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    DESKTOP-PVTKeyw ord

    Reference Manual 2001, 2002 Landmark Graphics Corporation

    Part No. 159678 R2003.4

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    This publication has been provided pursuant to an agreement containing restrictions on its use. The publication is also

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    Note

    The information contained in this document is subject to change without notice and should not be construed as a

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    R2003.4 - Landmark iii

    Table of Contents

    About This Manual

    Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

    Audience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

    Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

    Related Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

    Chapter 1Introduction

    1.1 Overview of the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

    1.2 Free Field Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2

    1.3 FORTRAN File Assignments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3

    Chapter 2

    Equation-of-State Properties

    2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5

    2.2 Equation of State (EOS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6

    2.3 Component Names (Components) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8

    2.4 Component Characteristics (PROPERTIES) . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-9

    2.5 Binary Interaction Coefficients (DJK and DJKCOR) . . . . . . . . . . . . . . . . . . . 2-12

    2.6 Lohrenz-Bray-Clark Viscosity Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-14

    2.7 Pedersen et al. Viscosity Correlation (VISPE, VISK and VISKJ) . . . . . . . . . 2-15

    2.8 Component K-Value Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-17

    2.9 Correlation of CO2 Saturated Water Properties . . . . . . . . . . . . . . . . . . . . . . 2-182.10 Ideal Gas State Enthalpy Coefficients (HIDEAL) . . . . . . . . . . . . . . . . . . . . 2-22

    2.11 End of EOS Data (ENDEOS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-23

    2.12 Output File for PVT Properties (PVTFILE) . . . . . . . . . . . . . . . . . . . . . . . . . 2-24

    2.13 Output File for K-values (KVFILE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-25

    2.14 Selection of Water in Oil Option (WINOIL) . . . . . . . . . . . . . . . . . . . . . . . . . 2-25

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    2.15 Thermal Option (THERMAL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-26

    Chapter 3

    Simulating Laboratory Measurements

    3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-33

    3.2 Gas Z-Factor (Z-FACTOR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-33

    3.3 Liquid Density (LIQDEN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-36

    3.4 Vapor Pressure (VP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-38

    3.5 Saturation Pressure (PSAT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-40

    3.6 Liquid and Vapor Viscosity (VISC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-42

    3.7 Constant Composition Expansion (CCEXP) . . . . . . . . . . . . . . . . . . . . . . . . . 3-43

    3.8 Constant Volume Depletion (CVDEP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-48

    3.9 Swelling Test (SWELL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-543.10 Differential Expansion (DIFF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-55

    3.11 Multiple Contact Vaporization Test (MCVAP) . . . . . . . . . . . . . . . . . . . . . . 3-59

    3.12 Phase Envelope Calculation (ENVELOPE) . . . . . . . . . . . . . . . . . . . . . . . . . 3-62

    3.13 Enthalpy Calculation (ENTHV or ENTHL) . . . . . . . . . . . . . . . . . . . . . . . . . 3-64

    3.14 Liquid Water Properties (WATPRP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-66

    3.15 Saturation Pressure with Water (PSATW) . . . . . . . . . . . . . . . . . . . . . . . . . . 3-67

    3.16 Distillation Test (DISTIL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-69

    3.17 Complete Phase Envelope Calculation (ENVPT) . . . . . . . . . . . . . . . . . . . . 3-77

    3.18 Composition Variations with Depth (ZGRAD) . . . . . . . . . . . . . . . . . . . . . . 3-79

    3.19 Properties of Carbon Dioxide Saturated Water (CO2TAB) . . . . . . . . . . . . 3-84

    3.20 Multiple Contact Steam Vaporization Test (MCSVAP) . . . . . . . . . . . . . . . 3-86

    3.21 Two Phase Isothermal Flash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-91

    Chapter 4

    Simulating Multistage Separators

    4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-954.2 Separator Conditions Data (SEPARATOR) . . . . . . . . . . . . . . . . . . . . . . . . . . 4-95

    4.3 Separator Test with Regression (SEP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-97

    Chapter 5

    Automatic Parameter Adjustment

    5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-103

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    5.2 EOS Property Adjustment (REGRESS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-105

    5.3 Regression Variable Data (VARIABLE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-105

    5.4 Nonlinear Regression Process (IMAX) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-106

    5.5 Assignment of Regression Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-107

    5.6 End of Regression Data (ENDREG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-111

    Chapter 6

    Pseudoization

    Chapter 7

    Heavy Fraction Characterization

    Chapter 8

    Calculation Controls

    8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-125

    8.2 Selection of Flash Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-125

    8.3 Saturation Pressure Tolerance Card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-126

    8.4 Flash Calculation Tolerance Card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-128

    8.5 Expansion Tolerance Card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-129

    8.6 Saturation Pressure and Flash Calculations Output(DBUGS and DEBUGF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-130

    8.7 Selection of Viscosity Calculation Method . . . . . . . . . . . . . . . . . . . . . . . . . . 8-131

    Chapter 9

    Composition Specification

    Appendix A

    Unconstrained Minimization ofLeast-Squares Functions

    A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-137

    A.2 Gauss-Newton Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-139

    A.3 Advantages of the Gauss-Newton Method . . . . . . . . . . . . . . . . . . . . . . . . A-140A.4 Defects in the Gauss-Newton Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-141

    A.5 Method of Rotational Discrimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-142

    A.6 The Rotational Discrimination Algorithm . . . . . . . . . . . . . . . . . . . . . . . . A-144

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    Appendix B

    The Establishment of Bounds on Variables

    B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-149

    B.2 Our Treatment of Bounded Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-149

    Appendix C

    One-Dimensional Search Procedure

    C.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-151

    C.2 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-151

    C.3 Operating Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-152

    C.4 Description of the Search Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-152

    Appendix D

    Example ProblemsD.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-155

    D.1.1 Lab Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-156D.1.2 Sample Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-174

    D.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-222D.2.1 Lab Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-222D.2.2 Sample File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-236

    Appendix E

    References

    Keyword IndexSubject Index

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    Preface

    R2003.4 - Landmark vii

    About This Manual

    Purpose

    This manual describes the functions of DESKTOP-PVT, a program

    designed to simulate the behavior of hydrocarbon fluid mixtures.

    DESKTOP-PVTs purpose is to generate PVT properties or develop a

    mathematical model which can be used in a compositional reservoir

    simulator such as VIP-COMP to analyze oil and gas production

    characteristics.

