pressure transient analysis for multiple...

PRESSURE TRANSIENT ANALYSIS FOR MULTIPLE WELLS IN FIELD “X”

TUGAS AKHIR

By:

NGURAH ARYADHITA PRANATA

NIM : 12206012

Diajukan sebagai salah satu syarat untuk mendapatkan gelar

SARJANA TEKNIK

pada Program Studi Teknik Perminyakan

PROGRAM STUDI TEKNIK PERMINYAKAN FAKULTAS TEKNIK PERTAMBANGAN DAN PERMINYAKAN

INSTITUT TEKNOLOGI BANDUNG 2011

Ngurah Aryadhita Pranata,12206012

RESERVOIR DESCRIPTION ON FIELD X FROM DRILL STEM TEST ANALYSIS USING PRESSURE TRANSIENT

Ngurah Aryadhita Pranata* Dr. Ir Taufan Marhaendrajana.**

Abstract

Since the 1950’s when it was first introduced, pressure transient analysis has been a fundamental instrument in the oil and gas industry. Applicable of obtaining valuable reservoir characteristic through sophisticated analysis, it has been a formidable arsenal for the industry ever since; called upon to tackle tougher challenges in order to maintain supply of resources for our growing economy.

To perform a pressure transient analysis the rates from the tested wells are needed, thus the well must first be producing for the test to begin. In addition rate data, pressure response from a preferably down hole measurement is also needed and PVT data if available.

Such a way for obtaining rate and pressure data is through a drill stem test. There will be six different drill stem test from three different wells described in this paper. Each Drill stem test will be implemented on different formations having separate analysis for every formation.

This paper uses pressure transient analysis for reservoir description on field X to determine reservoir characteristics and key data such as skin, reservoir pressure, wellbore storage coefficient and permeability for further reservoir characterization. In addition to reservoir characteristic, the use of pressure transient software will also be able to provide reservoir and well models for better interpretation.

There will be three different types of reservoir models that are going to be described in this paper. They are the homogeneous, dual porosity and radial composite reservoir model. Each model has its own specific characteristic and key parameters, i.e, storativity ratio and Interporosity coefficient for the dual porosity model, and mobility ratio and diffusivity ratio for the radial composite model. This paper will also explain about the relationship of these parameters to predict reservoir performance.

This study involves thorough pressure transient analysis from actual field data of field X. And to increase the level of trust, validation will also be done for the data obtained from the software with the given geological data of field X.

Keywords : storativity ratio, interporosity flow coefficient, Mobility ratio, Diffusivity ratio

*) Undergraduate student in Petroleum Engineering – Bandung Institute of Technology **) Supervisor in Petroleum Engineering –Bandung Institute of Technology


I. Background

Finding and developing new energy sources is a major industry in our world today. We need energy to fuel our economy, harvest our crops and live the lives we take for granted today. It is this urge that has given the writer inspiration to do an analysis for one of Indonesia’s prospecting oil field.

Field “X” is a new developing field in the Javanese island of Indonesia located in the west java basin. The field consists of formation such as carbonate, sandstone and conglomerate rocks. Basement formation for field “X” is a naturally fractured marble formation which is also the main producing formation in this field. Other formation that has been in development and further testing is the carbonate and sandstone formation.

By the time this paper was written the status of the field is still in exploration. New wells are being added everyday to obtain reservoir characterization in field “X” for further future development. This paper uses actual reservoir data from field “X” for input in order to obtain reservoir parameters such as skin, wellbore storage coefficient, permeability, storativity ratio, Interporosity coefficient, etc. Output data from the software used in this paper will be validated from actual geological data in order to increase the level of trust, so that these data can further support future development in field “X”.

II. THEORY

2.1 Dual Porosity Reservoir

In a naturally fractured reservoir such as the basement of field “X” there are two different types of porosity, first is the matrix porosity and second is the fracture porosity. When the well is put into production in a dual porosity reservoir, a dominant flow regime is developed. This flow regime is called the fissure system radial flow as seen in Picture-1. In this regime the fissure system is producing all on its own as though it was the only system present at the time. Overtime this regime causes pressure to drop in the fissures, but no change is happing for pressure inside the matrix. Eventually this flow regime ends in a very short period of time and frequently masked by wellbore storage.

