

Thesis Assignment

MS Thesis Assignment

for

Mr. Hernan Aguilar Torres

Title: Analysis of hydraulic fracturing results in two Hungarian oil wells.

Main Tasks:

Describe the theory of well tests and pressure transient analysis.

Collect the relevant data of two wells and conduct a pre-frac pressure test

analysis using available software.

Analyze the skin removal in pre- and post-frac well tests.

Analyze the post-frac behavior of the reservoir.

Compare pre- and post-frac PI curves, analyze the production enhancement

achieved.

Conclusions, recommendations

Faculty Advisor: dr. Gábor Tákács, Professor

Field Advisor: Sári Zsófia, Well Test Engineer MOL GROUP

IV

Acknowledgments

I would like to thanks to MOL Hungarian Oil and Gas Plc, for providing the relevant

information and support during this project development.

To my Supervisors, on the University PhD. Gábor Tákács and to my Supervisor on the

Production and Optimization team Eng. Zsófia Sári, for all the help and guide provided.

My deariest gratitude to my family for supporting me on every stage of my career and throught

all my life. Specially to my father who has always been my role model on life. To my Sisters for

supporting me and give me advices all the time even thought the distance.

I humbly extend my deepest gratitude to all the people involve on this adventure and without

their help this project could not be possible.

Hernán Aguilar

V

Table of Contents

1 Thesis Assignment ............................................................................................................ III

2 Abstract ............................................................................................................................. IV

1 Well Testing Fundamentals ................................................................................................ 1

1.1 Reservoir response to pressure changes ....................................................................... 2

1.2 Dimensionless variables ............................................................................................... 3

1.3 Mathematical Model ..................................................................................................... 4

1.4 Types of Well Tests and obtainable parameters ........................................................... 5

1.5 Pressure Derivative ....................................................................................................... 8

1.5.1 Wellbore storage ................................................................................................... 8

1.5.2 Linear flow .......................................................................................................... 10

1.5.3 Spherical flow ..................................................................................................... 11

1.5.4 Radial flow .......................................................................................................... 12

1.5.5 Pseudo steady-State Flow Regime ...................................................................... 14

1.5.6 Boundary effects ................................................................................................. 15

1.5.6.1 Well in an infinite-acting reservoir ................................................................ 15

1.5.6.2 Linear no-flow boundary ............................................................................... 17

1.5.6.3 Linear constant-pressure boundary ................................................................ 18

1.5.6.4 Well in a channel ........................................................................................... 19

1.6 TYPE CURVE MATCHING ..................................................................................... 20

1.6.1 McKinley´s Type Curves .................................................................................... 21

1.6.2 Gringarten type Curves ....................................................................................... 23

1.7 Deliverability of wells ................................................................................................ 24

2 The studied wells .............................................................................................................. 26

2.1 Well 1 ......................................................................................................................... 26

VI

2.1.1 Production History .............................................................................................. 26

2.1.1.1 Petrophysical parameters ............................................................................... 28

2.1.1.2 Fluid Parameters. ........................................................................................... 28

2.1.1.3 Well test procedure ........................................................................................ 29

2.1.2 Well-2 .................................................................................................................. 29

2.1.2.1 Production History ......................................................................................... 29

2.1.2.2 Petrophysical parameters ............................................................................... 31

2.1.2.3 Fluid parameters ............................................................................................ 31

2.1.2.4 General Observations. ................................................................................... 31

2.1.2.5 Well test procedure ........................................................................................ 32

3 Modeling using the software package Kappa-Saphir ....................................................... 33

3.1 WELL TEST MODELING ........................................................................................ 33

4 Well analyses .................................................................................................................... 40

4.1 ANALYSIS WELL-1 ................................................................................................. 40

4.1.1 Pre frac stage ....................................................................................................... 40

4.1.1.1 The applied model: ........................................................................................ 40

4.1.1.2 Curve Fitting Results ..................................................................................... 40

4.1.2 Post-frac Stage..................................................................................................... 44



4.1.3 Comparative analysis .......................................................................................... 47

4.2 ANALYSIS WELL-2 ................................................................................................. 48

4.2.1 Pre frac stage ....................................................................................................... 48



VII

4.2.2 Post-frac stage ..................................................................................................... 50



4.3 Comparative analysis .................................................................................................. 54

4.3.1 Productivity Index Well 1 (PI) ............................................................................ 54

4.3.2 Productivity Index Well 2 (PI) ............................................................................ 55

5 Conclusions ....................................................................................................................... 57

6 Bibliography ..................................................................................................................... 58

7 Appendices ........................................................................................................................ 59

VIII

Table of equations

Eq. 1 Dimensionless radio ......................................................................................................... 3

Eq. 2 Dimensionless time .......................................................................................................... 4

Eq. 3 Wellbore storage ............................................................................................................ 10

Eq. 4 Linear flow equation ...................................................................................................... 11

Eq. 5 Permeability equation .................................................................................................... 13

Eq. 6 Skin damage ................................................................................................................... 14

Eq. 7 Volume of reservoir in function of m* .......................................................................... 14

Eq. 8 Change on ratio of pressure ........................................................................................... 21

Eq. 9 Productivity Index ......................................................................................................... 24

Eq. 10 Non Linear PI (Fetkovich) ........................................................................................... 25

Eq. 11 Voguel Equation .......................................................................................................... 25

IX

Table of figures

Fig. 1 Schematic of flow rate and pressure disturbance in a well. [1] ...................................... 2

Fig. 2 Schematic of direct and inverse problem solution. ......................................................... 5

Fig. 3 Typical derivative curve with different cases. ................................................................ 6

Fig. 4 Pressure derivative plot for the infinite-acting reservoir. ............................................... 8

Fig. 5 Pressure change vs Time. ................................................................................................ 9

Fig. 6 Wellbore storage on diagnostic plots. .............................................................................. 9

Fig. 7 Linear flow regime on the diagnostic and square root of time plots. ........................... 10

Fig. 8 Partial entry model. ....................................................................................................... 11

Fig. 9 Slope for spherical flow mode. ..................................................................................... 12

Fig. 10 MDH plot. ................................................................................................................... 12

Fig. 11 Horner plot. ................................................................................................................. 13

Fig. 12 Diagnostic plot for buildup test. ................................................................................. 16

Fig. 13 Diagnostic plot when the derivative is taken with respect to and plotted against radial

equivalent time. ............................................................................................................................. 17

Fig. 14 Diagnostic plot for constant-rate drawdown test influenced by a single no-flow

boundary. ...................................................................................................................................... 17

Fig. 15 Diagnostic plot for buildup test with derivative taken with respect to shut-in time. Long

producing time before shut-in produces curve resembling plot for drawdown test. .................... 18

Fig. 16 Derivative has a slope of -1 for a well located near a single, constant-pressure boundary.

