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Comparison of Black Oil Tables and EOS Fluid

Characterization in Reservoir Simulation

An MSc Thesis

by

Mihály Gajda

Submitted to the Petroleum and Natural Gas Institute of University of Miskolc

in partial fulfilment of the requirements for the degree of

MASTER OF SCIENCE

in Petroleum Engineering

Miskolc, 07/05/2014

i

Table of Contents List of Figures iv

Nomenclature vi

1. Introduction 1

2. Basic Description of PVT Calculation Models 2

2.1. Equation of State 2

2.2. Black-Oil Formulation 3

2.2.1. Traditional Black-Oil Formulation 3

2.2.2. Modified Black-Oil Formulation 4

2.3. Comparison 5

3. Fluid Samples Used for Comparison 6

3.1. Highly Volatile Under Saturated Oil 6

3.2. Rich Gas Condensate 6

3.3. Near Critical Gas Condensate 6

3.4. Saturated Oil 6

4. Development of PVT models 7

4.1. EOS Fluid Characterization 7

4.1.1. Check of Sampling 7

4.1.2. Check of Measurements 9

4.1.3. C7+ Characterization 11

4.1.4. EOS Tuning 14

4.1.5. Check of the Results 16

4.1.6. Grouping 17

4.2. Modified Black-Oil Tables 19

4.2.1. Methods for Black-Oil Table Creation 20

4.2.2. Whitson-Torp Method 21

4.2.3. Recommendation for Different Fluid Types 23

ii

4.2.4. Check of Tables 24

4.3. Summary for PVT Model Development 26

5. Description of the Numerical Reservoir Model 27

5.1. Grid and Rock Properties 27

5.2. Relative Permeability Curves 28

5.3. Wells 29

5.4. Development Strategy 29

6. Volatile Oil 30

6.1. Fluid Models 30

6.2. Development Strategies 30

6.3. Results 31

6.3.1. Case 1 (Depletion) 31

6.3.2. Case 2 (Aquifer) 32

6.4. Discussion and Conclusion 33

7. Gas Condensate 34



7.3. Results 35




8. Near Critical Gas Condensate 38



8.3. Results 39



iii


9. Saturated Oil Reservoir 43



9.3. Results 44




10. Summary and Conclusion 46

References 47

Acknowledgement 51

Appendix A 52

Appendix B 53

Appendix C 58

Appendix D 59

Appendix E 60

iv

List of Figures

Figure 2.1-Schematic of Traditional Black-Oil Formulation ................................................ 4

Figure 2.2-Schematic of Modified Black-Oil Formulation ................................................... 5

Figure 4.1-Hoffmann Plot for Sample NC ............................................................................ 8

Figure 4.2-Hoffmann plot for the CVD measurement of Sample NC................................. 10

Figure 4.3-Gamma Distribution Fitted on the C7+ fraction of Sample NC ........................ 12

Figure 4.4-Relationship Between Molar Mass and Density ................................................ 13

Figure 4.5-Simulation of CCE without Tuning (Sample NC) ............................................. 14

Figure 4.6-CCE Liquid Dropout After Matching for Sample NC ....................................... 16

Figure 4.7-Simulated CCE - Equilibrium Ratios for Sample NC ....................................... 17

Figure 4.8-CCE - Liquid Dropout - Comparison of the Original and Pseudoized Fluid

Characterization for Sample NC.......................................................................................... 19

Figure 4.9-Schematic of Whitson-Torp Method ................................................................. 21

Figure 4.10-Oil FVF vs Pressure ......................................................................................... 22

Figure 4.11-Oil Properties vs Pressure ................................................................................ 22

Figure 4.12-Gas Properties vs vaporized oil-gas ratio ........................................................ 23

Figure 4.13-Schematic of Black-Oil Table creation for Saturated Oil Reservoirs .............. 24

Figure 4.14-Density of Reservoir Oil and Gas Calculated with EOS and BO Table .......... 25

Figure 4.15-Compressibility of Reservoir Gas and Oil Calculated with BO Tables .......... 26

Figure 5.1-Grid Constructed for the Problem ...................................................................... 27

Figure 5.2-Location of Well and Faults............................................................................... 28

Figure 5.3-Oil-Water Relative Permeability Curves ........................................................... 29

Figure 6.1-Simulation Results of Sample VO - Case 1 ....................................................... 31

Figure 6.2- Oil and Gas in Place During Depletion (Sample VO - Case 1) ........................ 32

Figure 6.3-Simulation Results of Sample VO - Case 2 ....................................................... 33

Figure 7.1-Simulation Results of Sample GC - Case 1 ....................................................... 35

Figure 7.2-Simulation Results for Sample GC - Case 1 (Zoomed) ..................................... 36

Figure 7.3-Gas and Oil in Place During the Depletion ....................................................... 36

Figure 7.4-Simulation Results of Sample GC - Case 2 ....................................................... 37

Figure 8.1-Simulation Results for Sample NC - Case 1 ...................................................... 40

Figure 8.2-Free Gas and Liquid Oil in Place (Sample NC - Case 1) .................................. 40

Figure 8.3-Simulation results of Sample NC - case 2 (MBO-CVD vs. EOS15) ................. 41

Figure 8.4-Simulation Results of Sample NC - Case 2 (EOS15 vs EOS7) ......................... 42

v

Figure 9.1-Simulation Results for Sample VO - Case 1...................................................... 44

Figure 9.2-Simulation Results for Sample SO - Case 2 ...................................................... 45

vi

Nomenclature

Bg - Gas formation volume factor [m3/sm

3]

Bgd - Dry gas formation volume factor [m3/sm

3]

Bo - Oil formation volume factor [m3/sm

3]

cg - Gas compressibility (apparent) [1/bar]

co - Oil compressibility (apparent) [1/bar]

Fgsp - Mol fraction of separator gas [-]

Ki - Equilibrium ratio [-]

kij - Binary-Interaction-Parameter [-]

M - Molar mass [g/mol]

p - Pressure [bar]

pc - Critical pressure [bar]

Q - Gas rate [sm3/day]

Rs - Solution gas-oil ratio [sm3/sm

3]

Rsp - Separator gas-oil ratio [sm3/sep.m

3]

rs - vaporised oil-gas ratio [sm3/sm

3]

T - Temperature [°C, °F, °K, °R]

Tb - Boilingpoint temperature [°C, °F, °K, °R]

Tc - Critical Temperature [°C, °F, °K, °R]

xi - Liquid mole fraction [-]

yi - Gas mole fraction [-]

Z - Deviation factor [-]

γg - Specific gravity of gas [-]

γSTO - Specific gravity of oil [-]

ρg - Gas density [kg/m3]

ρo - Oil density [kg/m3]

Ωa - EOS numerical constant [-]

Ωb - EOSnumerical constant [-]

1

1. Introduction

PVT calculations are used to describe the phase behaviour and to determine the

thermodynamic properties of hydrocarbon systems at the given pressure and temperature.

PVT properties of reservoir fluids are required by the most of petroleum engineering

calculations including : reservoir simulation, well testing, pipeline flow calculations and

separator design and the accurate prediction of phase behaviour is essential in case of

planning some tertiary recovery methods like gas injection or in situ combustion. As this is

an input data for the mentioned calculations its accuracy is crucial, wrong PVT properties

lead to erroneous calculation results, so the applied calculation method must be chosen

carefully.

Beside accuracy, simplicity and calculation speed are also important aspects in the

selection. Due to technological improvements in the latest decades the calculation speed is

not as important as it was, except reservoir simulation where it is still an issue. In the

solution of a problem, it is a common practice to select the simplest method that provides

the desired accuracy [1], so simplicity can also be a favourable property of a calculation

method.

The first objective of this thesis is to briefly describe the creation of PVT calculation

models, equation of state and black-oil tables used in reservoir simulation. The two

calculation models will be compared in respect of accuracy and calculation speed. The

main objective of this thesis is to give some advice about which PVT model should be used

in case of different fluid types or recovery methods.

The EOS fluid characterizations are developed with PETEX PVTp, but black-oil tables

are created by hand based on simulation of PVT experiment with PVTp. Eclipse100 and -

300 were used for the simulations. All of the figures are created by me with MS Visio,

Excell or Eclipse.

2

2. Basic Description of PVT Calculation Models

In the petroleum industry two approaches are used to calculate the PVT properties of

reservoir fluids. The first and the simplest is the black-oil formulation that determines the

necessary properties of the fluid based on separation data. The second is equation of state

(EOS) which provides both the compositional and the volumetric properties of the

reservoir fluid at given conditions based on its overall composition. Both methods have

their advantages and disadvantages that have to be taken into consideration in the

selection. The methods will be detailed in the next subchapters.

2.1. Equation of State

Cubic equation of states provide relationship between pressure, volume and

temperature. They accurately describe the volumetric and phase behaviour of pure

compounds and mixtures. In addition, EOS gives information about the composition of

equilibrium gas and oil which is crucial in the planning of some recovery methods which

aim the increase of recovery of more valuable compounds.

van der Waals proposed the first cubic equation of state in 1873 [2]. Many EOS's have

been created with the modification of this equation since then. Nowadays Peng-Robinson

(PR) [3] and Soave-Redlich-Kwong (SRK) [4] are the two most commonly applied EOS's

in the petroleum engineering calculations. All of them use an attraction and a repulsion

parameter to account the non-ideal behaviour of the fluid. Their common weakness is the

poor liquid density prediction, which was eliminated by the introduction of the volume

translation parameter [5]. With this modification the PR and SRK EOS's provide

satisfactory vapour-liquid equilibrium and liquid density predictions.

The EOS's require the critical properties and the acentric factor of the components of

reservoir fluid and its overall composition. Two-phase flash calculation with EOS is an

iterative process, the calculation time increases as the number of components increases and

conditions approach the critical point of the fluid.

The main advantages of EOS are:

This is the most accurate method that is commonly used to calculate the PVT

properties of reservoir fluids.

Wide range of phase behaviour problems can be treated with EOS even the most

difficult ones like gas injection or multi-phase flash calculation.

3

The main disadvantages of the application of EOS are:

Significantly increased calculation time compared to other methods.

Development of an EOS fluid characterization requires detailed PVT reports that

seldom available in case of old fields.

Creation and application of EOS fluid characterization need more experience.

2.2. Black-Oil Formulation

Black-oil formulation is used to make relationship between surface and reservoir

volumes. In traditional black-oil formulation three engineering quantities are introduced

for this purpose : solution gas-oil ratio (RS), oil formation volume factor (Bo) and gas

formation volume factor (Bg). In modified black-oil formulation solution oil-gas ratio (Rv)

is introduced as the forth property to take vaporized oil into consideration, and gas FVF is

defined differently. The basic differences between the two formulations will be discussed

in the following subchapters.

2.2.1. Traditional Black-Oil Formulation

The definition of the three basic black-oil properties are:

(2.1)

(2.2)

(2.2)

Traditional black-oil formulation has the following assumptions [6]:

Reservoir oil consists of two surface "components", stock-tank oil and surface

(total separator) gas.

Reservoir gas does not yield liquids when brought to the surface.

Surface gas released from the reservoir oil has the same properties as the reservoir

gas has.

Properties of stock-tank oil and surface gas do no change during the depletion of a

reservoir.