    Audience

    This manual is intended to assist new and experienced users of

    DESKTOP-PVT in the generation of PVT properties where laboratory data

    is limited, or the development of a mathematical model that agrees with

    experimental data.

    Organization

    The information in this manual is arranged in a logical manner for

    maximum ease-of-use. The following chapters are included:

    Introduction.

    Equation-of-State Properties.

    Simulating Laboratory Measurement.

    Simulating Multistage Separators.

    Automatic Parameter Adjustment.

    Pseudoization.

    Heavy Fraction Characterization.

    Calculation Controls.

    Composition Speci cation.

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    Related Documentation

    The following manuals provide more information related to the material

    in this manual. For more information, please consult the appropriate

    manual listed below.

    DESKTOP-PVT Users Manual. Characterizing equations of state forcompositional simulation.

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    Chapter

    R2003.4 - Landmark 1-1

    1

    Introduction

    DESKTOP-PVT is used to simulate the behavior of fluid mixtures when

    they are subjected to any of a variety of laboratory procedures. The fluids

    may be either liquid or vapor and may undergo phase changes during the

    simulated experiments.

    The program can be used in a purely predictive mode to generate PVT

    properties where laboratory data is limited, or it can be used to develop a

    mathematical model that agrees with experimental data. In the latter case,the mathematical model of the fluid system can then be used in a

    compositional simulator such as VIP-COMP to analyze oil and gas

    production characteristics. In addition, the tabular data necessary to

    define fluid behavior in VIP-ENCORE may also be generated by

    DESKTOP-PVT.

    To aid in development of a fluid model that matches experimental data, a

    nonlinear regression package is provided as an integral part of DESKTOP-

    PVT. This facilitates the adjustment of unknown or uncertain parameters

    that affect fluid behavior.

    1.1 Overview of the Data

    The data for DESKTOP-PVT is divided into six major parts:

    1. Equation-of-state properties

    2. Laboratory procedures

    3. Surface separation

    4. Automatic parameter adjustment

    5. Pseudoization

    6. Heavy fraction characterization

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    Introduction DESKTOP-PVT Keyword Reference Manual

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    1.2 Free Field Input

    All data is read in "free field" format. Simply stated, this means that it is

    not necessary to type numbers in specific columns. DESKTOP-PVT reads

    each item of data or "word" by finding the leftmost character and then

    decoding each successive character until a blank column or a commasignifies the end of the word.

    The data stream contains both numbers and alpha code words, the latter

    used to identify subsequent numbers or to select program options. It is a

    general rule that each new type of data is introduced by an alpha code

    word.

    In the data descriptions that follow, code words are identified by being

    typed in upper case letters. They must appear in the data stream exactly as

    typed in this manual. The names of variables whose values must be

    supplied are typed in lower case letters. Appropriate numbers or names

    must be entered in their proper place.

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    1.3 FORTRAN File Assignments

    DESKTOP-PVT makes use of several different FORTRAN units for scratch

    files for input and output. Figure 1-1 illustrates schematically the

    DESKTOP-PVT I/O structure.

    Figure 1-1: DESKTOP-PVT I/O Structure

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    Chapter

    R2003.4 - Landmark 2-5

    2

    Equation-of-State Properties

    2.1 Introduction

    The PVT properties of both vapors and liquids are predicted byDESKTOP-PVT by means of a cubic equation of state. Available equationsof state include Redlich-Kwong (RK), Soave-Redlich-Kwong (SRK),Zudkevitch-Joffe-Redlich-Kwong (ZJRK), Peng-Robinson (PR), and thethree-parameter versions of PR, SRK, and RK.

    In order to completely define fluid properties it is necessary only to definefluid composition and various properties of individual components. Theindividual components may be pure components, but frequently they arethemselves mixtures. For example, isobutane (i-C4) and normal butane (n-C4) may be treated together simply as C4.

    Heavy fractions are normally grouped together over a reasonably widerange of molecular weights. For example, C16- C20may be groupedtogether as a single component that is designated as C18.

    The properties of a large number of components have been internallycoded, so they are automatically assigned unless the user elects to

    override the default. For light components the internal values usuallyrepresent pure component properties, but for heavier fractions the internalvalues have been adjusted to produce improved results for naturallyoccurring oils and gases at reservoir conditions.

    Table 2-1 and Table 2-2 summarize the internally coded properties for allcomponents that can be automatically determined. Using one of thecomponent identification codes contained in these tables as data in theCOMPONENTS input data will cause the tabulated values to be loaded.Unless these values are overridden by the user in the PROPERTIES datasection, they will be used by default.

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    2.2 Equation of State (EOS)

    The equation of state to be used for PVT properties is specified on the EOSdata card.

    EOS

    Definitions:

    Example:

    To specify the Peng-Robinson equation-of-state, the following data card isrequired:

    EOS PR

    NOTE: 1. The original Peng-Robinson equation of state uses the sameequation to calculate the temperature dependent term of "a" forall ranges of acentric factor. The default version of the Peng-Robinson equation of state used in DESKTOP-PVT employs adifferent equation to calculate the temperature dependent term of"a" when the acentric factor is greater than 0.49.

    RK Redlich-Kwong equation-of-state.

    PR Peng-Robinson equation-of-state.

    PRORIG Original Peng-Robinson equation-of-state.

    SRK Soave Redlich-Kwong equation-of-state.

    ZJRK Zudkevitch-Joffe-Redlich-Kwong equation-of-

    state.

    RK3P, PR3P,PROR3P, SRK3

    Three-parameter version of RK, PR, PRORIG andSRK respectively

    RK

    PR

    PRORIG

    SRK

    ZJRK

    RK3P

    PR3P

    PROR3P

    SRK3P

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    2. For compatibility with VIP-CORE, the user does not have to use adifferent keyword to specify the three parameter version of anequation of state. The program recognizes that the volume shiftparameter should be used if the keyword VSHFT is included onthe second line of the PROPERTIES data card. For example, thethree parameter version of the Seave-Redlich Kwong EOS can be

    spedifed by

    EOS SRK

    if VSHFT is also included on the PROPERTIES card.

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    2.3 Component Names (Components)

    The alphameric labels that will be used to identify the components aredefined here. If any of the component names contained in Table 2-1 orTable 2-2 is used, the properties data will be picked from the table, subjectto user override. If unrecognized labels are used, the user must directlyspecify at least molecular weight data.