As production continues the fissure system reaches a state where there is a significant differential pressure between the fissures and the matrix. The fissure system has a pressure Pwf and the matrix is still at its initial pressure Pi

2.1.1 Storativity Ratio

. The matrix then begins to produce at the wellbore into the fissure system and also effectively providing some pressure maintenance support. This now has become new flow regime called the total system radial flow shown in Picture-2.

The term Storativity ratio ( )ω is the comparison of fluid storativity between fracture storativity and the total formation storativity (matrix and facture). The equation is seen below:

mmff

ff

cccφφ

φω

+= ………................ (1)

From equation (1) assume that we were given the quantity of ω = 0 thus φmCm

The value of storage capacity ratio (ω) can also help us in determining the distribution of porosity in a naturally fractured reservoir. McNaughton and Garb (1975) describes the connection between the distribution of porosity and how it would effect in fluid storativity shown in Picture-3.

= 1. This tells us for that specific system there is no fracture storativity and all fluids are kept inside the matrix. If the value of ω = 0.1, then fluid storativiy in the matrix is approximately nine times (9x) larger that the storativity of the fracture. If ω = 0.01 then matrix storativity is approximately ninety nine times (99x) larger compared to the fracture storativity. From this we can conclude that the smaller the value of storativity ratio (ω), the larger the value of matrix storativity and the smaller the contribution of fracture storativity to the value of total storativity of the system.

In a naturally fracture reservoir fluids are kept inside either the matrix, fractures or even inside both. From Picture-3 we are able to see that there are three types of fluid storage capacity: Type A: Type A shows that matrix storage

capacity is larger than that of the fracture storage


capacity. This explains that most fluids are kept inside the matrix rather than the fractures.

Type B : Type B shows that there are equal amount of fluid storage capacity in both the matrix and inside the fracture.

Type C : Type C shows that there are no matrix storage capacity, and that all the fluids are kept inside the fractures.

2.1.2 Interporosity Coefficient

The Interporosity Coefficient (λ) is a parameter used to determine the capability of fluids stored inside the matrix to mobilize into the fractures. This event takes place during the total system radial flow. The value of interporosity coefficient is determined by the equation :

2w

f

m rkk

= αλ ………….................. (2)

The coefficient α is the block shape parameter and its value is determined by the matrix-fracture geometry given at the formation system. There is several geometry models used to express α, which is seen at Picture-4 where we can divide the geometry models into four different types:

a. Cubic matrix blocks

22

60w

f

m rkk

lm

=λ ……..……...…….. (3)

b. Spherical matrix blocks

22

15w

f

m

m

rkk

r

=λ ..…….............……... (4)

c. Horizontal strata (rectangular slab) matrix blocks

22

12w

f

m

f

rkk

h

=λ …………..……...... (5)

d. Vertical cylinder matrix blocks

22

8w

f

m

m

rkk

r

=λ .………………......... (6)

If we were to have a large value of λ then the value of km/kf would also be large. A small value of λ would also cause a decrease of km/kf. For example if λ = 10-2 it describes that the matrix permeability

is about 100x smaller that the fracture permeability, assuming that the value of rw

2

is constant. So with a small value of λ we can conclude that there is small matrix permeability and it would be difficult for fluids inside the matrix to mobilize into the fractures. It also means that fluids inside the matrix are difficult and at some cases impossible to produce without stimulation.

If we were able to obtain both the value of storativity ratio and interporosity flow coefficient. Then by using the equation (7) below we can have an idea about the characteristic of the naturally fracture reservoir that is being observed. The equation for a naturally fractured reservoir at infinite acting stage:

−

−−

−

−++=

)1()1(80908.0ln

21

ωωλ

ωωλ DD

iDdfttEtP … (7)

Picture-5 shows a relationship between storativity ratio with interporosity coefficient at different values. To explain more about dimensionless pressure (Pd) and dimensionless time (Td) visualization is given at Picture-6

As you can see the main factors to look for at Picture-6 are the three major lines in the graph Pd

vs Td. There are two lines with a slope of 1.15 and between them there is another line right on the inflection point. This middle line is called the transition period. The value of 1.15 is given by the result of ½ x 2.303; this is a characteristic feature for a radial flow in the relationship of Pd vs. T

Overtime during production, pressure starts to drop until eventually fluids inside the matrix are able to mobilize into the fracture. Due to this incident pressure is maintained and neglecting the previous pressure drop that has occurred. The decreasing of pressure drop also causes the slope of P

d.

d

The amount of time needed by the pressure response to change from the slope 1.15 is function of the Interporosity flow coefficient (λ), the smaller

to decrease until reaching the moment where fluid flow from the matrix starts to weaken. This is called the transition period, and at the end of this period fluid flow will come into balance once more and the system will again maintain a slope of 1.15. The end of the transition period is called the matrix-fracture flow composite.


the value of λ the longer the initial period with a slope of 1.15. On the other hand storativity ratio (ω) is a function of the length of the transition period. The longer the transition period is the smaller the value of storativity ratio (ω).