Figure 2.1 depicts the schematic of a traditional black oil formulation. Black-oil

properties can be calculated with correlations or tables. Black-oil tables contain the

properties of the reservoir fluid in tabular form. Black-oil correlations are simple empirical

equations, their predictive capability is often really poor, they have no advantage over a

4

well designed black-oil table, therefore they will not be discussed in the following

chapters. The proper creation of these tables is the topic of chapter 4.

The main advantages of using traditional black oil formulation:

Low calculation time and memory requirement.

Simple to use and create.

The main disadvantages of the method:

It cannot describe fluids with complex phase behaviour like gas condensates.

It cannot treat recovery methods where vapour-liquid equilibrium is crucial like in

gas injection.

Equilibrium

Reservoir Oil

Reservoir GasSurface Gas

Surface Gas

Surface Oil

From Reservoir Gas:

From Reservoir Oil:

Figure 2.1-Schematic of Traditional Black-Oil Formulation

Despite its drawbacks traditional black-oil formulation can be efficiently applied for

less volatile oil, dry gas and any oil reservoirs depleted above its bubble point.

2.2.2. Modified Black-Oil Formulation

Modified black-oil formulation introduces a new forth property, vaporised oil-gas ratio

that is defined as [7]:

(2.4)

The schematic of modified black oil formulation can be seen in Figure 2.2. The modified

gas FVF, called as "dry-gas" FVF is defined differently taking liquid dropout into

consideration [7].

These modifications greatly improve the accuracy of the method and make it capable to

treat volatile oil and gas condensate reservoirs. Several efforts were taken to take the

density change of surface gas and oil into consideration [8], but they are rarely available in

commercial software's, so they will not be detailed here. Therefore the surface oil and gas

5

densities are assumed to be constant during the depletion of the reservoir. In addition, the

density of the surface oil is the same whatever it originates from: reservoir gas or reservoir

oil and it is also true for the surface gas. Other modifications were also proposed to make

this method capable to treat gas injection [9, 10], but it is out of the coverage of this thesis.

Equilibrium

Reservoir Oil

Reservoir Gas

Surface Gas

Surface Oil

From Reservoir Oil:

Surface Gas

Surface Oil

From Reservoir gas:

Figure 2.2-Schematic of Modified Black-Oil Formulation

2.3. Comparison

EOS is more sophisticated calculation model than black oil formulation. Although the

EOS requires more calculation time and memory, it can provide the necessary accuracy in

a wide range of circumstances. Black oil tables can be generated from simple separation

data, but the best way is that if it is generated with a well tuned EOS characterization.

Therefore the creation of an adequate black oil table also requires detailed PVT report, so

this does not make difference between them. The most crucial factors are the calculation

time and accuracy in the decision. To save computation time, the simpler model - black-oil

table - should be chosen if it can provide the desired accuracy. Otherwise EOS must be

used regardless of the increased calculation time and memory requirement.

6

3. Fluid Samples Used for Comparison

Four fluid samples were chosen for the comparison: highly volatile under saturated oil,

rich gas condensate, near critical gas condensate and saturated oil. These four samples

represent the four most commonly occurring type of fluid systems whose phase transition

is significant. This chapter will briefly introduce these samples. The first three samples are

real, but the saturated oil sample is synthetically made from the volatile oil sample.

3.1. Highly Volatile Under Saturated Oil

The C1 content of this oil sample is 62.64 %, while its C7+ content is 18.44%, its

intermittent content is not significant. The reservoir temperature is 118 °C and the reservoir

pressure is 610 bars. The bubble point pressure is 379 bars at reservoir temperature. The

zero flash GOR of the oil is 416 sm3/m

3 and its API gravity is 35.8. More detailed

information can be found in Appendix A (short name of the sample in the followings :

Sample VO).

3.2. Rich Gas Condensate

The C1 content of this gas condensate sample is 66.9 %, it has a significant intermittent

content, 9.7 % CO2, and its C7+ content is 9.6%. The reservoir temperature is 191 °C and

the reservoir pressure is 505 bars. The dewpoint pressure is 338.3 bars at reservoir

temperature. The zero flash GOR of the sample is 1218sm3/m3 and the API gravity of the

stock-tank oil is 40.85. More information can be found in Appendix A (Sample GC).

3.3. Near Critical Gas Condensate

The C1 content of the sample is 69.03 %, its C7+ content is 13.11 % and its intermittent

content is not significant. The reservoir temperature is 91 °C and the reservoir pressure is

534 bars. The Dewpoint pressure of the sample is 467 bars at reservoir temperature. The

zero flash GOR of the sample is 776 sm3/m3 and the API gravity of the stock tank oil is

33.8. More detailed information can be found in Appendix A (Sample NC).

3.4. Saturated Oil

There was not available sample from a saturated oil reservoir, so it is made synthetically

by flashing of the volatile oil sample at 300 bars. Therefore the saturation pressure of the

oil and gas phase is 300 bars. The received gas phase represents the gas cap and the oil

phase represents the oil body. The composition of the phases can be found in Appendix A

(Sample SO).

7

4. Development of PVT models

Both PVT models can provide the necessary accuracy, but only then if they are

sufficiently developed. The creation of an accurate PVT table needs a well tuned EOS

characterization thus it is better to start with its description. The development of an EOS

characterization requires more experience and time. Presently lots of guidelines and case

studies are available in the literatures that make our work easier.

4.1. EOS Fluid Characterization

Peng-Robinson EOS is chosen for the calculations, because this is the most widely used

EOS in the petroleum industry. The main steps of the development of an EOS

characterization are the following:

1. Checking the PVT measurement and sampling

2. Characterizing C7+ fraction

3. Tuning of EOS to measurements

4. Checking the result

5. Reducing components

These steps are essential to gain reliable EOS characterization. However many practicing

engineers omit some of them, but this can lead to inaccurate or inconsistent model.

4.1.1. Check of Sampling

Sampling can be performed in two ways: bottomhole sampling and separator sampling.

All the samples were taken from the separator during the well test. Separator sampling

means two different samples from the produced liquid and gas, which are recombined later

to gain the wellstream fluid. It is highly recommended to check the consistency of the

sample and the quality of recombination.

The compositions of the samples taken from the separator are always measured.

Problems in sampling may occur, therefore it has to be checked to ensure the quality of the

samples (it should be done by the laboratory before recombination, although it is not done

many times). Thereafter the two samples get recombined based on production data.

Sometimes the composition of the wellstream determined only by mathematical

recombination of the compositions of the samples. In other cases after the physical

recombination the compositions of the received wellstream get measured and it should be

checked.

8

Hoffmann-Crump-Hocott proposed a method for checking the consistency of the

samples [11]. Equation 4.1 is the basic equation of the method, it says that if log(Ki*p)

values are plotted vs. Fi characterization factor (defined by eq. 4.2), the points have to be

on a straight line in the case of light components.

ii FAApK 10log (4.1)

sc

ci

cibi

bi

ip

p

TT

TTF log

11

11 (4.2)

where:

A0, A1 - parameters of the line

Temperature is in °K or °R.

Figure 4.1 depicts the Hoffmann plot for Sample NC, it can be seen that the light

components are on the line except C6. This is an anomalous behaviour, but the adequacy

of the sampling is still acceptable regardless of this anomaly. In case of the other samples

the accuracy is within the error range at all components.

Figure 4.1-Hoffmann Plot for Sample NC

-2

-1

0

1

2

3

4

-2 -1 0 1 2 3 4

Lo

g(K

∙p)

F Characterization Factor

N2 C1

C2 CO2

C3

C4 C5

C6

C7 C8

C9

9

The mathematical recombination of the sample pairs requires their mole fraction that

can be determined from the production data. First the measured gas rate must be corrected

with the measured gas properties, because assumed properties were used in the

measurement of the gas rate. The appropriate formula for this purpose is:

lablab

fieldfield

ggcZ

ZQQ

(4.3)

Thereafter the next step is the determination of gas-oil rate related to separator

conditions. It can be done in the following way from the production gas-oil ratio:

oo

cg

o

s

spBQ

Q

B

RR

(4.4)

The mol fraction of separator gas can be calculated in the knowledge of the separator

gas-oil ratio, the density and the average molar mass of separator liquid:

1

21301

spo

osp

gspRM

F

(4.5)

where units are ρosp in lbm/ft3, Mosp in g/mol and Rsp in scf/bbl.

Then everything is given for the mathematical calculation of the overall composition of

wellstream by the following equation:

igspigspi xFyFz 1 (4.6)

There is a decent match between the measured and mathematically recombined

composition for all samples.

4.1.2. Check of Measurements

The most commonly performed PVT measurements are: separator test, constant

composition expansion (CCE), constant volume depletion (CVD) and differential

liberation experiment (DLE). With CCE experiment the saturation pressure and the under

saturated density of the fluid are measured. The multistage separator test is conducted on

an oil sample primarily to provide basis for converting differential-liberation data from a

residual-oil basis to a stock-tank oil basis. CVD is intended to simulate the depletion of

gas/gas condensate reservoir and provide the desired volumetric and compositional

information that can be used to tune the EOS fluid characterization. As the quality of the

EOS characterization strongly depends on this sample, therefore it is recommended to

check it. The DLE has a similar purpose, but for oil reservoirs. Its adequacy should also be

checked, but the PVT reports seldom publish the data which would be necessary for the

10

check. The short summary of the most important measurements can be found in Appendix

B.

Whitson and Torp published an appropriate method for the check of CVD

measurements [12]. It is basically a material balance written up for every component.

During the CVD experiment the composition of the removed gas is measured. With the

help of this method the composition of the liquid, which is dropped out in the PVT cell,

can be calculated and in the knowledge of that it is easy to determine the equilibrium

ratios. Thereafter the Hoffmann plot [11] can be used to check the received results. Figure

4.2 depicts the results for Sample NC.

Figure 4.2-Hoffmann plot for the CVD measurement of Sample NC

The equilibrium ratios must decrease as the F characterization factor decreases and

values of a pressure step must be on a straight line. In this case these criterions are not

satisfied at the four highest pressure steps and the C6 differs from normal behaviour at

every pressure step. It seems in Figure 4.2, that C6+ components have higher equilibrium

ratio than C5's and C4's, and they seem to be on a different straight line than lighter

components. This is physically unrealistic behaviour resulting from measurements error.

The removed gas is separated into "produced" gas and liquid, their composition is

measured and recombined mathematically to gain the composition of the removed gas. The

fact is that C6+ components are on a different straight line indicating that perhaps the

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

-3 -2 -1 0 1 2 3 4

log(K

∙p)

F Characterization Factor

425 bar

375 bar

325 bar

275 bar

225 bar

175 bar

125 bar

75 bar

C5 C4 ←C6+

C1 C3

CO2 C2

N2

11

mathematical recombination was wrong, which may comes from the incorrect

measurement of liquid properties. Therefore these properties should not be used for the

tuning of the EOS fluid characterization of Sample NC, except liquid dropout and the

liquid density, because these are not affected by this error.

Other measurements have found to be correct.