    COMPONENTS

    cmp1cmp2. . . cmpn(NCV ncv)

    Definitions:

    Define the components in a fluid system that contains carbon dioxide,nitrogen, methane through hexane, and heptanes plus. Either of thefollowing is acceptable:

    (1) COMPONENTS

    CO2 N2 C1 C2 C3 IC4 NC4 IC5 NC5 NC6 C7+

    (2) COMPONENTSCO2 N2 C1 C2 C3 NC4 NC5 NC6 C7+

    In both components definitions, all components except C7+ will havedefault properties. The user must enter properties data for C7+.

    cmpn Component name. An alphameric label contain-ing up to 6 characters. Using a name contained in

    either Table 2-1 or Table 2-2 will cause the tabu-lated properties to be automatically loaded.

    ncv Number of volatile components. Use only inexperiments associated with VIP-THERM (STM-DIS, PSATW).

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    2.4 Component Characteristics (PROPERTIES)

    Properties data are entered to define the PVT characteristics of individualcomponents. These are combined by appropriate mixing rules and usedwith the equation of state to determine the properties of mixtures.

    Default properties for internally defined components are given in Table 2-1 and Table 2-2. Omitting the properties data card for these componentsresults in the use of the default properties.

    For non-internally defined components, a minimum of molecular weightdata must be entered on the properties data card. Default properties forthese components are determined by table lookup on the internallydefined hydrocarbon component properties based on molecular weight.

    All properties for internally-defined components and all except molecularweight for non-internally defined components may be defaulted byentering the alpha label X on the properties data card where the default

    value is desired. The properties table may be truncated at any point aftermolecular weight. All unread data is defaulted. The number of entries onthe table title and properties data must be the same.

    PROPERTIES

    COMP MW TC PC ZC ACENTRIC OMEGAA OMEGAB

    cmpi mwi tcipci zci wi

    . . . . . . . .

    . . . . . . . .

    . . . . . . . .

    Definitions:

    F, C, K, R Alpha label indicating that the units of all temperaturevalues are:

    F Degrees Fahrenheit, F. This is thedefault.

    C Degrees Centigrade, C.

    K Degrees Kelvin, K.

    F PSIA

    C PSIG

    K KPA

    R KGCM2

    alo

    blo

    PCHOR VSHFT NBP GRVL TREF

    pch or

    i

    s

    i

    nb p

    i

    grvl

    i

    tref

    i

    VSHFTD VSHFTE

    d e

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    R Degrees Rankin, R.

    (input optional)

    PSIA, KPA, PSIG,KGCM2

    Alpha label indicating that the units of the criticalpressure values (PC) are:

    PSIA Psia. This the default.

    KPA KPa.

    PSIG Psig.

    KGCM2 Kg/cm2.

    (input optional)

    cmpi Component name for component i. Must be identicalto one of the names included in the COMPONENTSdata.

    mwi

    The molecular weight of component i.

    tci Critical temperature of component i.

    pci Critical pressure of component i.

    zci Critical z-factor of component i. (This propertyaffects only viscosity calculations.)

    wi Acentric factor of component i.

    for component i. This is treated as a universalconstant in the original formulations of the equationsof state (0.4274802 for RK, SRK, and ZJRK; 0.457235529for PR). Additional flexibility in fitting data is gainedby allowing it to vary by component.

    for component i. This is treated as a universalconstant in the original formulation of the equations ofstate (0.08664035 for RK, SRK and ZJRK; 0.077796074for PR). Additional flexibility in fitting data is gainedby allowing it to vary by component.

    pchori Parachor for component i, .(This property affects only interfacial tension calcula-tions.)

    si Dimensionless volume shift parameter. (This property

    is used only if molar volume is corrected using thethree-parameter EOS option.)

    nbpi Normal boiling point temperature for component i.(This property is used in ZJRK only.)

    grvli Specific gravity of component iat temperature trefirelative to water at 60F. (This is used in ZJRK only.)

    aio ai

    o

    bio bi

    o

    g1 4

    -cm3

    s1 2

    mole( )

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    NOTE: l. If either of the temperature or pressure unit flags is specified,then both must be specified.

    2. Repeat the data card containing cmpi, mwi, etc. as necessary tospecify all properties correctly.

    3. Only 80 columns are allowed for each card. By entering the alpha

    label > at the end of a card, the data at the next card will betreated as a continuation of this card.

    4. For the non-internally defined components, the volume shiftparameters are calculated using d and e only if they are input,otherwise, they are determined by table lookup on the internallydefined hydrocarbon component properties based on molecularweight.

    Example:

    PROPERTIES

    COMP MW TC PC ZC ACENTRIC OMEGAA OMEGABC7+ 206. 895.1 302.6 .3121 .8643 X X

    C1 X X X X X .48521 .08261

    trefi Reference temperature for component ispecific grav-ity. Default is 60F. (This is used in ZJRK only.)

    d, e Parameters d and e for computing volume shiftparameter s,

    s = 1 - d M-e

    where M is the molecular weight of a component.

    The default value for d is 1.74 and is 0.133 for e.

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    2.5 Binary Interaction Coef cients (DJK and DJKCOR)

    DJK and DJKCOR data are used to define binary interaction coefficients(djk). The binary interaction coefficients are used in the mixing rules thatdetermine for mixtures the A parameter of the EOS. The binary interactioncoefficients are read in if the DJK card is specified, and are computed froma correlation [4] if the DJKCOR card is specified.

    Table 2-3 summarizes non-zero values ofdjkthat have been internallycoded for various combinations of components. These values will beautomatically loaded as data when the corresponding component namesare entered in the COMPONENTS data. In addition, default values for theinteraction coefficients between methane and heavy fractions from C6through C45 are given in Table 2-2. Interaction parameters between any ofthe heavy fractions in Table 2-2 and CO2, N2, C2,and C3are the same asgiven for NC18in Table 2-3.All binary combinations that involve anunrecognized component name will be assigned default values of zero.

    Any of the default values for binary interaction coefficients can beoverridden by means of the DJK or DJKCOR data.

    DJK cmpjcmpk djk

    Definitions:

    NOTE: 1. Enter one data card for each component kthat interacts withcomponent j.

    2. Enter anentire set ofdata including the DJK card and cmpk cards

    for each component jthat requires djk specifications.