....................................................................................................................................................... 18

Fig. 17 Diagnostic plot for buildup test with derivative taken with respect to and plotted vs.

shut-in time. .................................................................................................................................. 19

Fig. 18 Diagnostic plot for buildup test with derivative taken concerning and plotted against

equivalent time. ............................................................................................................................. 20

Fig. 19 Type curves of constant production rate, infinitely acting reservoir. ......................... 21

Fig. 20 Mckinley Type Curves. ............................................................................................... 22

Fig. 21 Gringarten Bourdet type curves. ................................................................................. 23

Fig. 22 Production History Gross. ........................................................................................... 27

Fig. 23 R-1 reservoir top map with Well-1. ............................................................................ 27

Fig. 24 Production History Well-2. ......................................................................................... 30

X

Fig. 25 Location Well-2. ......................................................................................................... 31

Fig. 26 Input data Shapir software. ......................................................................................... 33

Fig. 27 PVT properties. ........................................................................................................... 34

Fig. 28 PVT Data entry. .......................................................................................................... 35

Fig. 29 Reservoir boundaries. ................................................................................................. 36

Fig. 30 Pressure vs Production plot. ........................................................................................ 36

Fig. 31 Analytical Model. ....................................................................................................... 37

Fig. 32 Log-log plot. ............................................................................................................... 38

Fig. 33 History Match. ............................................................................................................ 38

Fig. 34 Semilog plot. ............................................................................................................... 39

Fig. 35 Dashboard menu. ........................................................................................................ 39

Fig. 36 Log plot well Well-1. .................................................................................................. 41

Fig. 37 Semilog Plot well Well-1. ........................................................................................... 41

Fig. 38 Pressure vs Flow rate Well-1. ..................................................................................... 42

Fig. 39 Grid plot well Well-1. ................................................................................................. 43

Fig. 40 Semilog Well-1. .......................................................................................................... 44

Fig. 41 Log-Log plot Well-1 Post frac. .................................................................................. 45

Fig. 42 Pressure vs RateWell-1 Post frac. ............................................................................... 46

Fig. 43 Semilog plot Well-1 Post-frac. ................................................................................... 46

Fig. 44 Horner extrapolated line Well-1 Post frac. ................................................................. 47

Fig. 45 Log-log plot Well-2. ................................................................................................... 49

Fig. 46 Pressure vs Rate Well-2. ............................................................................................. 49

Fig. 47 Horner plot Well-2. ..................................................................................................... 50

Fig. 48 Log-log plot Well-2. ................................................................................................... 51

Fig. 49 Pressure vs Rate Well-2. ............................................................................................. 52

Fig. 50 Semilog plot Well-2. ................................................................................................... 53

Fig. 51 Horner plot Well-2. ..................................................................................................... 53

Fig. 52 PI Well-1 pre-frac. ...................................................................................................... 54

Fig. 53 PI Well-1 pre-frac. ...................................................................................................... 54

Fig. 54 PI Well-2 post-frac. ..................................................................................................... 55

Fig. 55 PI Well-2 post-frac ...................................................................................................... 56

1

1. Introduction

The following project is proposed due to the necessity of accurate production forecast for

fracking candidate wells. The technique of well testing, especially pressure transient analysis

(PTA) is widely used since 1980. The main advantage of this technique is that it makes possible

to identify the main properties of the reservoir like permeability and skin damage in the formation.

Due to the lack of information of old wells, the importance of appropriate fracture- and reservoir

response modeling will enable proper forecast. The information obtained from the post-frac test

becomes crucial to this task because it is a reliable source of information. The thesis project focus

on pre-and post-frac data analysis of two wells fractured by MOL Hungarian Oil and Gas Plc. All

data was collected; such as production tests and build-ups before and after fracking. The selected

candidates were chosen based on the quality and reliability of the information stored by the E&P

Production and Optimization team and also by the representative of their respective reservoirs.

The software used to perform this analysis is Kappa Ecrin (licenses available) for pressure transient

analysis. Comparison of pre- and post-frac results is performed, then conclusions and suggestions

were made.

2

2. Well Testing Fundamentals

Well, testing is the technique most widely used around the world, due to the complexity of

physically accessing the system, which allows petroleum engineers to determine the basic

properties of a well/reservoir system that are interacting. The main objective is to determine some

specific properties needed by engineers to know the performance and capability of a reservoir.

Several studies were carried out around the world by different authors (Lee 1981; Streltsova 1988;

Raghvan 1993; Sabet 1991; Hasand and Kabir 2002); they focused on different areas regarding

well testing.

1.1 Reservoir response to pressure changes

Based on the idea that the system that we are working with is not accessible, to get to know the

system parameters, indirect methods are needed. based on this idea some properties like flow rate

and drawdown are known or can be measured. Creating a disturbance in one well that is producing

at a constant flow rate will produce a response inside the reservoir which can be recorded or

observed in the same (single well test) or in an offset well (multiple well test/interference test).

Through this disturbance, some properties of the reservoir can be determined indirectly. Fig 1

shows how the flowing bottomhole pressure (pwf or FBHP) decreases in the flowing period and

recovers after shut-in (pressure build-up).

Fig. 1 Schematic of flow rate and pressure disturbance in a well.

Source: (Kamal, July, 2009)

To describe the process in a HC reservoir, three basic equation types are needed. First of all,

transport-rate equation – Darcy’s law:

�⃑� = −𝜌

𝜇∙ �̅� ∙ ∇𝜓

3

where:

𝜓 = 𝑔 ∙ 𝑧 + ∫𝑑𝑝

𝜌

𝑝

𝑝0

To know how ρ is changing at different conditions, the equation of state is needed. For

incompressible fluids (water) it is constant:

𝜌 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

For slightly compressible fluids (oil), an exponential function is valid:

𝜌 = 𝜌𝑜 ∙ exp[𝑐𝑜 ∙ (𝑝 − 𝑝𝑜)].

In case of the highly compressible gas:

𝜌 =𝑀

𝑅𝑇∙ 𝑝

If the gas is not an ideal gas, real gas equation includes p/z(p) instead of only p.

The third equation needed representing the laws of continuity is the conservation of mass:

−𝜕

𝜕𝑡(𝛷 ∙ 𝜌) = ∇(𝜌 ∙ �⃑� ).

1.2 Dimensionless variables

The concept of dimensionless variables is very useful solving transient testing analysis, based

on the idea that if we connect different wells with different properties such as pressure, radius and

position there exist some terms that are equal for all of them.

The most useful dimensionless parameters are dimensionless pressure Eq. 1.

Dimensionless radius

𝑟𝑑 =𝑟

𝑟𝑤

Eq. 1 Dimensionless radio

Where:

r: radius belonging to the given point of the reservoir (ft)

4

rw: wellbore radius (ft)

Dimensionless time

These dimensionless variables can be used to show general solutions under various flow

conditions, by example dimensionless time can be calculated using the drainage area of an offset

well instead of using the square of the wellbore radius.

𝑡𝑑 =0.0002367 𝑘 𝑡

∅ 𝜇 𝑐𝑡 𝑟𝑤2

Eq. 2 Dimensionless time

Where:

k: permeability (mD)

t: time (hr)

ϕ: porosity (%)

µ: viscosity (cp)

ct: total compressibility (psi-1)


1.3 Mathematical Model

The main objective of the well test analysis is to match the properties of the reservoir and the

model in such way that the values of the different parameters measured with gauges like pressure

be equal or similar to the value calculated by the model. In other words, we should find and adjust

the values of the properties calculated in a model with the response of the well.

There are two ways to approach this problem the direct way and the inverse way.

These problems are called inverse order due that the user knows the input (flow rate change)

and the output (pressure change) data and needs to calculate the properties of the reservoir or a

find a set of properties that combined all together matches with the response of the well. The direct

approach is the case when the user knows the properties of the system and want to calculate the

output data. For example, if one user knows the input data obtained from the lab, then the user will

5

try to forecast the behavior of the well (e.g., well testing design). Inverse problem solving is the

PTA analysis of a measured data set of a well test. Figure 1.2 shows the schematic of direct and

inverse problem solution.

Fig. 2 Schematic of direct and inverse problem solution.


1.4 Types of Well Tests and obtainable parameters

Different kind of test can be performed on a well depending on the state of development like

transient test or well test that is applied during the various stages of reservoir discovery,

development, and production. Drillstem test (DSTs) and wireline formation tests are run in

exploration, and appraisal wells; drawdown, buildup, interference, and pulse tests are run during

secondary and enhanced recovery stages. Other specialized tests such as multilayer and vertical

permeability test are run throughout the whole life of the reservoir.