4.1.3. C7+ Characterization

EOS calculation needs the critical properties, acentric factor and binary-interaction

parameters (BIP) of the components, therefore they must be determined in case of

component of the reservoir fluid. The light components and their properties are well

known, the C7+ components deviate from them in many aspect that is why they treated

differently. However the mole fraction of the C7+ fraction is low, it still has a great impact

on phase behaviour [13]. Accordingly, the proper description of this fraction is crucial.

After C6, the number of isomers starts to increase rapidly; these isomers can be paraffinic,

naphthenic or aromatic with completely different properties. The whole C7+ fraction

contains thousands of different compounds, the identification of all of these compounds is

impossible, for this reason the measured composition is just an assumption. The other

problem is that the critical properties of the compounds heavier than C20 are not known.

Therefore this fraction must be approximated somehow; this procedure is the C7+

characterization. Both mathematical and empirical methods are used for this purpose. The

characterization can be grouped into three main tasks [14]:

Dividing the C7+ fraction into a number of fractions with known molar

compositions.

Defining the molecular weight, specific gravity, and boiling point of each fraction.

Estimating the critical properties, the acentric factor of each fraction and the key

BIP's for the specific EOS being used.

The composition of a reservoir fluid can be determined with true boiling point

distillation (TBP) or gas chromatography (GC). GC can determine the composition up to

C35-C40, meanwhile the limit is only C15-C20 for TBP distillation, but it determines also

the molar mass, density and boiling points of fractions. The other significant difference

between them, that the TBP distillation is more expensive and takes more time than GC. In

case of Sample VO both measurements were performed, the composition of Sample GC

was measured with GC, while the composition of Sample NC was determined with TBP

distillation.

12

Before the creation of C7+ sample, something must be cleared up. All of the

compounds with similar boiling points are grouped into single carbon number fractions

(SCN), therefore C8 means not only n-C8, but the mixture of compounds with boiling

point similar to n-C8 [15]. Grouping based on molar mass leads to inadequate

characterization. The molar mass of SCN fractions cannot be measured by GC, but Katz

and Firoozobadi published a table [16], which contains the average properties of the SCN

fractions and can be used for estimation.

When the composition is only determined up to C15 or so, it has to be extrapolated to

~C35. The best solution for the problem is to fit a distribution function on the C7+ fraction,

and then with the help of this function the molar mass and molar fraction of the heavier

components can be determined. The most recommended is the gamma distribution because

of its flexibility [17]. Three parameters of the distribution function used for the fitting are:

the smallest molar mass (η), the average molar mass of the C7+ fraction (MC7+) and α,

shape factor.

Figure 4.3 depicts the measured and the extrapolated composition of the C7+ fraction of

Sample NC. Measured composition is represented by red squares, blue squares represent

the values calculated by gamma distribution, and green triangles represent the composition

measured on another sample from the same reservoir. The values calculated by gamma

distribution show a decent match with the composition measured on another sample, which

proves the potency of gamma distribution.

Figure 4.3-Gamma Distribution Fitted on the C7+ fraction of Sample NC

13

After the composition is determined up to C35+, the SCN fractions have to be grouped

into pseudo components. Usually from two to seven pseudo components are required to

describe appropriately the phase behaviour of the fluid. Whitson published an empirical

rule that can be used to determine the number of required components and the molar mass

boundaries used to organise pseudo components [17]. Six pseudo components were formed

for all the three samples, because more complex phase behaviour requires more pseudo

components to describe.

Thereafter the densities of fractions have to be determined; hence a function is needed

to relate density to molar mass. Equation 4.7 is a flexible formula published by Søreide

that can be fitted to distillation densities [18].

cifi bMCa (4.7)

where a, b, c and Cf are the parameters of the function. (standard values: a=0.2855, b=66,

C=0.13 and Cf is between 0.27 and 0.31)

Figure 4.4-Relationship Between Molar Mass and Density

For Sample NC the measured densities, the fitted correlation and its parameters can be

seen in Figure 4.4. The fitted function accurately approximates the measured values,

therefore it is sufficient to determine the densities of the pseudo components. For Sample

GC, there was no distillation data, so standard values are used, and stock-tank density is

matched by adjusting Cf parameter.

14

There are many correlations in the literature that can be used to determine the boiling

point temperature from density and molar mass. Søreides correlation [18] is the most

recommended [19, 20] therefore it was used for all the three samples. The formula is the

following:

iiii

iibi

MM

MT

33

266.303522.05

10462.37685.410922.4exp

10695.13.1928 (4.8)

where Tbi is in °R.

The other required properties can easily be calculated in the knowledge of molar mass,

density and boiling point temperature. Twu's correlation was used for critical properties

[21], Edmister's correlation for acentric factor [22], and Chue-Prausnitz's formula for BIP's

[23]. The pseudo-component properties of Sample NC (for example) can be found in

Appendix C. Now the EOS fluid characterization is ready for the calculations.

4.1.4. EOS Tuning

Mostly even if the C7+ fraction is characterized appropriately, the predictions of the

EOS are inaccurate. The 10 % error in saturation pressure is usual, as well as 5% error in

density and several percent in mole fraction of key components. It can also happen, that the

EOS predicts bubblepoint as saturation condition instead of dewpoint or vice versa, this

problem can be seen in Figure 4.5 at Sample NC. This problem often occurs in case of near

critical fluid.

Figure 4.5-Simulation of CCE without Tuning (Sample NC)

0

20

40

60

80

100

120

0 100 200 300 400 500 600

Liq

uid

Dro

po

ut

[%]

Pressure [bar]

Measured

Calculated

15

The two main sources of prediction error are: assumptions of EOS and the uncertainty

in C7+ properties. Therefore, to receive accurate and reliable predictions the EOS fluid

characterization has to be matched to the measured data. The three main phase of the

tuning process:

Comparison of calculated and measured data

Matching measured data in several ways

Evaluation and choosing the best resulting model

Someone may think that it is meaningless to put so much energy into C7+

characterization, because the C7+ properties will be adjusted. It can be stated after many

attempts to match EOS to measurements, that if the C7+ characterization is inadequate, the

desired accuracy cannot be reached or only with a thermodynamically inconsistent model.

The matching is done by adjusting different properties of the fluid components. It can

be done with "trial and error" or regression. Trial and error is time consuming and tiring

[14], therefore it is seldom used nowadays. The tuning methods that use non-linear

regression are fast and automatic, but the result can be unrealistic, so they have to be used

carefully [24]. The regression based methods can be categorized into three groups [25]:

1. Modification of Ωa, Ωb numerical constants and BIP's.

2. Modification of critical properties and BIP's.

3. Modification of the inspection properties of C7+ fraction(molar mass, density,

boiling point or even molar distribution) and BIP's.

The method published by Coats and Smart can be classified into the first group [26]. It

changes the Ωa and Ωb numerical constant of methane and the heaviest fraction and BIP

between them. The method is really simple and efficient, it is recommended to choose if

someone does not have too much experience in fluid characterization. The phase behaviour

of a system is really sensitive for these parameters, so the search for optimal values is an

easier mathematical problem than in the other two cases.

There are lots of publications dealing with the second part including guidelines and case

studies [14, 27]. Therefore it is well documented and with a little bit more experience it

yields more accurate models than group one. These methods basically assume that the

basic properties of the C7+(molar mass, density and boiling point) are accurate, and the

error comes from the uncertainty of the critical property correlations. The method may

yields unrealistic results, so the checking after regression is crucial for this method.

The third group is the most novel, only some recently proposed method can be

classified into this one [19,20]. It can be interpreted as the method suppose that the

16

correlations calculating critical properties are accurate and the error comes from the

erroneous inspection properties of the C7+ fraction. It means that the regression re-

characterize the whole C7+ fraction in every iteration step. Although these methods require

the most experience, there is much lower chance for receiving unrealistic results. In spite

of these, methods are "superior" compared to the other two groups; they are still not

available in commercial software's.

The measurements were matched by adjusting critical pressure and temperature of C7+

components and BIP's between them and the methane. The results are evaluated in the next

subchapter. The modified critical properties of Sample NC can be found in Appendix C.

4.1.5. Check of the Results

After the EOS fluid characterization is matched to the measured data, its predictions are

greatly improved compared to its original accuracy. Figure 4.6 shows the liquid dropout of

the CCE experiment for Sample NC, as it can be seen that EOS predictions are almost

perfect after matching. After the matching the other parameters were also predicted with

the same accuracy for all samples.

Figure 4.6-CCE Liquid Dropout After Matching for Sample NC

To accept a fluid model, that is not enough to inspect only its accuracy, but also its

thermodynamic consistency should be checked. As a result of regression, the model is

physically unrealistic many times, even though it satisfies the problem mathematically.

Therefore the check of thermodynamic consistency is necessary.

0

20

40

60

80

100

120

0 100 200 300 400 500 600

Liq

uid

Dro

po

ut

[%]

Pressure [bar]

Measured

Original

After Matching

17

Thermodynamic consistency desires the increase of critical temperature and the

decrease of critical pressure as the molar mass increases. When other parameters are also

changed like BIP's and numerical constants, the check is not so simple. Whitson published

a method, which is sufficient for this purpose[19]. A CCE experiment has to be simulated

with the matched EOS fluid characterization and the equilibrium ratios have to be plotted

in the function of pressure. The plot has to fulfil two criterions:

The equilibrium ratios have to monotonically decrease as the molar mass increases

The equilibrium ratio line must not cross each other (mostly caused by alternating

BIP's)

Figure 4.7-Simulated CCE - Equilibrium Ratios for Sample NC

Figure 2.1 shows the mentioned plot for Sample NC, the fluid characterization satisfy

every expectation, therefore it is thermodynamically consistent. The other two tuned EOS

fluid characterization also fulfil these criterions.

4.1.6. Grouping

However, the technology has improved a lot in the previous decades, the computation

time and memory are still crucial issues in case of reservoir simulation. Flash calculations

have to be performed in every block during every time step, this means many million

times. The number of components is the main factor that affects the calculation time (and

can be changed). On the other hand, the number of components also has a significant effect

on accuracy; therefore the reduction of components has to be done carefully.

18

The accurate simulation of some recovery methods requires more components, while

others require less; there is no general rule for it. To reduce the number of components,

two or more of them are grouped into pseudo components. The grouping has to be based

on volatility [15]. Generally the N2 can be lumped with C1, and CO2 with C2, if the

intermittent content is not too high. The n-C4 can always be grouped with i-C4 and also n-

C5 with i-C5. Thereafter the grouping should be made by "trial and error" and step by step

followed by regression. That means one component grouped with another component or

group, and if the accuracy is deteriorated considerably, the component should be grouped

with other component or should not be grouped at all. After every step of grouping

matching with regression is suggested [14, 27].

The second task is to determine the properties of newly grouped pseudo components.

Mixing rules are used for this purpose. The most simple is Kay's mixing rule [28], which is

given by equation 4.9, it is basically a mole-fraction average. The molar mass of the

components should always be calculated by this rule.

Ii

i

Ii

ii

Iz

z

(4.9)

where θ=any property and I is the index for pseudo components.

The specific gravity of the pseudo components should always be determined with

equation 4.10 that assumes ideal solution mixing. The generalized mixing rule for BIP's is

given by equation 4.11.