    3. Remember that djk= dkj. It is not necessary to define both.

    4. In some experiments associated with VIP-THERM, water appearsimplicitly as a component. Binary interaction coefficients forwater may be input by replacing cmpjor cmpkwith the alphalabel H2O.

    cmpj Component name of one component in a binarymixture.

    cmpk Component name of the second component in abinary mixture.

    djk The binary interaction coefficient for mixtures ofcomponent jand component k.

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    DJKCOR djkcor

    Definition:

    Example:

    Specify the interaction parameters between heavy component C7+ andCO2, N2, C2, and C3:

    DJK C7+CO2 .15N2 .12C2 .01C3 .01

    Example:

    DJKCOR 1.2

    djkcor The exponent of the binary interaction coefficients as[4]:

    where and are the critical volumes for com-

    ponent j and k, respectively. Default is 1.

    dj k

    1

    2Vcj

    1 6Vck

    1 6

    Vcj

    1 3Vck

    1 3+

    ------------------------------

    d j kco r

    =

    VcjVck

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    2.6 Lohrenz-Bray-Clark Viscosity Correlation

    00 The Lohrenz-Bray-Clark viscosity calculation is as follows:

    00

    00 where is the phase viscosity, is a base viscosity, is a function ofpseudo critical pressures, pseudo critical temperatures, and mixturemolecular weight, and is a pseudo reduced phase density.

    00 By default, the coefficients C1, C2, C3, C4, and C5are equal to 0.1023,0.023364, 0.058533,-0.040758, and 0.0093324, respectively. Use of the LBCkeyword allows the user to modify these default coefficients to obtain abetter match with experimental viscosities.

    00 The LBC keyword is not required if the user wishes to retain the defaultcoefficients.

    00 The LBC keyword can appear anywhere after the PROPERTIES keywordand data and before the end of the ENDEOS keyword. The modifiedcoefficients will only apply for the current EOS table being defined.

    LBC

    C1C2C3C4C5

    b C1 C2r C3r2

    C4r3

    C5r4

    + + + +[ ]4

    104

    ( )+=

    b r

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    2.7 Pedersen et al. Viscosity Correlation (VISPE, VISK andVISKJ)

    The Pedersen et al. viscosity correlation is based on the correspondingstates principle [10,11]. A group of substances obeys the corresponding

    states principle if these substances have the same reduced viscosity at thesame reduced density and reduced temperature. In such case, onlycomprehensive viscosity data for one component (the referencecomponent) in the group are needed. Others can be calculated from thereduced viscosity. The Pedersen et al. viscosity correlation uses methane asa reference substance.

    This correlation is useful for heavy oils where the Lohrenz-Bray-Clarkcorrelation [2] fails to give a proper viscosity prediction for some cases. Toinvoke the Pedersen et al. viscosity option, a keyword "VISPE" should beentered before the laboratory test data (see Section 8.7).The user has theoption of specifying k1 to k7 (VISK card) for calculating the viscosity of the

    reference component and binary interacting coefficients Xkj(VISKJ card)for calculating the mixture pseudo-critical temperature used in theviscosity correlation. VISK and VISKJ cards are optional. Default valueswill be used if they are not entered. The default values are zero for all theinteracting coefficients Xkjand the following values for the coefficients kj.

    k1= 9.74602k2= 18.0834k3= 4126.66k4= 44.6055k5= 0.976544k6= 81.8134

    k7= 15649.9

    Only those data overwriting the default values need to be entered.

    VISK

    j kj . .

    . .

    . .

    VISKJ

    k j xk,j or cmpk cmpj xk,j . . . . . .

    . . . . . .

    . . . . . .

    ENDVIS

    Definitions:

    VISK The keyword for inputting kjvalues. Optional.

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    Example:

    VISK

    1 42.5

    2 0.0002279

    3 11770.0

    4 600.3

    5 16.49

    6 0.0552

    VISKJ

    3 5 -0.364093 6 -0.38517

    3 7 -0.8

    3 8 -0.62763

    ENDVIS

    j Index for kj.

    kj The kjvalues for calculating the viscosity of thereference component.

    VISKJ The keyword for inputting binary interaction

    coefficients xkj. Optional.k Component number k.

    j Component number j.

    cmpk Component name of component k

    cmpj Component name of component j

    xkj Binary interaction coefficient for components kand j for calculating critical temperature used inthe viscosity correlation. Default is 0.0

    ENDVIS The keyword marks the end of Pedersen et al.viscosity data input.

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    2.8 Component K-Value Correlation

    In DESKTOP-PVT the component K-values are usually computed usingan equation of state. For distillation test, a correlation is available tocomputed compute K-values of distillates. The component K-value isexpressed as

    (2-1)

    whereAito Eiare constant coefficients for component i, P is pressure inpsia and T is temperature in Rankin.

    KVCOR

    COMP A B C D E

    k ak bk ck dk ek. . . . . .

    . . . . . .

    Definitions:

    KVCOR Alpha label indicating the coefficients of componentK-values correlation are to follow. (Input Optional)

    k Component number k.

    akto ek Coefficients A to E of component K-valuecorrelation. (Input Optional)

    Example:

    KVCOR

    COMP A B C D E

    1 -1.0 0.1531431E+06 0.3614000E-02 0.7275900E+04 0.0

    2 -1.0 0.9296972E+06 0.4227000E-02 0.1214770E+05 0.0

    3 -1.0 0.3488022E+08 0.5141000E-02 0.2085317E+05 0.0

    4 -1.0 0.2121159E+12 0.1246900E-01 0.4656781E+05 0.0

    Ki AiBi

    P----- Ci+ + P exp

    Di

    T Ei---------------

    =

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    2.9 Correlation of CO2 Saturated Water Properties

    Correlations were developed to calculate properties of carbon dioxidesaturated water as functions of temperature, pressure and salinity. Theseproperties include carbon dioxide solubility, formation volume factor,compressibility and viscosity.

    The solubility of carbon dioxide in pure water is calculated as a function oftemperature and pressure.

    and

    where

    Rsw a P 1 b

    2---

    c Pc P 1+--------------------

    sin= if P Po h (A-31)

    5. If step 4 is terminated at the kth parameter for reason (b), set ykand

    all remaining yiequal to zero and skip to step 7. If it is terminated forreason (c), then

    (A-32)

    6. If there are parameters in the list after the kth one, calculate themaccording to the method of scaled steepest descent

    (A-33)

    where siis a scale factor defined by

    (A-34)

    where

    . (A-35)

    (Pis a constant, usually in the range of 10-100.)