As it was mentioned before, testing time and pressure change will be used. Testing time (Δt)

refers to the elapsed time since the beginning of the test. The test may be a drawdown or buildup

test in producing wells or an injectivity or falloff test in injection wells. The pressure change is the

absolute value of the pressure at any time during the test minus the pressure at the beginning of

the test. Therefore, the pressure will increase with time. Table 1 shows some of the parameters that

are possible to obtain a different kind of tests

Different kind of test like Step-rate test is performed to determine initial formation pressure,

the permeability of the layer or reservoir (all layers) together and skin damage to the sand face.

Fall off test is used to delimit the reservoir and, in some cases, know the shape of it (necessary for

IOR and simulation). Determine where is located the front of liquid injected or the mobility of it

is an important factor that can define the success or failure of a project, another use widely spread

determines the length of fractures (natural or induced) to design or evaluate the performance of a

6

stimulation job. Interference test is used to verify the connectivity of one or more wells and how

these are interacting to develop the best model of injection, displacing or recovery, increasing the

efficiency of the production system.

To fully understand the well testing analysis, three main factors should be understood to use

correctly the equations that describe steady-state flow, pseudo steady-state flow, and transient

flow. Steady-state flow exists where the pressure is stabilized at any position inside the reservoir,

this is rarely observed in a reservoir, but it’s very practical. A good example is pattern flooding

where the producing and injector wells are operated at a constant rate. Pseudo-steady state occurs

when the change in pressure through the reservoir is constant, in other words in reservoirs under

depletion. Unsteady state or transient flow occurs when the pressure change with time is different

at different locations. Transient flow occurs when a well is put into production/injection or shut in

for a build-up or a fall-off test.

Fig. 3 Typical derivative curve with different cases.

Source: (Fekete, 2009)

7

DSTs

Reservoir Behavior

Skin

Fracture length

Reservoir pressure

Reservoir limit

Boundaries

Permeability

Wireline Formation Test

Pressure profile

Fluid samples

Some reservoir priorities

Drawdown tests

Reservoir behavior

Permeability

Skin

Fracture length

Reservoir Limit

Boundaries

Buildup tests

Reservoir behavior

Permeability

Skin

Fracture length

Reservoir pressure

Boundaries

Step-rate tests

Formation parting pressure

Permeability

Skin

Falloff tests

Mobility in various banks

Skin

Reservoir pressure

Fracture length

Location of front

Boundaries

Interference and pulse tests

Communication between wells

Reservoir type behavior

Porosity

Interwell permeability

Vertical permeability

Layered reservoir tests

Property of horizontal layers

Horizontal permeability

Vertical permeability

Skin

Average layer pressure

Outer Boundaries Table 1Reservoir properties obtainable from various transient tests


8

1.5 Pressure Derivative

The derivative is one of the calculated parameters widely used in pressure transient analysis

test. The derivative was introduced by Bourdet et al. (1983,1989). The derivative plots provide a

simultaneous presentation of log Δp vs. log Δt and log tdp/dt as shows in the Fig. 4.

Since the derivative at the beginning of the log plot is a straight line with a unit slope as it shown

on the Fig. 4

Fig. 4 Pressure derivative plot for the infinite-acting reservoir.


1.5.1 Wellbore storage

Wellbore storage is the result of fluid compressible nature of the fluids in the wellbore (Ramey

1970; Agarwal et al. 1970). The data dominated by the wellbore storage characterizes by a straight-

line plot with a slope of unity on the log-log plot of pressure difference and pressure derivative vs.

time ((Ramey 1970; Agarwal et al. 1970; Bourdet 1983). In the Fig. 1.4 and 1.5 it’s possible to see

the wellbore storage flow regime on Cartesian and diagnostic plots.

9

Fig. 5 Pressure change vs Time.


Fig. 6 Wellbore storage on diagnostic plots.


The use of the diagnostic plot and pressure derivative can be used not only for determining the

wellbore storage but also to detect problems with the tool and correct the test starting times for

more exact results.

10

𝐶 =𝑞 𝐵 ∆𝑡

24 ∆𝑝

Eq. 3 Wellbore storage

where:

q: flow rate (STB/D)

B: formation volume factor (RB/STB)

Δt: running testing time (hr)

ΔP: pressure change (psi)

1.5.2 Linear flow

Linear flow occurs around the tested well as result of different configuration such as the early

time flow resulting when a fracture intersects whit the wellbore (Clark 1968; Raghavan et al. 1972;

Gringarten et al. 1974) or the late-time flow through a channel caused by two parallel no-flow

boundaries. Linear flow presents a slope of half of the unit when its plotted on a log-log graph. It's

important to mention that the position and the length of the fracture are indicatives of the presence

or not of skin on the face of the fracture. Fig 7 Shows the plots of linear flow regimens.

During linear flow, the plot of pressure vs. the square root of testing time yields a straight line.

Fig. 7 Linear flow regime on the diagnostic and square root of time plots.


11

The linear flow it’s described by the following equation

𝑃𝑤𝑠 = 𝑃𝑖 −4.064 𝑞 𝐵

ℎ √

𝜇 ∆𝑡

𝑘∅𝑐𝑡𝑥𝑓2

Eq. 4 Linear flow equation

1.5.3 Spherical flow

Spherical flows occur when the flow from the formation to the wellbore is channeled through

a short set of perforations or the small probe of a wireline formation tester (Streltsova; 1988) as

can be shown in Fig 8.

Fig. 8 Partial entry model.


The typical slope of spherical flow is -0.5 on the log-log plot as can be seen on the Fig. 9. This

flow period usually doesn’t last for a long time. Therefore, this plot is not used for calculating

permeability.

12

Fig. 9 Slope for spherical flow mode.

Source:(Kamal, July, 2009)

1.5.4 Radial flow

The radial flow regime is the most important. From this flow regime, the main parameters of

the formation can be calculated such as permeability, wellbore skin, reservoir pressure. The radial

flow characterizes by a zero slope for the pressure derivative on the diagnostic log-log plot. The

formation permeability can be calculated from the value of the pressure derivative when it becomes

flat. And the wellbore skin can be derived from the separation between the pressure derivative and

the pressure difference. The most famous plots of this type are the Miller-Dyes-Hutchinson plot

(Miller et al. 1950) Fig. 10. And the Horner plot (Horner 1951) Fig.11. This type of plots uses the

semi-log plots.

Fig. 10 MDH plot.


13

Fig. 11 Horner plot.


The permeability can be calculated by the following equation:

𝑘 =162.6 𝑞 𝐵𝑢

𝑚𝑟𝑓ℎ

Eq. 5 Permeability equation

Where:




µ: viscosity (cp)

mrf: slope on radial flow region (psi/√𝑡)

h: formation net pay (ft)

The value of the pressure at the intercept of the semi-log straight line at the testing time of 1

hour is called 𝑃1ℎ𝑟, the skin at the well can be calculated from this value using the following

equation

14

𝑠 = 1.1513 [𝑃1ℎ𝑟 − 𝑃𝑤(∆𝑡 = 0)

𝑚𝑟𝑓− log (

𝑘

∅𝜇𝑐𝑡𝑟𝑤2) + 3.2275]

Eq. 6 Skin damage

Where:

P1hr: pressure on a straight-line portion of the semilog plot after 1 hour of beginning a transient

test; usually a special kind of pint (psi)

Pw: bottomhole pressure (psi)

mrf: slope on radial flow region (psi/√𝑡)


ϕ: porosity (%)

µ: viscosity (cp)

ct: total compressibility (psi-1)


1.5.5 Pseudo steady-State Flow Regime

This flow condition refers to the flow when the boundaries have been reached in a closed

reservoir, and the formation is going under depletion. In this state, the pressure changes at the same

rate everywhere inside the reservoir.