2.2 Radial Composite Reservoir

Until now we have assumed for the other reservoir models that fluid saturation, mobility and effective permeability remains constant in a given radius of investigation. However this is not the case for some reservoir, because often reservoir behaviors are not uniformed. Thus it would be necessary to consider the variation of reservoir behavior.

A radial composite reservoir model refers the reservoir into two different sections or more Picture-7 where each section has its own fluid and rock characteristic. such as fluid saturation, mobility and effective permeability. The boundary which separates between parameters is ri

Causes for reservoirs to be radial composites are:

which the radius of the inner compartment or also known as the front radius.

• Saturation changes due to an aquifer.

• Saturation changes due to a gas cap.

• Change in saturation due to production below the bubble point pressure.

• Injection of fluid which is different than that of the reservoir.

• Actual changes in the reservoir characteristics.

When one reference is analyzed the other can be calculated using two parameters

Mobility ratio

2

1

)/()/(

µµ

kkM = …………............. (8)

Diffusivity Ratio

2

1

)/()/(

t

t

ckck

Dφµφµ

= ………............. (9)

Mobility and Diffusivity ratio travels from the inner compartment (measured by the distance of ri

III. ANALYSIS

), to the outer compartment. For instance if the value of M=D=1 then there would be no difference in the value of M & D for the inner and outer compartment, thus resulting in a homogeneous reservoir. The effects of different values of M=D can be seen on Picture-8

This paper describes the uses of derivative analysis to determine types of flow regime from the recorded pressure transient data obtain from the actual field. Analyzing reservoir model such as Homogeneous, Dual porosity and Radial Composite Picture-9 and also estimates the value of parameters such as skin and reservoir permeability in these flow regimes.

Horner plot is a build up pressure test plot where it determines the theoretic initial reservoir pressure (P*) by extrapolating given recorded pressure data from a build-up process. The slope (m) of the extrapolated line reflects the characteristic of the reservoir rock and the fluids flowing through them. With the Horner plot we are also able to obtain valuable information such as the effects of Skin (S) to the performance of the well. 3.1 WELL X1 DST #1 The first DST for well X1 was implemented in the basement of field X at depths of 8786 – 9760 ft. The basement formation consists of metamorphic rocks such as granite. For what we know granite has a very low porosity (Table-1) commonly around 0.4 – 1.5 %. Thus chances are for this formation to be a productive reservoir is to have a secondary porosity (ex: faults) to store hydrocarbon and also to increase the value of permeability. The tested basement formation is producing at a rate of Qo = 1618 bbl/d oil and a Qg = 3.209 MMscf/d gas. Well flow is required for DST testing, for initiating drawdown testing and also obtaining fluid characteristic.


3.1.1 Pressure Derivative For the first DST in well X1, we know that the well is producing in a state of limited entry; this is shown from completion data and also supported by the derivative curve analysis obtain from the software. Well limited entry model assumes that the well produces from a perforated interval smaller than that of the drained interval; it is called partial perforation Picture-10. During partial perforation, production time can be divided into three different regimes Picture-11. First (1) early production response can be radial in the perforated interval hw

. Assume that there is no vertical permeability present, thus this radial flow would be the only flow regime available during this time. Then on the second flow regime (2) vertical permeability plays a part in contributing flow to the wellbore. If the perforated interval is quite small then a -1/2 (negative half) slope is developed, creating a spherical or hemi-spherical flow. If the hemi-spherical flow is seen in the data, we can calculate the total skin value (St) with the equation

PPDT SSS += ................................ (10) Where SD is the mechanical skin and SPP

is the skin caused by the geometry of the well, in this case partial penetration. The value of both Mechanical and Geometrical skin will be discussed on the Horner plot section.