    (This expression produces scale factors that vary from 1 to Pas diivaries between dkkand zero.) If|yi|>hwhen calculated in thismanner, it should be truncated so that |yi| = h.

    7. Convert the resulting Y-vector back into a X-vector by Equation A-27:

    (A-36)

    8. Perform a one-dimensional search for the optimumalong the vector

    (A-37)

    dkk

    dii

    ----------- 108

    yk

    h sign Q

    yk

    -----------

    =

    yi

    yk

    si Q

    yk

    --------------

    Qy

    i-------------

    -------------------=

    si Pa

    =

    a 1 exp 0.5lnP---------- ln

    dkk

    dii

    -----------

    =

    X S Y=

    Xo X+=

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    9. Update the distance factor haccording to

    hk+1= hkexp[0.88255 tan-1(0.56654 ln)]

    This has the effect of multiplying hkby a factor between 0.25 and 4 asvaries from 0 to. For = 1, hk+1= hk.

    10. Convergence is achieved when either the change in Q over an iterationis within a tolerance, or the magnitude of X is very small. Ifconvergence is not met, update Xoand return to step 2.

    It is not difficult to demonstrate that the Y calculated in this mannerproduces aX with the property of truncation convergence. To do this, weexpand the differential of the objective function with respect toin termsof the yivariables.

    (A-38)

    The search for vector Y can be expressed as a function of in the followingmanner:

    For 0 < i < k,

    (A-39)

    Fori = k,

    (A-40)

    For k < i n,

    (A-41)

    Substituting these expressions into Equation A-38 we obtain

    (A-42)

    dQ

    d---------

    Qy

    i

    ---------

    dyi

    d-------------

    i 1=

    m

    =

    yi

    d

    ii

    -------- Qy

    i

    -------------=

    yi h sign

    Qy

    i

    -----------=

    yi

    = yk

    si

    Qy

    i

    ---------

    Qy

    k

    ----------- ---------------- h s

    i

    Qy

    i

    ---------

    Qy

    k

    ----------- ---------------- sign

    Qy

    k

    -----------

    =

    dQ

    d---------

    Qy

    i

    --------- 2 1

    dii

    -------- h Qy

    k

    ------------- signQy

    k

    -----------

    i 1=

    k 1

    =

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    (A-43)

    Since dii, h, and si are all positive by definition, it is obvious that dQ/d isnegative at the base point, and hence truncation convergence is achieved.This clearly remains true even if one of the yiis truncated, as described instep 6, or if one of the yiis set to zero as in step 5.

    h si

    .

    Qy

    i

    --------- 2

    Qy

    k

    ----------- ------------------- sign

    Qy

    k

    -----------

    i k 1+=

    n

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    Appendix

    R2003.4 - Landmark B-149

    B

    The Establishment of Bounds on Variables

    B.1 Introduction

    Oftentimes physical or practical considerations dictate that the value of anunknown parameter not exceed some upper or lower bound. Porosity, forexample, is restricted by its definition to lie between zero and one.Similarly, negative values of permeability are physically impossible. Atother times, a reasonably good estimate of the optimum value of someparameter may be available from previous work. Thus it is known that theoptimum should lie within some relatively narrow range of values.

    In such situations, it is usually desirable to establish inequality constraintson the parameters of a minimization problem. This often speedsconvergence to the proper solution, as well as preventing convergence toan infeasible or unlikely solution. This is particularly valuable in solvingproblems that are ill-conditioned, since it prevents excessively widefluctuations in parameter values.

    B.2 Our Treatment of Bounded Variables

    During the problem definition and initialization state of a least-squaresproblem, we require that both a lower bound, xi

    min, and an upper bound,xi

    maxbe specified for each minimization variable. Furthermore, we requirethat the initial estimate of the value of each parameter lie within itsbounds.

    Once the problem has been initialized, the base point for each succeedingiteration is determined by a one-dimensional search for the optimumalong the vector.

    X = Xo+.X. (B-1)

    If the base point for the iteration lies in the feasible region, we can alwayscalculate a numbermaxsuch that the constraints are satisfied for all max. This number is calculated as follows:

    (B-2)max

    0.999 MINx

    ib

    xio

    xi

    --------------------

    =

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    where MIN is the minimum over alli,

    (B-3)

    (B-4)

    If the optimum for an iteration is less thanmax, then the constraints areinactive and we proceed just as though the problem were unconstrained.If, on the other hand, the optimum value exceeds the maximum we setequal tomaxin computing the base point for the next iteration.

    When this is done, the resulting base point will lie very close to theboundary of the feasible region. Consequently, if the new iterationproduces a similar search direction, the distance from the base point to theboundary will be very short, and the search direction will be unprofitable.Therefore, when we find that

    (B-5)

    whereis a small positive number, we modify the minimizationprocedure to produce a more profitable search direction.

    In calculating this new search direction, we deactivate the variable that isattempting to violate its bounds, effectively reducing the dimensionalityof the problem. We then recalculate the incremental changes in theremaining variables and determine a new

    max. This is done just as before

    except that we use a Gauss-Newton matrix that has only (n-1)rows andcolumns rather than n. No additional function evaluations are required,since the necessary derivatives are always stored at the beginning of eachiteration.

    If necessary, the dimensionality of the problem for a given iteration can bereduced still further by repeated application of the above process.However, regardless of the number of variables deactivated in theprevious iteration, each new iteration begins with the full set ofnvariables. Thus a parameter constrained at an upper or lower bound forseveral iterations can move back toward the middle of its permitted rangein subsequent iterations.

    xi

    ximax

    ifxi

    0 and,>=

    xi

    xi

    minifx

    i0.

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    C

    One-Dimensional Search Procedure

    C.1 Introduction

    Each iteration of the minimization program concludes wicne-dimensionalsearch for theproducing the lowest sum-of-squares along the vector

    X = Xo+.X (C-1)

    The search procedure employed is designed to accomplish the followingobjectives:

    1. Locate a point at which the sum-of-squares is lower than at the basepoint.

    2. Determine values ofboth larger and smaller than the optimum value,and then perform a quadratic interpolation to estimate the optimum.

    3. Perform the smallest number of function evaluations possible withoutcompromising the first two objectives. This can often mean thatopt isdetermined with rather low precision; however, it is considered moreproductive to compute a new search direction than to further refine the

    estimate ofopt.