One example of this could be the case when the fluid in the wellbore is being depleted before

to produce the well before the flow from the formation begins. In this case, the reservoir volume

can be obtained from the following equation:

∅ℎ𝐴 =0.23395𝑞𝐵

𝑐𝑡𝑚∗

Eq. 7 Volume of reservoir in function of m*

Where:



15

ct : total compressibility (psi-1)

m* represents the slope of the Cartesian plot of pressure change vs. time

1.5.6 Boundary effects

According to the conditions present on different reservoirs the influence of boundaries can be

as significant as analyzing the test quantitatively. However, the problem is that many reservoir

models may produce similar pressure responses. According to the model selected to interpret the

test quantitatively must be consistent with geological and geophysical interpretations. Once the

proper reservoir model has been determined, test analysis may be relatively easy to match using

the modern well-test software.

“To further complicate matters for buildup test analysis, the shape of the derivative curve

depends on how the derivative is calculated and plotted. The derivative of pressure change may be

taken concerning the logarithm of either shut-in time or equivalent time. The derivative may then

be plotted vs. either of these time functions, and the shape differs for each plotting function. Some

pressure transient test analysis software allows the user a choice in the time function used in taking

the derivative and another choice in time plotting function” (Boundary effects in diagnostic plots,

2015).

1.5.6.1 Well in an infinite-acting reservoir

Infinite-acting reservoir, radial flow is described in Fig. 12 show the diagnostic curve. For this

plot, the derivative was taken with respect to shut-in time, and derivative and pressure change

curves are plotted vs. shut-in time. Both pressure and time are regarding dimensionless variables.

16

Fig. 12 Diagnostic plot for buildup test.

Source: (Boundary effects in diagnostic plots, 2015)

It should be mentioned that the significant difference in the shapes of both the derivative and

pressure change curves for buildup and drawdown tests, with the pressure change curves flattening

for buildup tests and the derivatives moving downward with an ultimate slope of –1. The time at

which the flattening of the pressure change curve (and corresponding downward movement of the

derivative) becomes apparent is a function of the producing time before shut-in. The longer the

producing time, the longer the flattening is delayed and the longer the time the buildup diagnostic

plot is virtually identical to the drawdown diagnostic plot.

Fig. 13 is the diagnostic plot that results when the derivative is taken with respect to radial

equivalent time, and the time-plotting function is radial equivalent time. The radial equivalent time

has a maximum value of the producing time before shut-in, so, for the buildup plot, the curve

terminates at this maximum value of the time plotting function, and all points "stack up" at these

limiting values of the plotting function. The radial equivalent time is more satisfactory as a variable

for taking the derivative and as a plotting function for an infinite-acting reservoir because the shape

of the diagnostic plot is the same as for a constant-rate drawdown test.

http://petrowiki.org/File:Vol5_Page_0771_Image_0001.png

17

Fig. 13 Diagnostic plot when the derivative is taken with respect to and plotted against radial equivalent time.


1.5.6.2 Linear no-flow boundary

When a well is near to one boundary than to any other, and when sufficient time has elapsed

for the boundary to influence the pressure response during the test, the typical diagnostic plot,

as Fig. 14 shows, results of a constant-rate drawdown test. The derivative will double in value over

approximately 1 2/3 log cycles (from 0.5 to 1.0 on a plot of dimensionless variables). Similar

responses occur in naturally fractured reservoirs with transient flow from the matrix to the

fractures.

Fig. 14 Diagnostic plot for constant-rate drawdown test influenced by a single no-flow boundary.


Fig. 15 describes the plot for a buildup test with the derivative taken with respect to shut-in

time and plotted vs. shut-in time. Wellbore storage may distort some of the earlier data on this plot.



18

The longer the producing time before shut-in, the more nearly the shape of the diagnostic plot for

a buildup test resembles the diagnostic plot for a drawdown test. The derivative has a slope of –1

for shut-in times much longer than producing time before shut-in.

Fig. 15 Diagnostic plot for buildup test with derivative taken with respect to shut-in time. Long producing time before shut-

in produces curve resembling plot for drawdown test.


1.5.6.3 Linear constant-pressure boundary

When a well is nearer a single boundary (similar to Fig. 14) but with a constant-pressure at that

boundary and boundary effects are encountered during the test, the diagnostic plot shown in Fig.

16 will result in a constant-rate drawdown test. The derivative has a slope of –1 at late times on

the diagnostic plot.

Fig. 16 Derivative has a slope of -1 for a well located near a single, constant-pressure boundary.




19

Fig. 17 (Boundary effects in diagnostic plots, 2015)the diagnostic plot for a buildup test, with

derivative taken with respect to shut-in time and plotted vs. shut-in time. This diagnostic plot is

identical to the drawdown plot if steady state was achieved during the flow period preceding the

buildup test, with shorter producing times, the derivative has a slope steeper than the drawdown

slope of –1.

Fig. 17 Diagnostic plot for buildup test with derivative taken with respect to and plotted vs. shut-in time.


1.5.6.4 Well in a channel

When a well is between two parallel no-flow boundaries and the transient pressure encounters

both during a test, long before the ends of the reservoir influence the test data. Diagnostic plots

with similar shapes occur for a well between two sealing faults, a hydraulically fractured well with

a high-conductivity fracture, and a horizontal well during early linear flow.

Fig. 18 is the diagnostic plot for a buildup test with derivative taken with respect to radial

equivalent time and plotted vs. equivalent time. This plot is not particularly useful for test analysis.

However, linear equivalent time produces a more useful diagnostic plot as long as channel ends

do not affect the pressure response.


20

Fig. 18 Diagnostic plot for buildup test with derivative taken concerning and plotted against equivalent time.


1.6 TYPE CURVE MATCHING

Type curves provide methods for analyzing transient well tests, using dimensionless variables

as Pressure (PD) and Time (TD). Type curve matching techniques may be used for drawdown,

build-up, interference, and constant pressure testing. The results obtained by different methods can

vary from one to another due to the complexity of the reservoir conditions or due to the experience

and accuracy of the read measurements.

Type curves are commonly used to determine the parameters of the reservoir such as,

permeability, damage or stimulated a status of the well, as other different factors that influence in

the performance index of the well. It should be mentioned that many of these curves were

simulating constant- rate pressure drops (draw-downs or build-ups).

Conventional test analysis techniques (Lee, 1982, p. 63) can be applied to find these parameters,

but the type curves are faster methods and provide similar results. One important advantage is in

the use of fractured wells. Combining linear flow that occurs at early times in many fractured

reservoirs, the radial flow that may occur later after radius of investigation has moved beyond the

region influenced by the fracture. The effects of the reservoir on the middle time region (MTR)

line is established in a pressure transient test on a fractured well.

Fundamentally, a type curve is a pre-plotted family of pressure drawdown curves. The most

fundamental of these curves, is a plot of dimensionless pressure change, PD, vs. dimensionless time

change, tD.


21

Fig. 19 Type curves of constant production rate, infinitely acting reservoir.

Source: (Lee, 1982)

1.6.1 McKinley´s Type Curves

McKinley (Mckinley, July, 1971, págs. 863-872) proposed type curves with the primary

objective of characterizing damage or stimulation in a drawdown or build-up, in this situation the

wellbore storage distorts most of the data.

In his work he proposed that the ratio of pressure change, ΔP, to flow rate causing the change,

qb, is a function of several dimensionless quantities:

∆𝑃

𝑞𝐵 = 𝑓 (

𝑘. ℎ. ∆𝑡

𝜇. 𝐶𝑠 ,

𝑘. ∆𝑡

∅. 𝜇. 𝑐𝑡. 𝑟𝑤2 ,𝑟𝑒𝑟𝑤

,∆𝑡

𝑡𝑝 )

Eq. 8 Change on the ratio of pressure

Where:

k: reservoir rock permeability, mD

h: net pay, ft (m)

Δt: time elapsed since the shut-in, hours

22

µ: flow rate per unit area, (volumetric velocity), 𝑅𝐵

𝐷−𝑠𝑞 𝑓𝑡 ,

𝑚3

𝑑.𝑚2

CS: wellbore storage, 𝑏𝑏𝑙

𝑝𝑠𝑖, (

𝑚3

𝐾𝑃𝑎)

ɸ: porosity of the reservoir, fraction, (%)

re: external drainage radius, ft, (m)

rw: wellbore radius, ft, (m)

Due to the high complexity of the last equation, it is almost impossible to use this equation,

that’s why Mckinley made the following assumptions:

• The well was produced for a long time enough (stabilization)

• The boundary effects are neglected (re/rw)

• The parameter considering the permeability and the mobility is neglected due to they do

not affect the shape of the curve type.