Curve matching analysis Picture-12 shows that a radial composite reservoir model best describes the derivate curve obtained from the field data. The derivate tends to have a slight drop at the end thus resulting in values of both M & D at 0.126 with a front radius (ri

3.1.2 Horner Plot

) of 17.8 ft. Values of permeability within the radius area is small up to 4.69 md.

From the Horner plot analysis Picture-13 for DST #1 there were two skin values available mechanical and geometrical skin, this is because of the limited entry well model used for analyzing the DST. The values of mechanical skin are 11.3 and 15.8 for the geometrical skin. Judging from the value of both skins alone we can assume that the geometric of the well effected well productivity more if compared to the mechanical skin due to completion and drilling

activities. Pressure loss due to skin is not too significant with a 529.6 psi of lost pressure due to skin. Reservoir pressure (Pi) of the formation was obtained at a value of 4741.2 psi and temperature up to 315o

F. With a loss of 529.6 psi due to skin, formation pressure is 4741.2 – 529.6 = 4211.6 psi when it reaches the wellbore. This value is still very large, enough to produce 1618 bbl/d of oil mentioned earlier.

3.2 Well X1 DST 2

The second Drill Stem Test at field X1 was implemented on the Pre-Talang Akar Formation. The target interval was 32 ft thick at 8403.2 ft – 8422.4 ft. After observing the derivate curve obtained from the software, the best match was given for the Dual Porosity Pseudo Steady State model. From the geological and Stratigraphy correlation it seems this DST took place between a sandstone formation and the basement (marbel). Not one type of lithology is dominant; there have been a mix of both marbel and a bit of sandstone in the formation, given its dual porosity characteristic.

The well produced a 37.8 degree of API with a GOR value of 1944 scf/STB. Production from the target layer was both oil and gas, at a value of 1405.5 bbl/d & 1.102 MMscf/d.

3.2.1 Pressure Derivative

Looking at the pressure derivative for DST #2 Picture-14 we can see the dual porosity characteristic where the pressure derivative tends to curve back upwards after an initial fall. Further analysis indicates a permeability of 227 mD, which is a very high value. But this is no surprise due to the fact that fractures tend to have a higher permeability than that of matrix, and because this formation is characterized as a dual porosity model there are bound to be a large amount of fractures/fissures producing hydrocarbon to the well.

From the derivate model both storativity ratio (ω) and Interporosity Flow Coefficient (λ) was given at a value of 0.214 and 2.38 x 10-7. A storativity ratio of 0.214 means that hydrocarbon are (1-0.214) x 100% = 78.6% stored inside the matrix compared


to the fractures/fissures. This means that type A fluid storage capacity is at place.

A vertical well model was used for this analysis with and infinite boundary type. Wellbore storage coefficient value of 7.82 x 10-4 bbl/psi means that there is little effect from wellbore storage and qsf

3.2.2 Horner Plot

≈ q.

From the Horner plot Picture-15 initial pressure is given at 4619.5 psia with a temperature of 309.2o

3.3 Well X2 DST 1

F. Surprisingly the pressure drop due to the relatively moderate skin value (skin 24) is not that significant. Analysis shows that there has only been a 285.4 psia of pressure lost due to skin, resulting in wellbore pressure of 4334.1 psi.

Well X2 is located near well X1, and determining by the seismic data it still passes through the same formation as well X1. Similar to the first DST of well X1, DST #2 for well X2 was implemented in the basement. Further know as a marbel formation in this field. The target interval was around 646 ft open hole at 9078 ft – 9724 ft. Qo = 2854 bbl/d oil and Qg


= 5.727.

Judging from the derivate curve that was obtained by the software, this reservoir at first glance was a dual porosity model. The common curve of an initial rise after a fall from the derivate curve is present at the model Picture-16. But further analysis shows that there is a better curve match than that of the dual porosity model. There seems to be some irregularity in Picture-16 where the curve drops significantly to the bottom, breaks apart and then finally appearing once again as it rises. The first thought that comes into mind is phase redistribution has occurred during the early stage of production, because phase redistribution is also visualized by a “break” in the derivate curve. But this still leaves a mystery because phase redistribution only happens at an early stage of production, and this “break” in the derivate curve took place far beyond an early production stage.

A simple explanation of phase redistribution is an event where gasses dissolved inside the oil is separated at an abnormal manner. This can be a

separation which is too fast, where due to the pressure drop from the reservoir to the wellbore causing the gas to immediately separate from the oil. Or a slow separation where the gas slowly separates itself from the oil.