    C.2 Assumptions

    In order to minimize the number of function evaluations required to locateopt, we make use of several assumptions.

    1. There is only one relative minimum along any given search direction.

    2. Objective function is continuous for 0 con, whereconis somepositive number.

    3. The optimumis always greater than or equal to zero. (This assumesthat the least-squares minimization program has the property oftruncation convergence, discussed in Appendix A.)

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    The search normally begins with a function evaluation for =1. (This ismodified whenmax Q2 < Q3 (C-3)

    1

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    (C-8)

    where

    (C-9)

    (C-10)

    In the event that2 .Xis reduced to a value smaller than, the searchis terminated andopt is set to zero.

    test

    12---

    C1

    C2--------=

    C1 dQd---------=

    C2

    Q2

    Qo

    C1

    2

    2

    ( )2

    -------------------------------------------------=

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    Appendix

    R2003.4 - Landmark D-155

    D

    Example Problems

    D.1 Example 1

    The following example documents the use of DESKTOP-PVT in theanalysis of a fluid sample with an equation-of-state. Included is a standardlaboratory report for a volatile oil sample, with a constant compositionexpansion test, a constant volume depletion test, and a surface separationtest. Following the laboratory report are three DESKTOP-PVT programoutput listings.

    The first listing shows the generation of a heavy fraction characterizationusing the SPLIT feature of DESKTOP-PVT. An extended analysis to carbonnumber 45is produced with a pseudoization back to three components.The resulting component properties are written to a disk file for use insubsequent runs.

    The second listing shows the use of non-linear regression to adjustequation-of-state parameters to match laboratory measurements. In thisexample,a, andb of each of the three heavy components and methane,and the binary interaction parameters between methane and the heavycomponents are adjusted to produce an excellent match of the observeddata.

    The third listing shows the adjustment of component zcparameters tomatch laboratory measured viscosity data. Note that changes ofzcdo noteffect the equation-of-state calculated PVT properties. The zcparametersare used only in the viscosity correlation.

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    D.1.1 Lab Repor t

    CORE LABORATORIES, Inc.Reservoir Fluid Analysis

    Reservoir Fluid Study

    forGOOD OIL COMPANYVolatile Oil No. 8 Well

    CORE LABORATORIES, Inc.Reservoir Fluid Analysis

    Good Oil Company

    P.O. Box 100

    Oil City, TX

    Attention: Mr. John Jones

    Subject: Reservoir Fluid Study

    Volatile Oil No. 8 Well

    Gentlemen:

    Samples of separator liquid and vapor were collected from the subject well by a representative of Core

    Laboratories, Inc. Presented in this report are the results of a reservoir fluid study performed using these

    samples.

    The producing gas-liquid ratio was measured to be 2527 cubic feet of separator gas at 14.696 psia and

    60F per barrel of stock tank liquid at 60F. This ratio has been corrected for gas gravity and

    supercompressibility. In the laboratory it was found that he ratio is equivalent to 2355 standard cubic

    feet of separator gas per barrel of separator liquid. This ratio was used in conjunction with the measured

    compositions of the separator products to calculate the composition of the well stream material. These

    data are reported on page two.

    The separator products were physically recombined to the producing ratio and examined in a visual cell

    at the reservoir temperature of 276F. During a constant composition expansion a bubble point was

    observed at 4375 psig. Comparison of this value to the reservoir pressure indicates that the fluid exists

    in an undersaturated condition. Observation of the system at pressures immediately below the bubble

    point pressure shows that the liquid exhibits a very rapid shrinkage which indicates this system to be avolatile oil, or one which is near critical in nature.

    Since a large amount of the production from this type of reservoir comes from the gaseous phase, a

    constant volume depletion study was performed on a sample of the recombined fluid to enable

    calculation of the production during depletion below the bubble point pressure. The depletion consisted

    of a series of expansions and constant pressure displacements terminating at the original cell volume.

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    This has the effect of maintaining a constant reservoir volume. The produced gas phase was charged to

    low temperature, fractional distillation equipment for analysis and volume measurement. The results of

    the depletion are tabulated on page five of the report.

    The quantity of plant products available in the gas phases alone is shown on page six. A plant efficiency

    of 100 percent has been assumed.

    The well stream composition and equilibrium ratios of the literature were used to calculate the stock

    tank liquid and sales gas recoveries that will be obtained as the pressure declines from reservoir

    pressure to the bubble point pressure. THese recoveries are based upon one MMSCF of the fluid in

    place at the bubble point pressure. One MMSCF is the gaseous equivalent of 842.8 barrels of bubble

    point liquid.

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    Good Oil Company Page Two

    Volatile Oil No. 8 Well

    The viscosity of the liquid phase was measured from pressures exceeding reservoir pressure to

    atmospheric pressure. These data are presented on page eight together with the calculated gas phase

    viscosity.

    The data concerning the shrinkage of the liquid in the reservoir are shown on page nine of this report.

    Thank you for this opportunity to be of service. If you have any questions or if we may assist you

    further, please do not hesitate to contact us.

    Very truly yours,

    CORE LABORATORIES, INC.