Ii

iii

Ii

ii

IMz

Mz

(4.10)

Ii Jj

ijjiIJ kzzk (4.11)

The critical properties can also be calculated with Kay's mixing rule. Some authors

suggest weight-fraction average [29], whereas others suggest the mix of weight- and

molar-fraction average [30]. Lee-Kesler proposed different mixing rules for every

property, that needed by EOS or viscosity calculation [31] and it has many advantages over

the simple mixing rules. Based on personal experience[25] and the recommendations of

some authors[14] the method published Coats [32] gives the best solution for the problem.

The approach is simple and accurate; it tries to eliminate the error caused by pseudoization.

The method forces the pseudoized fluid characterization to reproduce the volumetric

19

behaviour of the original fluid characterization in undersaturated condition, this is

succeeded by the determination of ΩaI and ΩbI with equation 4.12 and 4.13. For the

calculation of other critical properties and accentric factor any method can be used.

IcIcI

Ii

i

Ii Ij

ijjiji

aIpTR

zkaazz

22

2

1

(4.12)

IcIcI

Ii

i

Ii

ii

bIpTR

zbz

(4.13)

Coats' method and Kay's mixing rule were used to determine the properties of the

pseudo component. The number of components was reduced from 15-16 to 7 at each

samples, the further decrease of components seriously deteriorated the accuracy. The

accuracy of the pseudoized fluid characterization of Sample NC can be seen in Figure 4.8.

The properties of the pseudo-components can be found in Appendix D (for Sample NC).

Figure 4.8-CCE - Liquid Dropout - Comparison of the Original and Pseudoized Fluid

Characterization for Sample NC

4.2. Modified Black-Oil Tables

The creation of a modified black-oil table requires a matched EOS fluid

characterization. Thereafter the table is made by the simulation of a depletion experiment.

The kind of depletion experiment depends on the type of the fluid and depletion process

desired to simulate. Firstly, the general process of creation and then the differences for

20

each reservoir fluid type will be detailed. The check of tables are also recommended [33],

because a black-oil table may contain inconsistencies that cause non-physical behaviour in

reservoir simulation.

4.2.1. Methods for Black-Oil Table Creation

The biggest advantage of black-oil tables is the low calculation time, whereas their

accuracy is satisfying. Since that they are still the topic of research nowadays. The earliest

methods used for creating black-oil tables did not take vaporized oil-gas ratio into

consideration. Therefore their predictions were erroneous for volatile oils and gas

condensates. They are not recommended for this reason.

The first breakthrough was the method published by Whitson and Torp [11]. They

suggest the simulation of a depletion type experiment with EOS fluid characterization. At

every depletion stage, the equilibrium gas and oil are passed through a separator train to

determine the black-oil properties. Constant stock-tank gravities are considered during the

whole depletion, the reservoir densities can be calculated with equation 4.14 and 4.15. As

consequence the reservoir densities are wrong and don't satisfy the mass balance, which is

the biggest drawback of their method [32].

o

SgSTO

oB

R

0136.04.62 (4.14)

gd

SSTOg

gB

r

3500764.0 (4.15)

Coats claims that the Rs and Bo calculated by the Whitson-Torp method lack the

physical meaning [32]. He proposed a method similar to Whitson-Torp method, but Rs, Bo

and Bgd are rather determined by mass balance than flashing. The method provide correct

reservoir oil and gas density. Goldthorpe and Drohm suggest the correction of MBO

properties with surface densities[34]. As a result of this, it also yields correct reservoir

densities and satisfies the mass balance.

Recently Whitson et all published a new approach for the problem [33]. The saturated

fluid is passed through a separator train to get surface gravities, then the Rs and rs are

determined with the desired simulation experiment. Thereafter an EOS fluid

characterization is developed with two components: surface oil and gas. It is used to

calculate reservoir fluid densities. Finally equation 4.14 and 4.15 are rearranged to provide

Bo and Bgd.

21

Most of the mentioned methods are not implemented in commercial PVT software's, for

this reason the method published by Whitson and Torp will be detailed and applied to

create the black-oil tables.

4.2.2. Whitson-Torp Method

The method was already introduced briefly. The schematic of the method can be seen in

Figure 4.9. The applied separator train must be identical with the one used at the field. The

saturated Rs, rs, Bo, Bg, ηo and ηg are determined by this approach.

Saturation Pressure

Stage 1 Stage 2 Stage 3

Figure 4.9-Schematic of Whitson-Torp Method

It can happen that the pressure increases in the reservoir because of water injection for

example. In this case the saturated fluid becomes undersaturated due to pressure increase,

so variable saturation pressure model is needed. Therefore Rs becomes the primary

independent variable. For oils Rs vs pressure relationship determines that fluid is saturated

or not at specified Rs and pressure. Figure 4.10 depicts schematically the Bo vs pressure

relationship calculated for oil phase. At point A the oil is saturated, as the pressure

decreases to point B the oil remains saturated and its Rs will decrease. As the pressure

starts to increase due to water injection, the oil becomes undersaturated and its FVF will

decrease on B-C path to point B and while its Rs stays unchanged. If the pressure decreases

again, first the oil FVF will increase to Point B, the oil will be saturated again and while its

Rs remains unchanged. If the pressure decreases further, the oil FVF will decrease to point

D and its Rs will also decrease.

22

Pb1=originalPb2Pb3

Bo

Pressure

A

BCD

Rs1

Rs2

Rs3

Figure 4.10-Oil FVF vs Pressure

Figure 4.11 plots schematically the other two oil properties in the function of pressure.

Pressure

RS

Pressure

Vis

cosi

ty

Rs1

Rs2

Rs3

Figure 4.11-Oil Properties vs Pressure

The gas properties depicted in Figure 4.12. The problem for gas phase is similar, but the

function is not single-valued between dewpoint pressure and vaporised oil-gas ratio. This

means that vaporised-gas oil ratio does not identify the condition of the gas phase

certainly. Therefore pressure is the primary independent variable and the properties plotted

in the function of vaporised gas oil ratio.

23

rs

PD

EW

Bgd

Vis

cosi

ty

rs rs

p1

p2

p3

p4

p1

p2

p3

Figure 4.12-Gas Properties vs vaporized oil-gas ratio

Different depletion experiment(s) is/are required for every fluid type to create accurate

an black-oil table, therefore in the following subchapter every fluid type will be detailed

with respect to the suggested depletion experiment .

The black-oil table created for Sample GC (CVD) can be found in Appendix E.

4.2.3. Recommendation for Different Fluid Types

Undersaturated Oil Reservoirs

Usually two depletion-type experiments are performed on oil samples: constant

composition expansion (CCE) and differential liberation expansion (DLE). CCE is a flash

experiment, meanwhile DLE is a differential one, which mean the overall composition in

the PVT cell is changing during the experiment. Both methods can be used to create PVT

tables for undersaturated oil reservoirs. Whitson et al. suggest the CCE experiment for this

purpose [35]. In this thesis the tables were created by simulating a CCE experiment.

Gas Condensates

Also two depletion-type experiments can be performed on gas condensate samples:

CCE and constant volume depletion (CVD). CVD is a differential experiment, performed

24

on gas samples. Whitson et al. recommend the use of CCE for gas condensates [35], in this

thesis the two possible way of creation of black-oil tables will be compared.

Saturated Oil Reservoir

In Saturated oil reservoirs there are two phases initially at reservoir: gas cap and oil

body. The general recovery strategy for these reservoirs that first the oil body is depleted

with or without pressure maintenance, then the gas cap is depleted. Whitson et al. suggest

two different experiments for the two phases as it can be seen in Figure 4.13 [35]. The

properties of reservoir gas are determined with CVD experiment, while the properties of

the reservoir oil are determined with DLE. This recommended method was used to create

black-oil tables for Sample SO (Saturated Oil Reservoir Sample).

Gas

Oil

Water

Reservoir Gas

Reservoir Oil

Bubblepoint

Dewpoint

P1=Saturation Pressure P2 P3

Figure 4.13-Schematic of Black-Oil Table creation for Saturated Oil Reservoirs

4.2.4. Check of Tables

Erroneous PVT tables can even be created with consistent EOS fluid characterization or

measurements. The two most significant properties that can be wrong are fluid densities

and compressibility's. Both calculated from other properties and even if those properties

25

are adequate, the calculated properties can be inaccurate. The source of the error can be

different and sometimes cannot be perfectly eliminated.

The error in density originates from the assumption that the specific gravity of stock-

tank oil and gas are constant during the depletion. Figure 4.14 illustrates the problem in

case of Sample VO. The error varies with the pressure, for reservoir gas the maximum

error is 4.5% at bubblepoint, for reservoir oil the maximum error is 2% at low pressure.

Whitson suggests the adjustment of surface densities to gain accurate reservoir

densities[35]. With the application of this method the maximum error in reservoir densities

is reduced below 1%. If the error is still unacceptable in a particular case, then other PVT

method should be chosen.

Figure 4.14-Density of Reservoir Oil and Gas Calculated with EOS and BO Table

The compressibility's (apparent) can be determined with the following formulas [33]:

dp

dR

Rr

BrB

dp

dB

Bc s

ss

osgdo

o

o1

1 (4.16)

dp

dr

Rr

BRB

dp

dB

Bc s

ss

gdsogd

gd

g1

1 (4.17)

Figure 4.15 depicts the calculated compressibility values for Sample VO. The basic black-

oil properties were calculated at every 25 bar from 450 to 50 bars, plus at bubblepoint.

Negative oil compressibility can occur near the bubblepoint, this can be avoided by

including additional data close to saturation pressure. In this case the saturation pressure is

379 bars and the closest point at 375 bars, which is quite close; therefore there was no need

for additional pressure point. The discontinuities are caused by the change in derivates at

26

pressure nodes. As the difference between derivates increases the magnitude of

discontinuity also increases. The discontinuity influences the performance and stability of

simulation. The discontinuity can be reduced by including more pressure nodes in the

saturated region.

Figure 4.15-Compressibility of Reservoir Gas and Oil Calculated with BO Tables

After the check is performed on the created black-oil tables they are ready to be used in

simulation. Some other consistency checks are also recommended, but those are trivial or

important only for tables generated to simulate gas injection [33].

4.3. Summary for PVT Model Development

The two most important PVT calculation models were reviewed in this chapter. Both

models rely on PVT measurements preformed on reservoir fluid samples, this implies the

importance of the quality check of sampling and measurements. The methods used for the

creation of PVT models have to be chosen carefully in order to receive accurate and

consistent model. The consistency of each PVT model has to be checked as well, otherwise

it can lead to unexpected errors in simulation, material balance or pipe flow calculations.

Different tasks in reservoir engineering desire different PVT calculation methods.

Simulation of gas injection requires sophisticated and accurate PVT model. History

matching can be tiring and time consuming, where fast calculation models are favourable.

Memory requirements can also be a limiting factor in the simulation of huge fields.

Therefore there is no superior calculation method. For every particular case the appropriate

PVT model has to be chosen based on comparison.

27

5. Description of the Numerical Reservoir Model

A static reservoir model is artificially created for the comparison. The reservoir can be

found in an anticline structure, the grid generated for the reservoir can be seen in Figure

5.1. The reservoir rock is siliciclastic with single porosity and permeability. The top of the

reservoir is at -2800m, while the water-oil/gas contact is at -2900m. The reservoir is 2000

m long and 1500 m wide. Five wells were created for the depletion of the reservoir. Further

details will be described in the following subchapters.