• The skin effect is not considered in this equation, but it is also observed that in the

wellbore storage distorted are dominated by the effective transmissibility.

Fig. 20 Mckinley Type Curves.

Source: (Lee, 1982)

23

1.6.2 Gringarten type Curves

Gringarten et al. (Gringarten, 1974, págs. 347-360) developed type curves for hydraulically

fractured wells in which vertical fractures with two equal-length wing were created. These curves

assume uniform flux into the fracture. High fracture conductivity is required to achieve uniform

flux, but not identical to an infinitely conductive fracture (no pressure drop across the fracture) as

Gringarten et al. demonstrated (Gringarten, 1974, págs. 347-360).

This study was conducted for finite reservoirs, which means that the reservoir is at a uniform

pressure.

As can be seen in Fig. 21 the combined type curve Gringarten-Bourdet is widely used to match

and calculate the main properties of the reservoir as well as to model the reservoir behavior and

also to identify the boundaries in case the data suitable for it.

Fig. 21 Gringarten Bourdet type curves.

Source: (Bourdet, 2002)

24

1.7 Deliverability of wells

Since the invention of the bottomhole gage on the 1920s, the interest of the engineers was

focused on determining which will be the capacity of each well. With this idea in mind, the develop

of a simple equation that expresses the relationship between the reservoir pressure and the flowrate

were developed. The expression Inflow performance relationship (IPR) is used to describe this

relationship. Bottomhole flowing pressure (Pwf) and backpressure is used typically at a depth of

middle perforations.

The simple equation to describe this relationship mathematically speaking is a straight line were

the single-phase fluid rate (no free gas present) is proportional to the pressure drawdown in the

reservoir. The constant of proportionality J is called productivity Index, which is the ratio between

flowrate and pressure drawdown. As was mentioned before this equation only applies to

unsaturated oils (no free gas is present), the equation is presented as follow:

𝐽 =𝑄𝑜

(𝑃𝑅 − 𝑃𝑤𝑓)

Eq. 9 Productivity Index

Where:

PR: Reservoir pressure [psia]

Pwf: Bottomhole flowing pressure [psia]

Qo: the Flow rate of liquid [STB/D]

A limitation of the straight-line equation is the assumption of the fluid is single phase. In the case

of saturated reservoirs, it will be present gases and liquid. Gases and liquid are compressible, for

these reasons they behavior will change according to pressure: This phenomena was experienced

in the early 1920s and 1930s where engineers noted that a higher drawdown was required to

produce the same flow rate as before on undersaturated reservoir. J decreases as the flow rate is

increasing, for this reason the nonlinear IPR were introduced.

One empirical but simple equation was introduced by the Bureau of Mines engineers developed a

simple but accurate equation

25

𝑞 = 𝐶 (𝑃𝑅2 − 𝑃𝑤𝑓

2 )𝑛

Eq. 10 Non Linear PI (Fetkovich)

Where:

C: is the productivity index when (𝑃𝑅2 − 𝑃𝑓

2) = 1

PR: Reservoir pressure [psia]

Pwf: Bottomhole flowing pressure [psia]

q: Flow rate of liquid [STB/D]

n is a value of exponent that moves from 0.5 to 1 and depends on the deviation (slope) of the

curve

One of the most accepted and widely used equation is the Voguel equation, traditionally used

to describe oil well performance in saturated reservoirs, the equation used is as follows:

𝑞𝑜

𝑞𝑜 𝑚𝑎𝑥= 1 − 0.8 (

𝑃𝑤𝑓

𝑃𝑟) − 0.2 (

𝑃𝑤𝑓

𝑃𝑅)2

Eq. 11 Voguel Equation

Where the qo max is the AOF (Absolute Open Flow) capacity of the well

26

3. The studied wells

On this chapter the most relevant data has been collected, to give a better understanding of the

lifetime of the wells, to make it easier identify the most convenient solution and also support why

those two wells were selected as candidates to be hydraulically fractured. The reservoir reserves,

the position of the wells, facilities are existing, and economic analysis was performed to research

the availability of the process previously described.

1.8 Well 1

1.8.1 Production History

Well-1well used to be a gas lift oil well producing from R-3/A reservoir. After closing out the

perforations, the well was re-completed in 2013 January for R-1 oil producer reservoir. The

reservoir is currently producing through the 2573.0-2575.0 m MD (2488.5-2490.5 m TVDSS)

perforation.

The well started producing in mid-October 2013 from the reservoir through an 8 mm choke.

Gross fluid production was 23 m3/day water-freely, at the same time it also produced

30 000 m3/day gas at 48 bar wellhead pressure, R was 1300 m3/m3. Then oil production kept on

declining until 2014 September, and the water showed up in the well in the middle of the year. The

flowing wellhead pressure dropped to 25 bar. Gross fluid production stabilized at daily 6 m3.

The well is presently producing at 8 mm choke daily 5 m3 gross fluid and 1 m3 water. The

flowing wellhead pressure is 23 bar.

The well produced 7 Mm3 oil, 950 m3 water, and 13 MMm3 gas by the end of November 2015.

27

Fig. 22 Production History Gross.

Source: (MOL, 2016)

The well Well-1is located on the reservoir R-1 (Lower Pannonian sandstone) as it can be seen

in figure 22

Fig. 23 R-1 reservoir top map with Well-1.

Source: (MOL, 2016)

28

The well was a naturally flowing oil and gas producer. The planned well test program was:

production at original flow conditions, PSR, three-point deliverability test, and a final BUP, shut-

in and flowing p/T gradient survey included.

After dummy run, the well couldn’t start flowing naturally, lifting gas was needed. Even with

that, it did not start flowing continuously, so the gas lift valve hat to be set to a lower position in

the well. After that, the well was producing with lifting gas at 8-11-15 mm chokes.

1.8.1.1 Petrophysical parameters

The Petrophysical parameters of the tested formation are the following:

Formation net pay 9 m

Porosity 15 %

Water saturation 40 % Table 2. Petrophysical Parameters

Elaborated by: Hernán Aguilar

As can be seen on the chart the porosity is quite good, and the net pay zone is 9 m (27ft) with a

water saturation of 40%, this data indicates a good candidate for performing a further action to

improve the recovery of oil.

1.8.1.2 Fluid Parameters.

The well is a naturally flowing oil producer. The planned well test program was: production at

original flow conditions, PSR, three-point deliverability test, and a final BUP, shut-in and flowing

p/T gradient survey included.

After dummy run, the well couldn’t start flowing naturally, lifting gas was needed. Even with

that, it did not start flowing continuously, so the gas lift valve hat to be set to a lower position in

the well. After that, the well was producing with lifting gas at 8-11-15 mm chokes.

It was the first well with lifting gas measured in the Testing Campaign.

For the analysis the following fluid parameters were used:

• Gas specific gravity (15 oC): γg = 0.7

• Oil gravity (20 oC): ρo= 850.0 kg/m3

• Check pressure: p= 20 MPa

29

• Check temperature: T=140 oC

1.8.1.3 Well test procedure

The well test procedure proposed was developed as it follows, the company performed the work

according to the principal recommendations.