    Manager

    Reservoir Fluid Analysis

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    D.1.2 Sample Fil es

    ******************************************************************************

    * *

    * DDDDDD EEEEEEE SSSSS KK KK TTTTTTTT OOOOO PPPPPP *

    * DD DD EE SS SS KK KK TT OO OO PP PP *

    * DD DD EE SS KK KK TT OO OO PP PP *

    * DD DD EEEEE SSSSS KKKK TT OO OO PPPPPP *

    * DD DD EE SS KK KK TT OO OO PP *

    * DD DD EE SS SS KK KK TT OO OO PP *

    * DDDDDD EEEEEEE SSSSS KK KK TT OOOOO PP *

    * *

    * PPPPPP VV VV TTTTTTTT *

    * PP PP V V TT *

    * PP PP VV VV TT *

    * PPPPPP V V TT *

    * PP VVVV TT *

    * PP VV TT *

    * PP VV TT *

    * *

    * PHASE BEHAVIOUR PROGRAM *

    * *

    * COPYRIGHT 1984, 1985, 1986, 1987, 1988 *

    * 1989, 1990, 1991, 1992, 1993 *

    * 1994, 1995, 1996, 1997, 1998 *

    * LANDMARK GRAPHICS CORPORATION *

    * ALL RIGHTS RESERVED *

    * *

    * VERSION 1998.0.0 CREATED 01 MAR 1998 *

    * *

    * LL AAAAA N NN DDDDDD M M AAAAA RRRRRR KK KK *

    * LL AA AA NN NN DD DD MM MM AA AA RR RR KK KK *

    * LL AA AA NNN NN DD DD M M M M AA AA RR RR KK KK *

    * LL AAAAAAA NN N NN DD DD M MM M AAAAAAA RRRRRR KKKK *

    * LL AA AA NN NNN DD DD M M AA AA RR RR KK KK *

    * LL AA AA NN NN DD DD M M AA AA RR RR KK KK *

    * LLLLLLL AA AA NN N DDDDDD M M AA AA RR RR KK KK *

    * *

    * GGGGG RRRRRR AAAAA PPPPPP HH HH IIII CCCCC SSSSS *

    * GG GG RR RR AA AA PP PP HH HH II CC CC SS SS *

    * GG RR RR AA AA PP PP HH HH II CC SS *

    * GG RRRRRR AAAAAAA PPPPPP HHHHHHH II CC SSSSS *

    * GG GGG RR RR AA AA PP HH HH II CC SS *

    * GG GG RR RR AA AA PP HH HH II CC CC SS SS *

    * GGGGG RR RR AA AA PP HH HH IIII CCCCC SSSSS *

    * *

    ***************************************************************************

    1 ************************************************

    * *

    * D E S K T O P - P V T *

    * *

    * PHASE BEHAVIOUR PROGRAM *

    * *

    * VERSION 1998.0.0 *

    * *

    * COPYRIGHT 1984, 1985, 1986, 1987, 1988 *

    * 1989, 1990, 1991, 1992, 1993 *

    * 1994, 1995, 1996, 1997, 1998 *

    * LANDMARK GRAPHICS CORPORATION *

    * ALL RIGHTS RESERVED *

    * *

    ************************************************

    SEQUENCE

    NUMBER CARD IMAGES OF THE INPUT DATA

    -------- ---------------------------------------------------------------------

    X C

    X C EOSPAK EXAMPLE PROBLEM #1

    X C GOOD OIL #8 - SPLIT

    X C -------------------------

    X C

    X C ----------------------------------------

    X C MW OF PLUS FRACTION 183

    X C GRAVITY OF PLUS FRACTION 0.8345

    X C MOLE FRACTION OF PLUS FRACTION 0.1420

    X C CARBON NUMBER OF PLUS FRACTION 7

    X C NUMBER OF GROUP 3

    X C DISTRIBUTION PATAMETER (ALPHA) 1.0

    X C GROUPING MOLECULAR WEIGHTS 125 130

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    X C ----------------------------------------