Figure 5.1-Grid Constructed for the Problem

5.1. Grid and Rock Properties

Block centred grid is used for the problem; it consists of 14260 cells with 50*50*5

dimension (the height of the cells is slightly varying). Grid refinement was applied around

the wells. The reservoir model consists of two different layers. Two sealing faults are also

defined in the model; their position can be seen in Figure 5.2.

The reservoir rock is consolidated sandstone, rock properties defined as the most

common values specific for this rock type (at the boundary of medium and good reservoir

rock.). The porosity is 21% in the top layer and 19% in the bottom layer. The net-gross

ratio varies from 0.75 to 0.85. Horizontal permeability changes between 120 and 80 mD,

while vertical permeability changes between 50 and 30 mD. Hall correlation was used to

28

take compaction into consideration [36]. The permeability curve will be described in the

next subchapter. The capillary pressure was neglected in the absence of measurements.

The cells found under -2900m are saturated with water. In some cases, a Carter-Tracy

aquifer model [37] is assigned to the reservoir with the following parameters : 3000

external radius, 40 md permeability, 0.2 porosity and 50 m thickness.

Figure 5.2-Location of Well and Faults

5.2. Relative Permeability Curves

The Corey formula was used to describe the permeability curves [38]. The characteristic

points of the curves were taken from the literature [39]. The connate water saturation is

30%, the residual gas saturation is 20% and the residual oil saturation is 25%, critical gas

saturation is 5%. The end-point of oil and gas is 0.7, while the end-point of water is 0.25.

29

The Corey exponent of the oil phase is 3, it is 6 for gas and 4 for water. Figure 5.3 shows

the oil-water relative permeability curves.

Figure 5.3-Oil-Water Relative Permeability Curves

5.3. Wells

As it mentioned earlier five wells have been assigned to the reservoir. The location of

the wells can be seen in Figure 5.2. The well completion consist of a 5" casing and a 2 7/8

tubing, the perforation intervals are different in case of different reservoir fluid types. The

modified Hagerdon-Brown method [40] was used to calculate the vertical-lift performance

curves, because it is considered to be accurate over a wide range of liquid rate and gas-oil

ratio [41].

5.4. Development Strategy

The development strategy is different in all cases. The object of this thesis is to compare

the PVT models and not to find the development strategy providing the highest recovery,

therefore in many cases the aim is to reach the highest drop in the average reservoir

pressure.

30

6. Volatile Oil

This chapter deals with the comparison of different fluid models developed to simulate

the phase behaviour of a volatile oil sample. The volatile oil sample was introduced in

chapter 3.1. The fluid sample has a high degree of phase transition due to pressure drop,

which makes it a good choice for comparison. The following two subchapters describe the

different fluid models and development strategies used for the comparison. Thereafter the

results will be detailed and discussed.

6.1. Fluid Models

The process of PVT model development has been already described in chapter 4. This

subchapter will briefly introduce the four PVT models developed for Sample VO with

respect to the most important differences.

First an EOS fluid characterization was made, which consists of 10 normal components

and 6 pseudo components. Thereafter this model was used to create the other three models.

The EOS model with 16 components resulted unacceptable computation time in simulation

runs, therefore it was not used in the comparison.

With the pseudoization of the previous fluid characterization an EOS model with 8

components was created (Comp). This provided almost the same accuracy, but required

much less calculation time.

Two black-oil tables were created by using the 16 component EOS. The first uses the

traditional gas FVF (BO), while the second uses the modified black-oil formulation,

therefore it contains dry-gas FVF instead of the traditional (MBO). The formulation of the

second table is suggested in the literature, but many programs like PVTp create PVT tables

using traditional gas FVF, which makes it necessary to include them in the comparison.

Vaporised oil-gas ratio is included in both tables.

6.2. Development Strategies

Two cases were defined, one without aquifer (Depl) and another with aquifer (Aquifer).

The aquifer makes a great difference between the two cases, so two different development

strategies were worked out for them. The manifold pressure is 20 bars in both cases and the

applied separator train is also (first stage: 20 bars 20 °C, second stage : standard condition).

In the first case, when no aquifer was added , the target liquid rate was 100 m3/day/well

and the gas production limit was 1 106 m

3/day. The production period was 10 years. Full

implicit solution scheme was used for both cases with maximum time step of 15 days.

31

In the second case Carter-Tracey aquifer model was added to the reservoir. The target

liquid rate was 150 m3/day/well; the limitation for water production was 450 m3/day and

0.97 WOR. The production period was 25 years. Adaptive implicit solution scheme was

applied in both cases with maximum time step of 15 days.

6.3. Results

The OOIP is 6.37 106 sm

3 and the OGIP is 2.354 10

9 sm

3. The results of two cases will

be exhibited separately.

6.3.1. Case 1 (Depletion)

The computation time of the black-oil simulation runs were 102 and 105 seconds (two

different black-oil tables), while 1208 seconds were required for compositional simulation.

The most important production factors can be seen in Figure 6.1, oil production rate

represented by green, gas production by red and reservoir pressure by gray. Traditional

black-oil table is represented by dotted line, modified black-oil table by solid line and EOS

fluid model by stripped line. Significant difference can be noticed between the traditional

black-oil model and the other two fluid models, the possible reason will be discussed in

chapter 6.4.

Figure 6.1-Simulation Results of Sample VO - Case 1

Another useful diagram that can help to understand the difference can be seen in Figure

6.2, where oil and gas in place are plotted against production time. The line styles are the

32

same, but orange represents gas in place, green - oil in place, pink - liquid oil in place and

pale blue - free gas in place. The difference can be perceived only in free gas in place and

liquid oil in place.

Figure 6.2- Oil and Gas in Place During Depletion (Sample VO - Case 1)

6.3.2. Case 2 (Aquifer)

The traditional black-oil table were not used in this development strategy because of its

failure in the previous case. The black-oil simulation required 307 second computation

time, while 768 seconds were needed for the compositional simulation. Figure 6.3 shows

the simulation results, the legend is the same as it was in the previous case, but this time

the water production is plotted instead of gas production with blue colour (pressure was

above bubblepoint pressure during the whole production period, so there was no change in

gas production). Well 3 and 5 are shut down at the end of the production period because of

exceeding the WOR limit. The only significant difference can be noticed in the shut down

date of these wells.

33

Figure 6.3-Simulation Results of Sample VO - Case 2

6.4. Discussion and Conclusion

The results provided by compositional simulation are considered to be the perfect

solution for the problem, therefore the other models are compared to that to determine their

accuracy.

In case 1, significant difference could be noticed between traditional black-oil table and

the other two models. As it can be seen there were no difference between oil and gas

production, but the difference in predicted pressure exceeded 20 bars. Oil and gas in place

did, but the liquid oil and free gas did not correspond to the results of the other two models.

These observations imply that the error originates in the material balance. The reservoir

simulator uses mass balance instead of volume balance [42], which is not widely known

among practicing engineers. The traditional definition of gas FVF does not take vaporised

oil into consideration, therefore it predicts lower gas FVF, that cause mass "gain" in CCE

experiment. As a result in reservoir simulation higher pressure drop is required to satisfy

the mass balance below the bubblepoint. The modified black-oil table performed well both

in accuracy and calculation time.

In case 2, basically there were no difference regarding pressure and cumulative oil

production.

The modified black-oil table proved its applicability in reservoir simulation in case of

volatile oil, on the other hand, the usage of traditional black-oil tables should be avoided.

34

7. Gas Condensate

After the volatile oil fluid models were compared the comparison of gas condensate

models is coming. It is a common belief among engineers that the gas condensate reservoir

cannot be treated with black-oil PVT models, which makes this comparison interesting.

The following subchapters will summarize the fluid models and development strategies

used for the comparison and finally the simulation results will be detailed and discussed.

7.1. Fluid Models

Five different fluid models were developed for the problem, two EOS characterization

and three differently created black-oil tables.

Firstly a detailed EOS fluid characterization is developed from the measurements, that

consists of 15 components. This model was used to create the other four models. 15

components lead to high computation cost, accordingly this model was not included in the

comparison.

Subsequently a 7 component EOS model (Comp) is created by the lumping of

components. This model provided both decent accuracy and calculation time that made it

adequate for the simulation runs.

As it was mentioned, three different black-oil tables were created. The first was

generated by simulating a CCE (MBO-CCE), while the second was by simulating CVD

experiment (MBO-CVD). Both tables use dry-gas FVF instead of its traditional definition.

The third table was created by simulating CCE experiment (BO-CCE), but it contains

traditionally defined gas FVF (this table was automatically created by PVTp). All of the

tables include vaporised oil-gas ratio.


Two cases were created; the first model doesn't have aquifer model assigned (Depl.),

whereas the second include a Carter-Tracy aquifer model (Aquifer). The second model

requires the treatment of water production, that makes working out a different development

plan necessary for it. The initial reservoir pressure is 370 bars (the dewpoint pressure is

338.3 bars) and the reservoir temperature is 191°C in both cases. The manifold pressure is

the same, 20 bars. The separator train used is also the same, the condition of the first stage

is 20 bars and 20 °C, the second stage is atmospheric.

When no aquifer is assigned to the reservoir model, the target rate was 100 103sm

3/day/.

The lack of water production makes further constraints unnecessary.

35

When aquifer was linked to the reservoir the target gas rate was the same as it was in

the first case. 200 m3/day was set as the water production limit of the field. If the water cut

of an individual well exceeded 0.1, then the worst perforation section was shut off.

Full implicit solution scheme was used for all black-oil simulation runs, whereas

adaptive implicit method was sufficient for compositional runs, since saturation changes

were not so high, the oil phase was not mobile, and big difference in densities makes water

conning less likely to happen [42].

7.3. Results

The resources are the following : OGIP is 1.867 109 sm

3 and OOIP is 1.89 10

6 sm

3

(vaporised). The next subchapters will introduce the results of simulation runs.


There was a significant difference in the computation cost, 243 seconds were required

for the compositional simulation, and meanwhile 76 seconds were enough for the black-oil

simulation runs. Figure 7.1 shows the results including: pressure (gray), gas production

(red) and oil production (oil).(EOS - solid line, MBO-CCE - stippled, MBO-CVD - dotted

and BO - stipple-dot). The black-oil table using traditional gas FVF differs from the others,

the rest shows good correspondence.

Figure 7.1-Simulation Results of Sample GC - Case 1

36

The end of depletion period is zoomed in Figure 7.2, which makes the detection of the

difference between the well corresponding fluid models easier. The black-oil table created

by simulating CVD experiment provides slightly more accurate results.

Figure 7.2-Simulation Results for Sample GC - Case 1 (Zoomed)

The changing in oil and gas in place is depicted in Figure 7.3, gas in place is marked

with orange, oil in place is represented by pale blue. A great difference can be noticed in

the values between black-oil table with traditional gas FVF(BO) and the others (MBO).

Figure 7.3-Gas and Oil in Place During the Depletion

37


Due to some initialization errors; Eclipse300 had to be also used for black-oil

simulations, therefore the difference in calculation time was not as big as it was in the first

case, 268 seconds were required for compositional and 197 seconds for black-oil

simulation runs. The black-oil table using traditional gas FVF has been left out, because it

gave disastrous results in the first case including a huge error in OGIP and OOIP. Figure

2.1 shows the result for case 2 with the same notation as before. The results are nearly the

same for all the three fluid models.