The cause of the disturbance in the derivate curve was initially caused by the difference in reservoir characteristic around the well. Thus assuming the well was divided into two different segments A and B. It was then the radial composite model was applied and made a more appropriate match compared to that of only the dual porosity model.

The value of permeability was very small 2.43 md. This would explain the radial composite reservoir model in the area. Where permeability in a given ri

3.3.2 Horner Plot

around the well has a small permeability compared to the surrounding area which in general has a high permeability value because of the naturally fractured reservoir characteristic of the basement formation.

Analyzing the Horner plot Picture-17, the writer was able to determine the formation pressure and temperature. The given values were 5016.7 psi and 285.78o

There are some reasons why this formation was able to have a stimulated skin value. One of them is the fact that this formation is open holed, which means that no perforation is required unless the formation was damaged previously by drilling fluids/mud.

F with a relatively low skin of -0.831. The skin value for this formation is negative, but normally you need stimulation to decrease skin and enhanced reservoir production.

3.4 Well X2 DST 2 The second DST for well X2 is located at depths of 8976 ft – 8986 ft. The target formation was able to produce 765 bbl/d of oil and 1.255 MMscf/d of gas from a 10 feet pay zone. Further analysis from the log data concludes that the formation in the area were conglomerate rocks. These rocks are sedimentary rocks usually found in areas near lakes and streams. Conglomerate rocks can be great hydrocarbon reservoirs because their characteristics fulfill the two upmost basic components of a reservoir, which is porosity and permeability.


By plotting the derivative curve using the software, the best match was given by the dual porosity model PSS model. It is not rare for a carbonate rock to have dual porosity, because fractures and vugs are often commonly found in these rocks.


There seems to be a lot of disturbance in the derivative curve for DST 2. At the beginning of the curve, there is a substantial drop which is the cause of a changing wellbore storage in the well Picture-18. Further analysis concludes that the well may have reached a specific boundary such as parallel or intersecting faults and thus through further analysis the Dual Porosity Pseudo Steady State model was used to best match the derivate. Pseudo Steady State meaning that the pressure distribution from the well has indeed reached a specific boundary.

The boundary type used for the model was an intersection fault at any angle Picture-24. This model describes that the well is surrounded by two fault at a certain angle. By using the software and validating the distance of the fault from the geological data. Type curve matching for DST #2 increased substantially, able to create an almost perfect match.

From the value of storativity ratio we can tell that a type A fluid storage is in place. Readings for storativity ratio for this DST is 0.0407, which means only 4% of hydrocarbons are stored inside the fracture. Interporosity coefficient value 1.78 x 10-8

3.4.2 Horner Plot

, this is the smallest value if compared to the other dual porosity model for well X1 & X3. This value describe that there is almost none or only a small fraction of fluid able to mobilize into the fractures from the matrix. Permeability in the reservoir is high reaching to a value of 105 md.

From the Horner plot analysis Picture-19 the value of the given formation pressure and temperature for DST #2 is 4572.66 psi and 285.53o

The pressure loss due to the high value of skin, is a staggering 2794.27 psi. This value is more than half the amount of the initial reservoir pressure

(4559.24 psi) which means that by the time the fluids reaches the wellbore, there will only be less than half of the initial reservoir pressure to flow the fluid up the well.

F with a relatively high skin of 54. A high positive skin value means that there has been damage around the wellbore, due to drilling and completion activities.

3.5 Well X2 DST 3 DST #3 was implemented at a shallower depth compared with the second and first DST for well X2. The interval was between 8688 ft – 8714 ft and according to geological data the formation the drill stem test was being implemented on is a sandstone formation with porosity within the area about 15%.


Knowing from geological data that the tested formation is sandstone the derivate model would most likely be a homogeneous model. Since sandstone are not too familiar having dual porosity (fracture and matrix) unlike the carbonate formation. Further evaluation and analysis also proved that the homogeneous model is the best match Picture-20. by analyzing the derivate curve; we can see that there is a steep downhill at the beginning of the curve. This is caused by what is known as changing wellbore storage.

For what we know constant wellbore storage occurs when the difference between the sandface flow rate and the surface flow rate is proportional to the speed of the pressure change. On the other hand changing wellbore storage occurs when fluid compressibility varies in the wellbore during test operations. This causes fluid flow rate to vary and difficult to maintain, difference in the derivative curve due to changing wellbore storage can be seen in picture-25.