Three flow periods are recommended after the first technical build up to obtain a stabilization

and prepare the reservoir for the build-up test. These three flow periods are performed on steps

using different diameter chokes to generate drawdowns on the wellbore and record a response from

the well, the most used sizes are

1.8.2 Well-2

1.8.2.1 Production History

Well-2 was completed in September 2013 as a dual string gas lift oil producer for R-2 and R-3

reservoirs. R-2 was producing from the interval 2367.5-2370.0 m MD (2280.92-2283.34 m

TVDSS) through the short string, but it watered out right after completion. R-3 (Ap-13/D) has

been producing from the perforation 2469.0-2482.0 m MD (2378.01-2390.28 m TVDSS), this one

will be tested and fracked.

The well started to produce from R-3 reservoir in May 2014 @20 mm surface choke; it flowed

naturally. Choke size was constant all the time. Gross fluid rate was 2-4 m3/d with 1-2 m3/d water

@25 bar WHP. In the beginning, GOR was high, then after one month of production net oil rate

increased to 7 m3/d, and the well produced with 1700 m3/m3 GOR, without water. From early June

2014, oil production dropped to half of the previous value.

30

Fig. 24 Production History Well-2.

Source: (MOL, 2016)

Until mid-April 2016 the well produced 1 005 m3 oil, 758 m3 water well started to produce

water as well.

From 17.02.2015 the well has been producing with lift gas, with 50% water cut since then. The

well is currently still producing with lifting gas, and 1.9 MMm3 gas from R-3 (Ap-13/D) reservoir.

R-3 is an Upper Pannonian sandstone oil reservoir, Well-2 is producing it via gas lift. R-3 (Ap-

13/D) was tested in this well in 2013; the results were: “With CT @2300 m MD, 3.6 m3/d oil could

be swabbed using N2 intermittently with flammable gas.” There was no gauge measurement.

Therefore no well and reservoir parameters were calculated

31

Fig. 25 Location Well-2.

Source: (MOL, 2016)

1.8.2.2 Petrophysical parameters

Petrophysical parameters of the tested formation are the following:

Formation net pay 10 m 33 ft

Porosity 15 % 15%

Water saturation 45 % 45% Table 3 Petrophysical Parameters


1.8.2.3 Fluid parameters

For the analysis the following fluid parameters were used:

• Gas specific gravity (15 oC): γg = 0.75

• Oil gravity (20 oC): ρo= 879.1 kg/m3

• Check pressure: p= 18.168 MPa

• Check temperature: T=131.408 oC

1.8.2.4 General Observations.

During the test, artificial gas lift was done to produce the well. The test has 3 section: PSR

, production with continuous gas lift, and final BUP.

32

During the PSR period, the BHP showed increasing trend. After that, in the production period,

the well could produce 0.72-3.36 m3/d gross fluid (6-28 STB/D) @ ~3.5 MPa (507 psia)BHP. The

usual decreasing BHP trend was not observed, due to gas lift production.

PSR BHP values are greater than final BUP BHP values. Our explanation is, that before setting

downhole gauges, gas lift valve replacement was conducted, and during this operation first the

casing and tubing pressure was equalized to be able to POOH the valve, then the pressure was bled

off through the SIFO, and finally, the 3 mm DKO valve was installed. After this operation, lift gas

was trapped in the well, and caused a constant BHP, upon what the reservoir effect was observed

too. So it seemed like PSR caught a later part of BUP than the final shut-in.

As artificial gas lift was used to produce the well, during the final BUP phase redistribution can

be seen, it was modeled via changing wellbore storage. In the later section of the BUP the BHP

continuously increased, which suggests that the permeability is low. No reservoir boundary effect

could be seen.

1.8.2.5 Well test procedure

The well test procedure proposed was developed as it follows, the company performed the work

according to the principal recommendations.

Three flow periods are recommended after the first technical build up to obtain a stabilization

and prepare the reservoir for the build-up test. These three flow periods are performed on steps

using different diameter chokes to generate drawdowns on the wellbore and record a response from

the well, the most used sizes are

Additional gradient and temperature surveys were taken on this well during the flow period in

order to accurate stablish the points where the change of phases occur inside the system and have

more reliable data to optimize through nodal analysis this well.

33

4. Modeling using the software package Kappa-Saphir

1.9 WELL TEST MODELING

For the modeling of the different properties of the two selected wells, the chosen software was

Saphir, the description of the modeling process and how was performed will be described on this

chapter.

The first step is fill all the properties of the reservoir that the software will request such as: well

radius, pay zone, rock compressibility, porosity, top of the reservoir depth and the type of reservoir,

in case that the reservoir or analysis wanted to be performed on unconventional reservoirs we

should select this option, the values marked in red are preselected values or default values that the

software assigns as we can see the Fig. 26. As an additional comment, the units next to the value

can be changed in this step if the user omitted this step at the beginning of the wizard charger.

Fig. 26 Input data Shapir software.


34

The next step is the input of the PVT properties of the reservoir, the most important factor is

chosen accurately the fluid type, in this case, will be Oil, in case that and complete compositional

PVT analysis exist it should be selected the option Defined, as is shown on the Fig. 27

Fig. 27 PVT properties.


It is important to load on the PVT properties load as much information as we have. in order to

obtain better results, for each phase (depending on the reservoir conditions) we will have to input

the data available, in case of data missing data, one correlation can be selected, in order to calculate

some parameter that could be missing and would affect the behavior of one or more properties. it

should be mentioned that bubble pressure (Pb) temperature (ºC) and reservoir pressure (Pr) are

mandatory in order to obtain realistic results. Parameters such as rock and total compressibility

35

(fluid + matrix) can have big impact on well test modeling, due to the relation between properties

of fluid and matrix and how this interacts under specific conditions.

Fig. 28 PVT Data entry.


The next step is select the reservoir physical properties, such as: storage, well model, reservoir

model and boundary. these properties affect the response of the well – reservoir system in the case

of undefined or unknown reservoir, the most common approach is select and homogeneous

reservoir acting as infinite boundary with a constant wellbore storage. on this way is possible to

obtain some information with limited data. In case that the reservoir is well known and the pressure

data allows to correctly define a boundary, the most similar model should be selected. boundaries

could be infinite, pressure supporting or closed boundary. each one of this model will affect the

shape of the derivative pressure data. All the combination and available models for a simplified

well can be seen in Fig. 29.

36

Fig. 29 Reservoir boundaries.


Moving forward we should set in the pressure data (months, date, hour, seg) from the pressure

gage. Production rates during the flow test (pre-stabilization period) are also required to perform

the analysis of each well.

Fig. 30 Pressure vs Production plot.


37

The analytical model is where we can select the different properties of our model, this step is

the most relevant outcome of the analysis, because based on this model all the properties of the

reservoir will be calculated.

Fig. 31 Analytical Model.


The log-log plot makes possible determine the most important factors on well testing. these

parameters are wellbore storage and radial flow. Wellbore storage enables to see the early response

of the system on the well while radial flow allows to see the response inside the reservoir. Fig. 32

shows a well where radial flow has not been achieved. With this information it is possible to know

that the transmissibility of the reservoir is very poor.

38

Fig. 32 Log-log plot.


The history matching allows to corroborate how good is the model itself and how reliable are

the results presented about the different values calculated by the software, it should be mentioned

that many times the use of correlations and analog well data is needed due to the lack of

information.

Fig. 33 History Match.


39

The Semilog Plot is an indicator of the model, special analysis such as Horner plot can be

selected on the menu as can be seen on Fig. 26, this parameter is vital because it is the result of

the extrapolated time when the time is zero.

Fig. 34 Semilog plot.


On the dashboard panel section, the Horner plot model can be selected. The parameters shows

on the screen are the result of each specific case. These values depend on the preset input values.

the value shown corresponds to the extrapolated pressure.

Fig. 35 Dashboard menu.