Figure 7.4-Simulation Results of Sample GC - Case 2


The assumption in the definition of traditional gas FVF makes it incapable to simulate

gas condensate reservoirs. On the other hand black-oil tables using dry-gas FVF performed

well both in accuracy and calculation time. However, the black-oil table created by

simulating CVD experiment provided slightly better accuracy, black-oil table created by

simulating CCE experiment also give satisfactory results. The difference occurs at low

pressure and originates from the re-vaporisation of oil, that is higher in case of CVD. This

could be expected, because CVD experiment approximate more better depletion processes

where oil phase is immobile. As a consequence modified black-oil tables created by

simulating CVD experiment can be used to substitute EOS fluid model in the simulation of

gas condensate reservoirs, where gas injection is not applied.

38

8. Near Critical Gas Condensate

Modelling the phase behaviour of a near critical gas condensate is a challenging task.

The current PVT calculation methods including EOS are not considered to be capable of

describing near critical fluids theoretically, although no one have ever published a better

method that can be applied in practice. Therefore the engineers are forced to treat them

with the currently available methods. Despite these theoretical problems, some recently

published papers show off promising results in the topic. Many recently found reservoirs in

great depths can be classified into this category, so the problem is getting more important.

The following subchapters will introduce the fluid models and development strategies used

in the simulation. After that the results will be detailed and discussed.

8.1. Fluid Models

Four fluid models were developed for the problem, this time the black-oil table using

traditional gas FVF has been left out, because it is proved in the case of previous problems

that it is both theoretically and practically unable to treat the gas phase correctly. Therefore

the four models include two EOS models and two black-oil tables.

In the case of previous problems, a detailed EOS fluid characterization is created first

that having 15 components (EOS15). This fluid model was used to create other models.

Although the detailed EOS model was not included in the comparison in other cases, this

time it is considered to be necessary because of the complex phase behaviour.

The second step was the creation of the pseudoized EOS fluid characterization, the

number of components was reduced from 15 to 7 to save computation time and keep

accuracy accordingly (EOS7).

Two different black-oil tables were created by simulating CCE (MBO-CCE) and CVD

(MBO-CVD) experiments. Both include vaporised oil-gas ration and use dry gas FVF

instead of the traditional definition.


For this problem two different development strategies were created as well. The first

model represents a reservoir without aquifer model (Depl.), the second model has a Carter-

Tracy aquifer model (Aquifer). The initial reservoir pressure was 500 bars (where the

dewpoint pressure was 467 bars) and the initial reservoir temperature was 91 °C. The two

different development strategies were developed for the two cases which differ in the

treatment of water production. The minimal manifold pressure was 20 bars in both cases,

39

the applied separator train is also the same, the condition of the first stage was 20 °C and

20 bars, the second stage is atmospheric. The production time was 10 years.

In the first case where no aquifer model was assigned, the target gas rate was 500 103

sm3/day/well. The maximum allowed water production was 300 m

3/day.

In the second case (Aquifer), he target gas rate was the same as it was in the first case.

The maximum water production was set to 200 m3/day and if it was exceeded the worst

interval of perforation was shut off.

Significant phase transitions that cause sharp saturation changes were expected.

Accordingly, full implicit solution scheme was applied for all cases and fluid models [42].

8.3. Results

The resources are the following : OGIP is 2.355 109 sm

3 and the OOIP is 3.72 10

6 sm

3.

The next subchapters will show the most important plots depicting the results.


Similarly to other fluid models there was a great difference between the computation

costs. The 15-component-EOS model required 3501 seconds for the simulation, 7-

component-EOS model needed 976 second, and meanwhile 172 seconds were enough for

the black-oil table model. That means the simulation using black-oil tables was 20 times

faster than the one using detailed EOS fluid characterization, and it was even 5.5 times

faster than the lumped EOS model.

Figure 8.2 shows the results of the simulation including : red - gas rate, dark green - oil

rate, blue - water rate, gray - pressure, light green - producing - GOR (solid line - EOS15,

stippled dot - EOS7, stippled MBO-CCE, dotted MBO-CVD). Surprisingly the 7-

component EOS model mostly differs from the 15-component EOS model. The

performance of two black-oil tables is nearly the same, the highest difference in pressure

does not exceed 5 bars, and there is only a little difference in water production.

The variation of free gas and liquid oil can help to investigate the problem (see Figure

8.2, free gas - light blue, liquid oil - pink). Figure 8.2 implies that EOS7 fluid model

incorrectly describes the phase transition due to pressure decrease, as a result it predicts

higher oil saturation that yields lower gas permeability, little higher water production

(because the target rate is gas, and the ratio of their permeability is deteriorated by higher

oil dropout) and the oil phase becomes mobile sooner.

40

Figure 8.1-Simulation Results for Sample NC - Case 1

Figure 8.2-Free Gas and Liquid Oil in Place (Sample NC - Case 1)


In this case three phases were mobile at the same time during the depletion, as a result

the difference increased in the calculation times. The black-oil simulation runs required

147-150 seconds, while 3500 seconds were required for the simulation that used the 7-

41

component-EOS fluid model. The 15-component-EOS fluid model resulted in hours of

calculation time and around at the beginning of the 8th year convergence errors were

occurred, so only few days were simulated in an hour, therefore the simulation was stopped

after 8 hours of total.

Figure 8.3 compares the results of simulations using detailed EOS fluid model and

black-oil table, created by simulating CVD experiment. The two black-oil models provided

almost identical results, therefore the other one has been left out, the comparison of the

detailed and pseudoized EOS fluid model can be seen in Figure 8.4 (the notation is the

same that it was in the case 1). The black oil-models show decent accuracy, the difference

in pressure does not exceed 2.5 bars and even the water production is correct.

Figure 8.3-Simulation results of Sample NC - case 2 (MBO-CVD vs. EOS15)

The accuracy of the pseudoized EOS fluid model is unsatisfactory. As in the first case

when the pressure decreased below the dewpoint pressure, the inaccurate phase behaviour

prediction yielded wrong pressure and production predictions.

42

Figure 8.4-Simulation Results of Sample NC - Case 2 (EOS15 vs EOS7)


The results have disproved the common belief that rich/near critical gas condensates

cannot be simulated with black-oil fluid model. Near critical condition increases the

number of iteration required for the flash calculation, which also increases the computation

cost of simulation. On the other hand, the complex phase behaviour has a slight effect on

the computation time of black-oil fluid model. As a result the difference between the

computation cost of the two different fluid models increases with the complexity of the

phase behaviour.

The black oil tables provided appropriate accuracy in simulations. The two differently

created black-oil tables performed almost identical results. The pseudoized EOS fluid

model performed poorly, which is surprising. There were also some problems with the

detailed EOS model, when the pressure started to increase and exceeded the dewpoint it

caused serious convergence error, which affected both calculation time and accuracy.

As a consequence properly created black-oil tables can provide the desired accuracy

even if the reservoir fluid is a near-critical gas condensate. Meanwhile its computation time

is much lower, which is an important factor when someone would like to choose the

adequate fluid model for history matching. Therefore the idea of the application of black-

oil tables for near-critical fluids should not be rejected, but few simulation runs are

recommended to compare the performance of different fluid models before making the

final decision.

43

9. Saturated Oil Reservoir

Saturated oil reservoirs are well known as oil reservoirs with gas cap. They are

commonly found in small and average depth, Due to this most of these reservoirs were

discovered decades ago, therefore the industry has a lot of experience about them. These

reservoirs are mostly depleted by water flooding that means slight or no pressure change

during the life of the reservoir. As a consequence it is a commonly approved fact that these

reservoirs can be easily and accurately treated with black-oil tables. But, as it was pointed

out in chapter 4.2 the density prediction of these tables is not always satisfactory, which

can be a problem, hence gravity plays a crucial role in the recovery of these reservoirs.

Therefore the way of the black-oil table creation is important.

9.1. Fluid Models

Three different fluid models were created for this problem. The two EOS models are

identical, those which were created for the simulation of the volatile oil reservoir (Comp).

The third fluid model is a modified black-oil table (MBO).

The detailed EOS fluid characterization was used to create the black-oil table. As for the

gas cap, a CVD experiment was performed to determine the black-oil properties of the gas

phase, while a DLE experiment was conducted on the oil column to determine the black-

oil properties of the oil-phase.


Two different cases were assumed, the first with no aquifer model assigned (Depl.),

while in the second case a Carter-Tracy aquifer model was attached to the reservoir model

(Aquifer). The reservoir pressure was 325 bars in both cases and the reservoir temperature

was 118 °C. The manifold pressure was 20 bars in both cases. The applied separator train

was the following : first stage 20 bars and 20°C, second stage is atmospheric.

When no aquifer is assumed, the target liquid rate was 60 m3/day/well, the production

time was 5 years. The minimum bottomhole pressure was set to 100 bars.

In the second case, when aquifer is added to the reservoir model, the target liquid rate

was the same; meanwhile the maximum water production was set to 200 m3/day. The

production time was assumed to be 15 years.

44

9.3. Results

The resources are the following : OOIP is 4.124 106 sm

3 and OGIP is 1.702 10

9 sm

3.

The next subchapters will introduce the results of simulation runs.


The calculation time required for the compositional simulation run was 366 second,

while only 133 seconds were needed for the black-oil model. Figure 9.1 shows the

simulation results, solid line represents the compositional fluid model, dotted line

represents the black-oil fluid model, and colours assigned below refer to different

properties which are identical to previous figures. The difference in pressure reaches 5 bars

at the end of the production period, meanwhile the difference in production rates are on a

small scale except gas production.

Figure 9.1-Simulation Results for Sample VO - Case 1


In the second case, the difference in calculation time was more significant, while the

compositional simulation run required 707 seconds, the black-oil model needed only 144.

Figure 9.2 shows the simulation results (same notation as in the previous subchapter). The

only significant difference occurs in the pressure prediction. In case of the black-oil fluid

45

model the pressure started to increase after the third year, the highest difference exceeded 2

bars. The production rates shows decent match. No significant difference can be detected

in the solution gas, vaporised oil, free gas and liquid oil in place that implies the error may

comes from another source and not from PVT properties.

Figure 9.2-Simulation Results for Sample SO - Case 2


The performance of the modified black-oil table was satisfactory, although the

discrepancy between black-oil and EOS model was the highest in the case of this fluid

type. Perhaps, the way how the black-oil table was created is not the best, because no PVT

experiment adequately approximates the process takes place during the depletion of a

saturated oil reservoir. The compositional simulation runs required higher computation

cost in both cases as expected. As a consequence, black-oil tables can be used for the

simulation of saturated oil reservoirs in order to save computation time and without losing

accuracy.

46

10. Summary and Conclusion

The objective of this thesis was to compare the performance of black-oil and

compositional fluid models in reservoir simulation with respect to accuracy and

computation time. First, the two different fluid description methods were briefly outlined,

then four different fluid samples were introduced and used for the comparison. Thereafter

the developments of PVT models were described in details.