A typical case of changing wellbore storage is at a tight gas reservoir. Where the pressure drop in the well is considerable thus causing the compressibility of the fluid within the well to vary. Another case is for wells flowing below the bubble point pressure. This phenomenon would be called “increasing” wellbore, where initially at reservoir pressure oil compressibility would be dominant and as pressure drops eventually solution gas would have been coming out after reaching the wellbore. The initial dominance of oil compressibility is suddenly changed by the solution gas which is coming out more and more as pressure drops below the bubbly point pressure.


Other conditions that may cause a changing wellbore storage:

Pressure dependant gas PVT during build-up or production.

Diameter change in the well completion with rising of falling liquid level.

Phase redistribution in the wellbore

The derivate curve also shows that the pressure disturbance has reached a specific boundary. Analysis shows that there is a fault nearby at a distance of approximately 447 ft from the well. Permeability in this formation is not that big, reaching to a value of 14 md.

3.5.2 Horner Plot

Through the Horner plot analysis Picture-21, reservoir pressure was given at 4548.42 psi with formation temperature up to 296o

Regardless of the pressure loss the formation is still able to produce 624 bbl/d and 2.171 MMscf/d of oil and gas. There was also no water produced at the pay zone (water cut 0%).

F. There was a high skin value of 29.2 for this test, resulting in a pressure lost of 2841.57 psi due to skin.

3.6 Well X3 DST 1

Well X3 is located a few kilometers away from well X1 and X2; the formation it penetrates is similar to those in well X1 and X2. DST#1 for well X3 is implemented in depths of 9334.4 – 11040 ft; the formation it was testing is the basement formation, currently known as a naturally fractured reservoir.


Unlike previous analysis in well X1 and X2 which uses the radial composite reservoir model for the basement. Well X3 shows a more accurate model by using the dual porosity reservoir model. This is shown from the derivate created from plotting the rate and pressure data Picture-22. The derivative curve also shows that there are faults within the area. Intersecting faults at distance of 2185.95 ft and 3396.6 ft from the well and the value for well bore storage coefficient is 0.0109, meaning that wellbore storage had little effect during testing. Though a dual porosity model was the best match for DST#1 in well X3, the

permeability value is relatively small 7.83 md. This value is similar to that acquired from the basement formation in recent DST on well X1 and X2, though the model used was a radial composite model.

Storativity ratio was obtained at a value of 0.0113 and interporosity coefficient at 0.00107. This describes that only 1.1% of hydrocarbons are stored in the fractures while the remaining 98.9 % are stored within the matrix. This is a type A storage capacity similar to those obtained from DST 3 at well X2 and DST 2 for well X1. An interporosity coefficient value of 0.00107 means that the capability of fluid stored inside the matrix to mobilize into the fractures is very low.

3.6.2 Horner Plot

By plotting the Horner plot Picture-23, formation pressure was given at a value of 4559.24 psi with temperature up to 328o

Skin for this test was relatively low with a value of positive 5.13, resulting in pressure loss due to skin as large as 48.1016 psi. Due to the small pressure loss from the skin the well was able to produce 2328.4 bbl/d of oil 3.54 MMscf/d of gas, these values reached more that those able to obtain from previous basement formation at well X1 and X2.

F. This value is similar to those recorded in the basement formation for well X1 and X2.

IV. Model Validation

Analysis Validation for this paper was done by comparing and inputting actual geological data to the software, thus creating more valid results. An example of actual results seen in the software is described in picture-26.

Result from this validation model concludes that the derivate analysis for field X is reliable and can be used as a baseline for future analysis to come.

Results obtained from all the DST in field X can be seen in Tabel-2.

V. CONCLUSIONS

• DST analysis shows that there are faults

within the drainage area of the well X2 & X3.


• Fault boundary model are present in well X2 DST # 3 & #4 and well X3 DST #1.

• Hydrocarbons in Field X are more likely to be stored in matrix rather than in fractures.

• Fluid capability to mobilize from the matrix into the fractures is very low.

• Permeability in the basement formation is relatively low, despite it being a naturally fractured reservoir.

• Type A storage capacity is most common in Field X.

VI. SUGGESTION

• Additional study is necessary to determine

the cause of low permeability value and such the radial composite models in the basement formation.

• Further development and research is

needed to improve the type curve matching on field X.