40

5. Well analyses

1.10 ANALYSIS WELL-1

1.10.1 Pre frac stage

1.10.1.1 The applied model:

Wellbore storage: Variable

Well model: Finite radius

Reservoir model: Homogeneous

Boundary model: No Boundary

1.10.1.2 Curve Fitting Results

The parameters obtained from the matching is summarized in the next table:

Well 1 Pre-frac

Parameter Value Unit

Reservoir formation capacity kh 2.259 md.ft

Effective permeability k 0.073 mD

Wellbore storage Cs 0.01763 STB/psi

Wellbore storage amplitude Cf 0.00113

Wellbore storage time constant t 0.007 hr

Skin S 0.2763

Pressure loss due to Skin DPs 148.6 psi

C[initial]/C[final] Cd 0.091

Calculated reservoir pressure Pi 2652 psi

Table 4 Well-1 Pre-frac Results


Log-Log plot

As it can be appreciated on the Fig. 36 there is not an exact match between the pressure

derivative and the pressure data. One possible cause for this is the model selected. Another possible

reasons are related to operative issues during the test. All these factors can induce a false response

on well. Problems that affect the performance of the gauges on the pressure record are not rare,

usually on almost all test carried is possible to appreciate some of these disturbances.

41

Fig. 36 Log plot well Well-1.


On the semi-log plot Fig. 37 it is possible to appreciate the match between the pressure recorded

by the gauge, plotted on the semi-log scale and the pressure calculated by the computer model. On

the early time the matching is not good due to perturbances on the pressure. The modeling is

focused on the build-up section, therefore other parameters acting on the tubing string can be

disorienting the response on the probe.

Fig. 37 Semilog Plot well Well-1.


42

The Fig. 38 shows typically the relationship between pressure and production rate during the

flow or stabilization period. Prior the main build up, as the pressure decreases the rate increase and

vice versa as the response of the drawdown produced on the wellbore. These interactions are

recorded by the pressure gage.

Fig. 38 Pressure vs Flow rate Well-1.


Grid Model

The new version of the software allows to construct a grid model where the different properties

of the reservoir can be shown. These new tools allow understanding on a better way the response

of the system. Been able to see how pressure is changing, especially on a complex system, allows

engineers take best actions to develop the reservoir on an appropriate way.

A new advantage of the software is the possibility to choose between an analytical or numerical

model. An analytical model is usually used on PTA while numerical models are present on

reservoir simulation. Regarding to the reservoir, the simulation forecast results are the main

objective, the new plugins make it possible to export directly the data to software simulators as

Eclipse or Petrel. These tools can help to deliver more precise information in order to maximize

the potential of each field and well. One example can be observed in the Fig. 39.

43

Fig. 39 Grid plot well Well-1.


The semi-log plot described the superposition time vs the pressure on the same plot. As it was

seen on the previous plot the first section of the test is not matching. A slight difference can be

appreciated on the build-up test. The build-up section represents the reservoir response, therefore

our interest is a good match on the late-time response. In case that the values obtained are quite

similar to the real values obtained by cores it is possible to say that the model matches. From grid

plot the reservoir pressure can be calculated, or taken directly from Horner plot when the

extrapolated line cuts the zero superposition time.

44

Fig. 40 Semilog Well-1.


1.10.2 Post-frac Stage


Wellbore storage: Constant

Well model: Vertical Fracture Finite Conductivity





Well 1 Post-frac







Skin S -5.31

Pressure loss due to Skin DPs 8524 psi

Fracture half Length Xf 87.86 ft

Calculated reservoir pressure Pi 2652 psi

Table 5 Well-1 Post-frac


45

The log-log plot indicates the match existing between the model and the derivative pressure,

due to some operative problems the buildup has some distortion. If some distortions are noticed

on the build-up test, it is recommended use a smoothing higher than 0.1. The well model and the

response of the reservoir shown on in Fig. 41 match quite well. In this case this response is

typically associated with fracture channels. Channels are a good indication that the fractures on

the reservoir are open and are conducting fluid from the inner reservoir to the wellbore.

Fig. 41 Log-Log plot Well-1 Post frac.


As was mentioned before the historical matching shown in Fig 42 is not the best due to the

complexity of the reservoir. Considering that we are using a simplified model to identify only the

reservoir properties which are our main goal (last section of the plot). It is possible to say that the

match is quite good, ensuring that the qualitative data would be useful for further analysis.

Additionally, it should be mentioned that in order to have a “clean buildup”, the closing point was

shifted to the right to avoid some disturbance caused by the storage and gas presence on the well.

46

Fig. 42 Pressure vs RateWell-1 Post frac.


The semi-log plot shown in Fig. 43 described the superposition time vs the pressure on the same

plot. The model generated and the recorded pressures from the probe show a disturbance, this

disturbance was manually overridden in order that the software doesn’t take into account this

section. Usually from this plot the reservoir pressure can be calculated.

Fig. 43 Semilog plot Well-1 Post-frac.


47

The Horner plot shown in Fig. 44 is one of the most useful tools that engineers use to identify

the extrapolated pressure from the test. On practical terms this extrapolated pressure could be

considered as reservoir pressure. With this assumption engineers can perform simulations, to

forecast the behavior of the well, or in some cases take the decision to perform any remedial job.

Fig. 44 Horner extrapolated line Well-1 Post frac.


1.10.3 Comparative analysis

It is interesting the results founded on the pre and post fractured system, it is visible that the

permeability is increased significantly after the fracturing job. At the pre-frac stage the response

of the well was really slow: This was an indication of low permeability, as can be seen in Fig 36.

In that figure it was not possible to distinguish the radial flow or the boundaries of the well, only

the wellbore storage is present there. On the other hand, after the intervention shown in Fig. 42, it

is possible to appreciate the wellbore storage, and the behavior of the well. This behavior

corresponds as a fractured well, which is the response expected to ensure that the fractures are

open after the flow back period.

This increasing on the response of the reservoir system is due to the increased conductivity and

high transmissibility of the fractures. In future it could be possible to repeat this process during

several stages increasing the recovery of the well and reservoir, because in each new fracture

process new zones inside the reservoir will be contacted increasing the amount of oil recovered.

48

1.11 ANALYSIS WELL-2

1.11.1 Pre frac stage


Wellbore storage: Changing

Well model: Finite radius





Well 2 Pre-frac







Skin S -1.82

Pressure loss due to Skin DPs 1035.8 psi

Distance to the boundary L 14.5 ft

Calculated reservoir pressure Pi 2870 psi Table 6 Well-2 Pre-frac results


The response of the well described in Fig. 45. This respond shown apparently the presence of

a channel, or parallel faults. Additional information from geology is needed to determine the exact

model, for practical terms of analysis a channel and fault was chosen as model. the permeability

of this well is not that high, this could be seen from the graph due to the response is slow even

when the oil is not viscous as a heavy oil. It should be mentioned that this well was under gas lift

in order to produce, this is because the reservoir is depleted.

49

Fig. 45 Log-log plot Well-2.


The Fig. 46, describe the history matching, in this concrete situation the match is better than on

other wells analyzed. Disturbances on the beginning of the build-up can be noticed, for this reason,

the initial build-up point was shifted to the right. The presence of gas during the test caused that it

needed to be bleed of, these disturbances were recorded by the probe.

Fig. 46 Pressure vs Rate Well-2.


50

Semilog-plot in Fig. 47 describes the model pressure and the superposition time vs pressure.

As was mentioned before a good matching could be seen along all the test. On this well is a good

indicator of the veracity of the data and the model, selected. Extrapolated pressure by the Horner

method also is congruent with the measured data, giving the confidence of reliable values.

Fig. 47 Horner plot Well-2.


1.11.2 Post-frac stage


Wellbore storage: Changing

Well model: Vertical fractured finite conductivity





51

Well 2 Post-frac







Skin S -4.65

Pressure loss due to Skin DPs 2600 psi

Fracture half Length Xf 126.13 ft

Calculated reservoir pressure Pi 2253 psi Table 7 Well-2 Post-frac results.