The same static reservoir model was used in every case, only the fluid model and the

development strategy were changed. Relative permeability curves were originated from

literature average values. In sandstone reservoirs the capillary pressure hardly affect the

result, but greatly reduce the calculation speed, therefore it is neglected.

In the subsequent chapters, the two different fluid description methods were compared

on the four different fluid samples. For each comparison, two different cases were created,

one without aquifer to represent simple depletion and one with aquifer to represent

pressure maintenance. The simulation results were introduced and discussed at the end of

each chapter.

The black-oil tables using traditional gas FVF lead to erroneous simulation results, but

the modified black-oil tables provided promising results which proves the crucial role of

the proper creation of black-oil tables. The computation cost of black-oil simulation runs

was much lower than compositional ones' in every case. On the other hand, the accuracy of

black-oil model was nearly the same; it is proved to be adequate even in the case of near-

critical gas condensate. Therefore the automatic rejection of black-oil tables in case of gas

condensates and volatile oils is proved to be a wrong practice.

As a consequence, modified black-oil tables are capable for the simulation of reservoirs

with complex phase behaviour and exploited by simple recovery method (no gas injection

or temperature change). The proper creation of the fluid models is also proved to be

important. Some assumptions can be fatal, black-oil tables neglecting vaporised oil in the

calculation of gas FVF have yielded catastrophic simulation results, therefore their use

should be avoided. At the beginning of every reservoir study require simulation, several

sensitivity runs should be done to select the fluid model that is the most adequate for the

objective of the study. Among the fluid models, that model should be chosen which is the

most simple and requires the least calculation time and provides the necessary accuracy.

47

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50

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51

Acknowledgement

Foremost, I would like to express my sincere gratitude to my industrial advisor, István

Papp for his continuous theoretical and practical help. Beside my industrial advisor, I

would also like to thank my University advisor, Dr. Tibor Bódi for his the priceless

recommendations. My sincere thanks also got to Károly Bali who helped me in spelling

and grammar check.

52

Appendix A

Table 1-Composition of the Samples

Component

Composition [mol %]

Sample

VO

Sample

GC

Sample

NC

Sample SO

Gas

Cap

Oil

Column

N2 0.83 0.89 0.57 1.20 0.72

CO2 0.66 9.68 1.44 0.72 0.64

C1 62.18 66.92 68.78 79.47 56.78

C2 6.43 7.37 6.71 6.24 6.49

C3 4.65 2.78 4.03 3.89 4.89

i-C4 1.05 0.82 0.94 0.79 1.12

n-C4 2.17 0.98 1.79 1.56 2.37

i-C5 0.99 0.52 0.84 0.64 1.10

n-C5 1.13 0.46 0.80 0.70 1.26

C6 1.47 1.20 0.99 0.80 1.68

C7 2.41 1.35 1.53

3.99 22.95 C8 2.59 1.19 1.86

C9 1.72 1.08 1.62

C10+ 11.71 4.77 8.10

Sum 100.00 100.00 100.00 100.00 100.00

Molar Mass [g/mol] 242.5 150.7 227.5

C10+ Density [g/cm3] 0.8744 0.7766 0.8668

53

Appendix B

Table 2-DLE measurement (Sample VO)

Pressure Oil FVF Solution

GOR

Liquid

Density

psia bbl/STB scf/STB g/cc

10015 2.469 0.582

9015 2.504 0.574

Pres=8846 2.51 0.573

8015 2.548 0.564

7015 2.602 0.552

6015 2.678 0.537

5733 2.695 0.533

5557 2.714 0.53

Pb=5500 2.719 2933 0.529

5300 2.553 2591 0.538

4500 2.209 1929 0.569

3700 1.953 1415 0.6

2900 1.762 1062 0.631

2100 1.605 774 0.664

1300 1.463 521 0.7

500 1.325 290 0.74

14.7 1.095 0 0.783

Residual Oil Desnity on 60°F g/cc 0.857

°API 33.4

Table 3-Separaor Test (Sample VO)

Pressure Temperature Solution

GOR

Liquid

Density

Specific

Gravity

(gas)

Molar

Mass

(gas)

Oil FVF

psia °F Scf/STB g/cc - g/mol bbl/STBB

Pb=5500 244 2.247

1500 110 1632 0.726 0.662 19.16 1.313

14.7 60 607 0.828 0.943 27.3 1

Stock-Tank Oil

Molar Mass g/mol 171.88

Density g/cc 0.827

°API 39.3

54

Table 4-CVD Experiment (Sample GC)

Pressure Liquid dropout

Bg

Z

Bar % of system % of Vdew Wellstream Gas Two

Phase

Pres=338.3 0 0 0.004883 1.0255

1.0255

321.1 4.82 4.99 0.005141 1.0025 1.1136 1.008

301.1 9.05 9.46 0.005271 0.9853 1.0656 0.991

281.1 11.55 12.13 0.005528 0.9648 1.0321 0.9755

251.3 13.05 14.23 0.006055 0.9447 1.0019 0.9555

220.7 13.57 15.08 0.006809 0.9329 0.9785 0.9383

190.5 13.39 15.16 0.007841 0.9274 0.9656 0.9375

Table 5-Properties of the Produced Fluid(CVD)(Sample GC)

Pressure GCR Produced fluid [mol % Cum]

Bar m3/m

3 Wellstream Gas Condensate

Pr=338.3

321.1 1404.1 3.436 3.162 0.274

301.1 1519.2 7.897 7.287 0.61

281.1 1780 12.65 11.73 0.92

251.3 2126.6 20.279 18.923 1.356

220.7 2690.3 28.698 26.949 1.748

190.5 3252.9 37.44 35.345 2.094

Table 6-Properties of the Produced Fluid 2(CVD)(Sample GC)

Pressure Well-

stream Gas (atm sep.) Condensate (atm sep.)

bar Molar

Mass

Molar

M.

Density

[kg/m3]

Rel.Density Molar

M. MC10+ MC7+

Density

[kg/m3]

Pr=338.3

321.1 33.79 23.327 0.9867 0.8052 154.3 200.4 163.8 794.2

301.1 32.78 23.099 0.9771 0.7973 151.1 198.6 160 791.1

281.1 31.5 23.158 0.9796 0.7993 150.5 196.1 159.1 790.3

251.3 28.88 22.961 0.9712 0.7925 143.5 188.7 152 782.8

220.7 28.64 23.175 0.9803 0.7999 140 182.9 148.2 778.8

190.5 27.62 23.144 0.979 0.7988 136.5 177.4 143.3 774.5

55

Table 7-Composition of the Produced Fluid (CVD)(Sample GC)

Comp. Pressure [bar]

321.1 301.1 281.1 251.3 220.7 190.5

N2 1.82 1.21 1.18 1.15 1.12 1.14

CO2 10.54 10.27 10.55 10.12 10.99 10.88

C1 66.12 67.38 68.07 69.26 69.5 70.1

C2 7.58 7.75 7.76 7.85 7.79 7.92

C3 2.54 2.56 2.56 2.57 2.55 2.57

C4 1.98 1.86 1.79 1.77 1.76 1.73

C5 1.07 1.04 1.03 1.01 0.97 0.94

C6 1.27 1.23 1.24 1.22 1.21 1.2

C7 1.05 1.07 0.92 0.88 0.71 0.66

C8 0.94 1.02 0.83 0.79 0.67 0.61

C9 1.01 0.95 0.87 0.81 0.69 0.62

C10+ 4.08 3.66 3.2 2.57 2.04 1.63

Sum 100 100 100 100 100 100

Table 8-CVD Experiment (Sample NC)

Pressure Gas Phase Liquid

Dropout Recovery

Density Z Bg

bar kg/m3 - - % mol%

Pres=534 510 1.487 0.00356 0 0

Pdew=467 495 1.338 0.00367 0 2.9

425 419 1.147 0.00346 44.5 5.3

375 370 1.035 0.00353 49.2 9.3

325 317 0.952 0.00375 49.5 14.6

275 264 0.893 0.00416 48.3 20.6

225 202 0.874 0.00497 46.7 28.7

175 148.5 0.857 0.00627 44.7 39.8

125 99.5 0.871 0.00892 42.4 52

75 56 0.916 0.0156 39.8 65.3

56

Table 9-Properties of the Condensate (CVD) (Sample NC)

Pressure Bc (Bo) Rs Density Viscosity

bar m3/m

3 m

3/m

3 kg/m

3 mPa*s

425 1.76 251 635 0.22

375 1.7 229 645 0.23

325 1.63 204 657 0.24

270 1.56 177 671 0.26

220 1.48 149 688 0.29

170 1.39 119 708 0.33

120 1.3 86 731 0.4

70 1.2 50 758 0.52

Table 10-Properties of the Produced Condensate (CVD) (Sample NC)

Pressure GCR Density Molar

Mass

bar m3/m

3 kg/m

3 g/mol

Pres=534 586 820.7 157

Pdew=467 586 820.7 157

425 895 806.5 144.5

375 1260 792.5 133

325 1680 779.5 124

275 2270 767.5 116.5

225 3520 755 111

175 6130 745 107

125 11900 735 103.5

75 16600 726.5 101

57

Table 11-Composition of the Produced Fluid (Sample NC)

Comp. Pressure [bar]

467 425 375 325 275 225 175 125 75

CO2 1.44 1.49 1.52 1.54 1.55 1.57 1.61 1.66 1.7

N2 0.57 0.72 0.78 0.84 0.82 0.8 0.78 0.75 0.69

C1 68.78 73.48 75.97 77.85 79.51 81.13 82.63 83.5 83.4

C2 6.71 6.63 6.59 6.59 6.61 6.68 6.76 6.86 6.98

C3 4.03 3.45 3.36 3.34 3.37 3.39 3.4 3.42 3.48

IC4 0.94 0.73 0.68 0.66 0.65 0.64 0.62 0.62 0.66

NC4 1.79 1.41 1.25 1.18 1.13 1.08 1.05 1.04 1.14

IC5 0.84 0.63 0.54 0.5 0.48 0.44 0.4 0.37 0.39

NC5 0.8 0.62 0.54 0.5 0.48 0.43 0.37 0.34 0.34

C6 0.99 0.89 0.8 0.73 0.66 0.55 0.42 0.33 0.32

C7 1.53 1.34 1.15 1.02 0.86 0.69 0.48 0.33 0.32

C8 1.86 1.64 1.4 1.19 0.99 0.75 0.47 0.29 0.26

C9 1.62 1.41 1.18 0.98 0.79 0.55 0.34 0.19 0.16

C10 1.24 1.08 0.9 0.71 0.53 0.36 0.2 0.11 0.07

C11 0.8 0.71 0.56 0.42 0.31 0.2 0.11 0.05 0.03

C12 0.65 0.54 0.43 0.31 0.22 0.14 0.07 0.03 0.02

C13+ 5.41 3.23 2.35 1.64 1.04 0.6 0.29 0.11 0.04

MC13+ 268 247 229 220 212 208 205 203 202

58

Appendix C

Table 12-Inspection properties of C7+ Components (Sample NC)