• A full scale reservoir model is necessary to

determine more accurate results to the data obtained using the pressure transient software.

• Further study is needed to analyze the

actual cause of skin in well X1, X2 & X3.

VII. LIST OF SYMBOLS

Cf = Fracture Compressibility, Psi-1

Cm = Matrix Compressibility, Psi-1

Co = Oil Compressibility, Psi-1

Cr = Rock Compressibility, Psi-1

Ct = Total Compressibility, Psi-1

Cw = Water Compressibility, Psi-1

D = Diffusivity Ratio GOR = Gas Oil Ratio, scf/stb hf = Height of fractured matrix slab, ft kf = Fracture Permeability, md km

P

= Matrix Permeability, md M = Mobility Ratio

D = Dimensionless Pressure

Pi = Reservoir Pressure, psi Qo = Oil Rate bbl/d Qg = Gas Rate MMScf/d ri = Front Radius SD = Mechanical Skin So = Oil Saturation SPP = Geometrical Skin ST = Total Skin Sw = Water Saturation WC = Water Cut tD = Dimensionless time µo = Oil Viscosity, cp α = Block shape parameter, ft-2 λ = Interporosity flow coefficient φf = Fracture Porosity φm

1. Ahmed, Tarek: Advanced Reservoir Engineering, Elsiever Inc, Texas, 2005.

= Matrix Porosity ω = Storativity ratio VIII. REFERENCES

2. Hawkins Jr., Murray F. Et al.: A Note on the Skin Effect. Paper SPE 732-G.1956

3. Nelson, R.A: Geologic Analysis of Naturally Fracture reservoir, Gulf Professional Publishing, Houston, 2001.

4. Tiab, Djebbar and Erle C. Donaldson: Petrophysic: Theory and Practice of Measuring Reservoir Rock and Fluid Transport, Gulf Professional Publishing, USA, 2004.

5. Viturat, Didier and Fjaere, Ole: Dynamic Flow Analysis, Kappa DFA BOOK, 1988


VII. APPENDIX

Picture-1.Fissure System Radial Flow (Matrix & Fracture)

Picture-2.Total System Radial Flow (Matrix & Fracture)

Picture-3. Porosity distribution for a naturally fractured reservoir (McNaughton dan Garb)

Picture-4. Different types of matrix geometric model


Picture-5. Theoretical drawdown pressure for naturally fractured reservoir.

Picture-6. S-shape characteristic for naturally fractured reservoir

Picture-7.Radial Composite Reservoir Model

Picture-8.Effect from the different values of M=D


Picture-9. Pressure derivative models

Picture-10. Partial perforation Schematic

Picture-11 Flow Regime in partial perforation


Picture-12.Derivative well X1 DST #1

Picture-13.Horner Plot well X1 DST #1


Picture-24. Intersection fault boundary at any angle

Picture-25.Changing storage & Constant Wellbore Storage

Picture-25. Results of model validation using actual geological data

Tabel-1. Porosity ratios for different rock types

POROSITY RATIOS %

Granite 0.4 - 1.5 Slate 0.4 - 5 Marble 0.5 - 2 Limestone 0.6 - 31

Quartzite 0.4 - 3.9 Sandstone 0.5 - 35

Before

After


Field X

Well X1 Well X2 Well X3 DST #1 DST #2 DST #1 DST #2 DST #3 DST #1

Reservoir Model

Radial Composite

Dual Porosity

Radial Composite

Dual Porosity Homogeneous Dual

Porosity Boundary

Model Infinite Infinite Infinite Intersecting Faults One Fault Intersecting

Faults Pi (psi) 4742.3 4619.52 5016.77 4572.66 4548.42 4441.62 k (md) 6.65 227 2.43 136 28.1 11.2

kh (md.ft) 6770 7430 1570 1340 737 17100 Skin 11.3 24 -0.831 54 29.2 3.88

∆Pskin (psi) 529.675 285.422 -102.609 2794.27 2841.57 36.3855 C (bbl/psi) 0.00179 7.82 x 10-4 0.0282 0.00282 0.00204 0.0108

ω - 0.214 - 0.0407 - 0.0113 λ - 2.38 x 10-7 - 1.76 x 10-8 - 0.00107 M 0.012 - 999 - - - D 0.012 - 1 x 10-3 - - -

Tabel-2. Final Results from Pressure Transient Analysis in field “X”

pressure transient analysis for multiple...

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