The post-frac model is described in Fig. 48. This stage analysis was modeled as a fracture

reservoir on the first stage to simplify the response. On this way the data provided by the model of

the reservoir can be compared with after flow tests. Due to the uncertainty a smoothing higher than

0.3 was used to appreciate the most relevant information and eliminate some disturbances.

Fig. 48 Log-log plot Well-2.


The Fig. 49, describes the production history matching. On this concrete situation the match is

quite good, no disturbances along the buildup can be noticed. This matching Supports the idea that

52

the generated model for this well is accurate, even when the fractured well and the reservoir model

differs from the expected response. For this specific well, three phases were used on the flow

model, oil, gas, and water. Properties of the fluid were adjusted and the information missing was

calculated with the use of correlations.

Fig. 49 Pressure vs Rate Well-2.


Semilog plot in Fig. 50 described the model pressure and the record superposition time vs

pressure. These matching as could be seen along all the test is not the best one. On the middle

section are present big disturbances. This phenomenon is present since the first step and also can

be seen on the history production, the use of gas lift was needed to perform the test which is the

cause of disturbance, in that section the flow rate was unstable.

53

Fig. 50 Semilog plot Well-2.


Horner plot in Fig. 51 shows the extrapolated pressure of the well. The most important factors

are the extrapolated pressure and the pressure at 1 hr. These values are needed to calculate

permeability, well storage, skin damage and many other factors that influence the performance of

the well reservoir system.

Fig. 51 Horner plot Well-2.


54

1.12 Comparative analysis

1.12.1 Productivity Index Well 1 (PI)

Fig. 52 PI Well-1 pre-frac.


As it can be seen in Fig. 52 the deliverability of the well is really low. this due to the permeability

and the presence of gas. gas has higher mobility which blocks the liquid to flow from the reservoir

to the well. the oil production is low around 11 STB/D and the reservoir is on saturated state which

makes even more complicated the movement of the liquid increasing the pressure losses.

Fig. 53 PI Well-1 pre-frac.


55

A big improvement can be seen on the potential of the well shown in Fig. 53. Fractures are

filling the fluid from the reservoir to the well. In this case the oil capacity is around 48 STB/D this

is an improvement of more than 400%. Analyzing this result is possible to say that the frac

performed to this well was successfully.

It is interesting observe the results founded on the pre and post fractured system. Permeability

is substantially increased after the frac job. On the pre-frac stage the response of the well was really

slow as an indication of low permeability. As can be seen on Fig 36, it was not possible to

distinguish the radial flow or the boundaries of the well, only the wellbore storage is present there.

On the other hand, after the intervention Fig. 42, is possible appreciate the wellbore storage, and

the behavior of the well. This behavior is the same as a fractured well which is the response

expected to ensure that the fractures are open after the flow back period.

1.12.2 Productivity Index Well 2 (PI)

Fig. 54 PI Well-2 post-frac.


The well-2 as was mentioned has low permeability and is on saturated state, the capacity of

produce oil is less than 10 STB/D. This production is not economically the best scenario. As

addition, the wellbore storage is high due to the completion conditions and the need of use, gas lift

to produce this well.

56

Fig. 55 PI Well-2 post-frac


Since the point of view of permeability and transmissibility. It is possible to said that the job

fulfills the objective. Permeability increased from values close to 0.1 mD to values higher than 2.4

mD. This is a big increase on the wellbore, the conductivity of the fracture system and the length

of the fractures are also satisfactory. It can be said that some of the fractures were closing or closed

after the flow back of the proppant affecting the full potential of the well. However, it is still a

good result due to the high increasing on deliverability of the well going from 8 to almost 50

STB/D.

The permeability of the fractures has increased as they are open and allowing the liquid to flow

from the reservoir to the well, analyzing this result we can say that the fracturing job was

successfully and the fractures are open inside the reservoir.

The response of the reservoir is faster compared to the previous build-up. Where the limits of

the system were not possible to analyze. On the post-frac model the initial section of the limits of

the reservoir seems to be present but a longer build-up is needed in order to obtain more reliable

data, and make possible to verify the border limits of the well.

57

6. Conclusions

After the analysis of the pre and post frac, it can be said that the job performed on the two wells

was successful. The permeability on both wells is evidently increased. This means that after the

flowback period the fractures created remained open. New areas of the reservoir that were not

accessible before were contacted.

The transmissibility of the fluid was increased on both study cases. Even when the total mobility

has not dramatically increased on the same proportion as the permeability. It can be said that the

result is satisfactory.

Due to some problems not related to the technical analysis some data on the raw files and the

presented files was intentionally deleted. The purpose of delete this data is to give to the lector a

better perspective of the relevant data. Disturbing data was introduced due to operative actions

needed to be performed in order to obtain more information about the reservoir and the fluid

(Pressure Gradients).

An inconvenient on the modeling was the lack of reliable data due to actions and limitans out

of control on this project. Production rates are not reliable due to the difference presented between

the historical production and the reported production during the test. Some average values between

them productive history and productive period were selected as input for models.

Operative problems related to the facilities were detected during this analysis. these kinds of

disturbances are not possible to handle and were delete it from this report on the data processing.

With the hydraulic-fracture the permeability and the productivity index were increased. Trough

the fracture new areas were contacted by the drainage radius. The high permeability fracture also

increases the capacity of the well, increasing the Productivity Index. With the combination of these

two factors is possible to conclude that the job performed on these two oil wells was successful.

58

7. Bibliography

“Boundary effects in diagnostic plots”, Society of petroleum Engineers, June, 2015,

http://petrowiki.org/Boundary_effects_in_diagnostic_plots

Clark, K.K.: “Transient pressure Testing of Fractured Water Injection Wells”, J. Pet. Tech.,

June, 1968, 639-643; Trans. AIME 243.

D. Bourdet. “Well Testing and Interpretation”, Handbook of Petroleum Exploration and

Production 3. Elsevier Science, 2002.

Gringarten, A.C., Ramey, H.J., Jr., and Raghavan, R.:“Unsteady State Pressure Distribution

Created by a Well with a Single Infinite-Conductivity Vertical Fracture,” Society of petroleum

Engineer Journal, August, 1974, 347-360.

Homer, D. R.: “Pressure Build-ups in Wells”, Proc., Third World Pet. Cong., E. J. Brill, Leiden

II, 1951, 503-521.

Kabir, S.:”Wellbore Effects”, In M., Kamal (Ed.), Monograph series: Vol. 23. Transient well

testing (1sted.) (pp.91–127), Dallas, Society of Petroleum Engineers.

McKinley, wellbore transmissibility from “Afterflow – Dominated pressure Build Up Data”, J

Pet, Tech, July, 1971

Medhat M Kamal.: “Transient Well Testing”; Society of Petroleum Engineers, July, 2009,

several pg 2-100

MOL Hungarian Oil and Gas Plc. :“Well Fracture Report”; Production and Optimization, 2016,

Budapest.

Raghavan, R., Cady, G.C. and Ramey, H.J., Jr.:“Well Test Analysis for Vertically Fractured

Wells,” J. Pet. Tech., Aug., 1972, 1014-1020; Trans., AIME 253

Streltsova, T.D.: “Well Pressure Behaviour of a Naturally Fractured Reservoir,” SPEJ, October,

1983, 769-780.

W. Jhon. Lee : “Well testing”, Society of Petroleum Engineers of AIME, December,1982, 63-

75.

59

8. Appendices

Appendix A

Well-1 Completion Diagram

60

Appendix B

Well-1 Reservoir location

61

Appendix C

Well 1 Electrical Logging

62

Appendix D

Well-2 Completion Diagram

63

Appendix E

Reservoir Position

64

Appendix F

Well 2 Electrical Logging

Documents

University of Miskolc Faculty of Earth Science and ...midra.uni-miskolc.hu/document/29770/25645.pdf · The technique of well testing, especially pressure transient analysis (PTA)