Component z M γ Tb Kw

% g/mol - °R -

C6-7 2.52 86.4 0.7104 173.3 11.98

C8-10 4.57 112.2 0.7677 261.3 11.67

C11-14 2.95 161.1 0.8229 407.4 11.62

C15-21 2.41 233.4 0.8698 571.3 11.73

C22-29 1.04 336.7 0.9126 739.5 11.91

C30+ 0.61 516.1 0.9610 932.2 12.17

Table 13-Critical Properties of C7+ Components (Sample NC)

Component Tc pc ω vc Volume Shift BIP-C1

°C bar m3/(kg*mol)

C6-7 255.8 31.76 0.2715 0.4249 -0.0352 0.03295

C8-10 315.9 28.74 0.3229 0.5104 0.0214 0.04035

C11-14 402.8 23.05 0.4422 0.6968 0.0945 0.04747

C15-21 491.7 18.05 0.5985 0.9525 0.1640 0.05352

C22-29 577.8 14.38 0.7800 1.2459 0.2273 0.05904

C30+ 674.9 11.58 1.0053 1.5785 0.2951 0.06529

Table 14-Critical Properties of C7+ Components After Regression (Sample NC)

Component Tc pc ω vc Volume Shift BIP-C1

°C bar m3/(kg*mol)

C6-7 281.2 27.52 0.2715 0.4249 -0.0352 0.03688

C8-10 297.1 26.74 0.3229 0.5104 0.0214 0.04516

C11-14 373.0 21.59 0.4422 0.6968 0.0945 0.05312

C15-21 472.3 17.10 0.5985 0.9525 0.1640 0.0599

C22-29 574.7 15.43 0.7800 1.2459 0.2273 0.06607

C30+ 738.9 13.20 1.0053 1.5785 0.2951 0.07307

59

Appendix D

Table 15-The Properties of Grouped Components (Sample NC)

Comp. z Tc pc ω ΩA ΩB vc M

% °C bar - - - m3/kg*mol g/mol

PS1 69.35 -83.0 46.30 0.0112 0.43555 0.07344 0.0991 16.14

PS2 8.15 31.9 53.28 0.1237 0.45453 0.07933 0.1387 32.56

PS3 6.76 116.6 40.50 0.1694 0.46233 0.07843 0.2270 49.75

PS4 1.64 191.9 33.52 0.2387 0.45340 0.07779 0.3050 72.20

PS5 7.09 284.7 31.04 0.3047 0.46371 0.07760 0.4800 103.03

PS6 6.40 461.0 20.00 0.5560 0.48553 0.08044 0.8824 216.84

PS7 0.61 672.1 11.40 1.0053 0.52224 0.07309 1.5785 516.14

Table 16-BIP's of the Grouped Components (Sample NC)

PS1 PS2 PS3 PS4 PS5 PS6 PS7

PS1 0.016744 0.015769 0.009267 0.021093 0.036239 0.052557

PS2 0.016744 0.023631 0.024175 0 0 0

PS3 0.015769 0.023631 0.012447 0 0 0

PS4 0.009267 0.024175 0.012447 0 0 0

PS5 0.021093 0 0 0 0 0

PS6 0.036239 0 0 0 0 0

PS7 0.052557 0 0 0 0 0

60

Appendix E

Table 17-MBO - Gas Properties (Sample GC)

Pres rs Bg ηg

Pres rs Bg ηg

Pres rs Bg ηg

50 0.00045 0.03334 0.0163

200 0.00050 0.00828 0.0227

275 0.00068 0.00638 0.0296

0.00000 0.03300 0.0162

0.00045 0.00828 0.0224

0.00061 0.00636 0.0286

75 0.00045 0.02193 0.0169

0.00045 0.00830 0.0223

0.00055 0.00634 0.0278

0.00040 0.02187 0.0170

0.00042 0.00828 0.0222

0.00050 0.00633 0.0272

0.00000 0.02181 0.0170

0.00040 0.00828 0.0221

0.00045 0.00631 0.0268

100 0.00045 0.01632 0.0177

0.00040 0.00827 0.0221

0.00045 0.00633 0.0265

0.00040 0.01629 0.0177

0.00039 0.00827 0.0220

0.00042 0.00631 0.0264

0.00039 0.01627 0.0177

0.00000 0.00827 0.0220

0.00040 0.00630 0.0262

0.00000 0.01626 0.0177

225 0.00055 0.00747 0.0246

0.00040 0.00630 0.0262

125 0.00045 0.01302 0.0186

0.00050 0.00746 0.0242

0.00039 0.00630 0.0261

0.00040 0.01300 0.0186

0.00045 0.00746 0.0238

0.00000 0.00630 0.0260

0.00040 0.01299 0.0186

0.00045 0.00748 0.0237

300 0.00078 0.00602 0.0329

0.00039 0.01299 0.0186

0.00042 0.00745 0.0236

0.00068 0.00598 0.0314

0.00000 0.01299 0.0186

0.00040 0.00746 0.0234

0.00061 0.00596 0.0303

150 0.00045 0.01088 0.0197

0.00040 0.00745 0.0234

0.00055 0.00594 0.0294

0.00042 0.01085 0.0197

0.00039 0.00745 0.0234

0.00050 0.00592 0.0287

0.00040 0.01086 0.0196

0.00000 0.00745 0.0233

0.00045 0.00590 0.0282

0.00040 0.01085 0.0197

250 0.00061 0.00685 0.0269

0.00045 0.00591 0.0280

0.00039 0.01085 0.0196

0.00055 0.00684 0.0262

0.00042 0.00589 0.0279

0.00000 0.01085 0.0196

0.00050 0.00683 0.0257

0.00040 0.00589 0.0276

175 0.00045 0.00936 0.0211

0.00045 0.00682 0.0253

0.00040 0.00588 0.0276

0.00045 0.00938 0.0210

0.00045 0.00684 0.0251

0.00039 0.00588 0.0275

0.00042 0.00936 0.0209

0.00042 0.00682 0.0250

0.00000 0.00588 0.0274

0.00040 0.00937 0.0208

0.00040 0.00682 0.0248

325 0.00092 0.00576 0.0371

0.00040 0.00936 0.0208

0.00040 0.00681 0.0248

0.00078 0.00570 0.0355

0.00039 0.00936 0.0208

0.00039 0.00681 0.0247

0.00000 0.00936 0.0207

0.00000 0.00681 0.0246

61

Table 18-MBO - Gas Properties (continued) (Sample GC)

Pres rs Bg ηg

Pres rs Bg ηg

335 0.00099 0.00569 0.0392

350 0.00101 0.00556 0.0410

0.00092 0.00565 0.0379

0.00099 0.00554 0.0405

0.00078 0.00559 0.0355

0.00092 0.00550 0.0391

0.00068 0.00554 0.0338

0.00078 0.00543 0.0365

0.00061 0.00551 0.0325

0.00068 0.00539 0.0348

0.00055 0.00548 0.0316

0.00061 0.00535 0.0335

0.00050 0.00546 0.0308

0.00055 0.00532 0.0325

0.00045 0.00544 0.0303

0.00050 0.00529 0.0317

0.00045 0.00545 0.0300

0.00045 0.00527 0.0311

0.00042 0.00543 0.0298

0.00045 0.00528 0.0308

0.00040 0.00542 0.0295

0.00042 0.00526 0.0307

0.00040 0.00542 0.0295

0.00040 0.00525 0.0303

0.00039 0.00541 0.0294

0.00040 0.00525 0.0303

0.00000 0.00541 0.0293

0.00039 0.00525 0.0302

338.3 0.00101 0.00567 0.0400

0.00000 0.00524 0.0301

0.00099 0.00565 0.0395

375 0.00101 0.00534 0.0430

0.00092 0.00562 0.0381

0.00099 0.00533 0.0424

0.00078 0.00555 0.0357

0.00092 0.00528 0.0409

0.00068 0.00551 0.0340

0.00078 0.00521 0.0383

0.00061 0.00547 0.0328

0.00068 0.00515 0.0364

0.00055 0.00544 0.0318

0.00061 0.00511 0.0351

0.00050 0.00542 0.0310

0.00055 0.00508 0.0340

0.00045 0.00540 0.0304

0.00050 0.00505 0.0331

0.00045 0.00541 0.0302

0.00045 0.00503 0.0325

0.00042 0.00539 0.0300

0.00045 0.00504 0.0322

0.00040 0.00538 0.0297

0.00042 0.00501 0.0320

0.00040 0.00538 0.0297

0.00040 0.00501 0.0316

0.00039 0.00538 0.0296

0.00040 0.00500 0.0317

0.00000 0.00537 0.0294

0.00039 0.00500 0.0315

0.00000 0.00500 0.0314

62

Table 19-MBO - Oil Properties (Sample GC)

Rs Pres Bo ηo Rs Pres Bo ηo

Rs Pres Bo ηo

20.24 50 1.242 0.8120

64.88 125 1.415 0.3791

154.71 225 1.742 0.1784

75 1.226 0.9372

150 1.392 0.4338

250 1.708 0.1985

100 1.211 1.0669

175 1.372 0.4911

275 1.679 0.2196

125 1.198 1.2010

200 1.355 0.5508

300 1.654 0.2417

150 1.187 1.3390

225 1.339 0.6128

325 1.631 0.2647

175 1.177 1.4807

250 1.325 0.6771

335 1.623 0.2742

200 1.168 1.6256

275 1.313 0.7435

185.85 250 1.854 0.1511

225 1.159 1.7735

300 1.301 0.8119

275 1.817 0.1667

250 1.152 1.9242

325 1.291 0.8822

300 1.785 0.1831

275 1.145 2.0773

335 1.287 0.9108

325 1.757 0.2002

300 1.138 2.2326

83.44 150 1.484 0.3083

335 1.746 0.2073

325 1.132 2.3899

175 1.458 0.3507

222.78 275 1.987 0.1286

335 1.130 2.4533

200 1.436 0.3953

300 1.946 0.1406

33.44 75 1.295 0.6087

225 1.417 0.4418

325 1.910 0.1532

100 1.277 0.7018

250 1.400 0.4903

335 1.897 0.1584

125 1.260 0.7986

275 1.385 0.5406

268.26 300 2.153 0.1093

150 1.246 0.8991

300 1.371 0.5927

325 2.107 0.1185

175 1.233 1.0029

325 1.358 0.6464

335 2.090 0.1222

200 1.222 1.1098

335 1.354 0.6683

328.41 325 2.377 0.0921

225 1.212 1.2196

104.28 175 1.560 0.2542

335 2.355 0.0948

250 1.202 1.3321

200 1.532 0.2873

359.79 335 2.497 0.0854

275 1.194 1.4471

225 1.508 0.3220

338 2.490 0.0861

300 1.186 1.5643

250 1.487 0.3584

325 1.179 1.6835

275 1.468 0.3963

335 1.176 1.7318

300 1.451 0.4356

48.28 100 1.353 0.4745

325 1.436 0.4765

125 1.332 0.5454

335 1.430 0.4932

150 1.314 0.6195

127.82 200 1.645 0.2120

175 1.298 0.6965

225 1.615 0.2378

200 1.284 0.7764

250 1.588 0.2649

225 1.271 0.8589

275 1.565 0.2932

250 1.260 0.9439

300 1.544 0.3228

275 1.249 1.0312

325 1.526 0.3536

300 1.240 1.1207

335 1.519 0.3663

325 1.231 1.2123

335 1.228 1.2494

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