    X C

    1 S SPLIT

    X C

    2 S MWPLUS GPLUS ZPLUS NCOMP NG ALPHA MWGRP

    3 S 183 0.8345 0.1420 7 3 1.0 125 300

    X C

    4 S END

    1HEAVY FRACTION CHARACTERIZATION

    -------------------------------

    SPLIT ITERATION SUMMARY

    -----------------------

    ITR ALPHA M. W.+ GRAV+ NLAST N45 Z45+ MW45+ GV45+

    --- ----- ------ ------ ----- --- ------ ------ -------

    0 1.000 183.0 0.829 45 45 0.0065 656.0 1.0017

    CONTROL DATA

    ------------

    MOLECULAR WEIGHT OF THE PLUS FRACTION ...... MWPLUS 183.00000

    SPECIFIC GRAVITY OF THE PLUS FRACTION ...... GPLUS 0.83450

    MOLE FRACTION FOR THE HEAVY FRACTION ....... ZPLUS 0.14200

    WEIGHT FRACTION FOR THE HEAVY FRACTION ..... WTPLUS 0.00000

    CARBON NUMBER OF THE HEAVY FRACTION ........ NCOMP 7

    HIGHEST CARBON NUMBER IN THE DISTRIBUTION .. NLAST 45

    FINAL NUMBER OF PSEUDO COMPONENT GROUPS .... NG 3BRACKET MOLECULAR WEIGHTS FOR REGROUPING ... MWGRP 125.00000 300.00000

    GAMMA DISTRIBUTION ALPHA PARAMETER ......... ALPHA 1.00000

    MINIMUM MOLECULAR WEIGHT IN PLUS FRACTION .. ETA 92.00000

    AVERAGE WATSON CHARACTERIZATION FACTOR ..... WAT 0.00000

    MAXIMUM NUMBER OF ITERATIONS ............... MAXIT 20

    CRITICAL PROPERTIES COMPUTED FROM .......... CORRELATIONS

    CRITICAL TEMPERATURE CORRELATION ........... RIAZI AND DAUBERT

    CRITICAL PRESSURE CORRELATION .............. RIAZI AND DAUBERT

    CRITICAL Z-FACTOR CORRELATION .............. RIAZI AND DAUBERT

    ACENTRIC FACTOR CORRELATION ................ EDMISTER

    SPECIFIC GRAVITY AND BOILING POINT DATA .... SIMULATION

    CONSTANT MOLECULAR WEIGHT INTERVAL ......... MWINC 12.00000

    C6 TO C7 MOLECULAR WEIGHT BOUNDARY ......... MWC6C7 92.00000

    SCN MOLE WEIGHT MOLE FRACTION WT FRACTION SPEC GRAV BOIL PT F UPPER WAT

    DATA CALC DATA CALC DATA CALC DATA CALC DATA CALC MW BD K-FAC

    --- ----- ----- ------ ------ ------ ------ ----- ----- ----- ----- ----- -----

    7 0. 98. 0.0000 0.0175 0.0000 0.0000 0.000 0.740 0. 218. 104. 11.86

    8 0. 110. 0.0000 0.0154 0.0000 0.0000 0.000 0.754 0. 256. 116. 11.86

    9 0. 122. 0.0000 0.0135 0.0000 0.0000 0.000 0.767 0. 292. 128. 11.86

    10 0. 134. 0.0000 0.0118 0.0000 0.0000 0.000 0.778 0. 327. 140. 11.86

    11 0. 146. 0.0000 0.0104 0.0000 0.0000 0.000 0.789 0. 359. 152. 11.86

    12 0. 158. 0.0000 0.0091 0.0000 0.0000 0.000 0.799 0. 391. 164. 11.86

    13 0. 170. 0.0000 0.0080 0.0000 0.0000 0.000 0.808 0. 421. 176. 11.86

    14 0. 182. 0.0000 0.0070 0.0000 0.0000 0.000 0.817 0. 450. 188. 11.86

    15 0. 194. 0.0000 0.0061 0.0000 0.0000 0.000 0.825 0. 478. 200. 11.86

    16 0. 206. 0.0000 0.0054 0.0000 0.0000 0.000 0.833 0. 506. 212. 11.86

    17 0. 218. 0.0000 0.0047 0.0000 0.0000 0.000 0.841 0. 532. 224. 11.86

    18 0. 230. 0.0000 0.0041 0.0000 0.0000 0.000 0.848 0. 558. 236. 11.86

    19 0. 242. 0.0000 0.0036 0.0000 0.0000 0.000 0.855 0. 583. 248. 11.86

    20 0. 254. 0.0000 0.0032 0.0000 0.0000 0.000 0.861 0. 607. 260. 11.86

    21 0. 266. 0.0000 0.0028 0.0000 0.0000 0.000 0.868 0. 631. 272. 11.86

    22 0. 278. 0.0000 0.0024 0.0000 0.0000 0.000 0.874 0. 654. 284. 11.86 23 0. 290. 0.0000 0.0021 0.0000 0.0000 0.000 0.880 0. 677. 296. 11.86

    24 0. 302. 0.0000 0.0019 0.0000 0.0000 0.000 0.885 0. 699. 308. 11.86

    25 0. 314. 0.0000 0.0016 0.0000 0.0000 0.000 0.891 0. 720. 320. 11.86

    26 0. 326. 0.0000 0.0014 0.0000 0.0000 0.000 0.896 0. 742. 332. 11.86

    27 0. 338. 0.0000 0.0013 0.0000 0.0000 0.000 0.901 0. 763. 344. 11.86

    28 0. 350. 0.0000 0.0011 0.0000 0.0000 0.000 0.906 0. 783. 356. 11.86

    29 0. 362. 0.0000 0.0010 0.0000 0.0000 0.000 0.911 0. 803. 368. 11.86

    30 0. 374. 0.0000 0.0008 0.0000 0.0000 0.000 0.916 0. 823. 380. 11.86

    31 0. 386. 0.0000 0.0007 0.0000 0.0000 0.000 0.921 0. 843. 392. 11.86

    32 0. 398. 0.0000 0.0006 0.0000 0.0000 0.000 0.925 0. 862. 404. 11.86

    33 0. 410. 0.0000 0.0006 0.0000 0.0000 0.000 0.929 0. 881. 416. 11.86

    34 0. 422. 0.0000 0.0005 0.0000 0.0000 0.000 0.934 0. 899. 428. 11.86

    35 0. 434. 0.0000 0.0004 0.0000 0.0000 0.000 0.938 0. 917. 440. 11.86

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    36 0. 446. 0.0000 0.0004 0.0000 0.0000 0.000 0.942 0. 935. 452. 11.86

    37 0. 458. 0.0000 0.0003 0.0000 0.0000 0.000 0.946 0. 953. 464. 11.86

    38 0. 470. 0.0000 0.0003 0.0000 0.0000 0.000 0.950 0. 971. 476. 11.86

    39 0. 482. 0.0000 0.0003 0.0000 0.0000 0.000 0.954 0. 988. 488. 11.86

    40 0. 494. 0.0000 0.0002 0.0000 0.0000 0.000 0.957 0. 1005. 500. 11.86

    41 0. 506. 0.0000 0.0002 0.0000 0.0000 0.000 0.961 0. 1022. 512. 11.86

    42 0. 518. 0.0000 0.0002 0.0000 0.0000 0.000 0.965 0. 1039. 524. 11.86

    43 0. 530. 0.0000 0.0002 0.0000 0.0000 0.000 0.968 0. 1055. 536. 11.86

    44 0. 542. 0.0000 0.0001 0.0000 0.0000 0.000 0.972 0. 1071. 548. 11.86

    45 0. 656. 0.0000 0.0009 0.0000 0.0000 0.000 1.002 0. 1218. 0. 11.86

    1PLUS FRACTION EXTENDED ANALYSIS

    -------------------------------

    SCN MOL FRAC M. W. TC PC ZC AC GRAV P-R DJK

    (F) (PSIA)

    --- -------- ------ -------- -------- ------- ------- ------- -------

    7 0.01754 97.9 549.83 442.10 0.2651 0.2913 0.7403 0.0368

    8 0.01538 109.9 590.04 406.13 0.2590 0.3232 0.7541 0.0388

    9 0.01348 121.9 627.43 376.39 0.2536 0.3537 0.7666 0.0405

    10 0.01181 133.9 662.45 351.33 0.2488 0.3832 0.7781 0.0421

    11 0.01035 145.9 695.46 329.88 0.2445 0.4117 0.7888 0.0436

    12 0.00907 157.9 726.71 311.29 0.2406 0.4395 0.7988 0.0450

    13 0.00795 169.9 756.43 295.00 0.2371 0.4666 0.8081 0.0463

    14 0.00697 181.8 784.68 280.64 0.2338 0.4932 0.8169 0.0476

    15 0.00611 193.8 811.82 267.79 0.2308 0.5195 0.8252 0.0487

    16 0.00536 205.8 837.86 256.25 0.2280 0.5454 0.8332 0.0498

    17 0.00469 217.8 862.91 245.81 0.2254 0.5710 0.8407 0.0509

    18 0.00411 229.8 887.07 236.33 0.2230 0.5965 0.8479 0.0519

    19 0.00361 241.8 910.41 227.67 0.2207 0.6217 0.8548 0.0529

    20 0.00316 253.8 932.99 219.73 0.2185 0.6469 0.8614 0.0538 21 0.00277 265.8 954.88 212.41 0.2165 0.6720 0.8677 0.0547

    22 0.00243 277.8 976.12 205.64 0.2146 0.6970 0.8738 0.0555

    23 0.00213 289.8 996.76 199.36 0.2127 0.7220 0.8797 0.0564

    24 0.00187 301.8 1016.84 193.52 0.2110 0.7470 0.8854 0.0572

    25 0.00163 313.8 1036.40 188.06 0.2093 0.7721 0.8909 0.0579

    26 0.00143 325.8 1055.48 182.95 0.2077 0.7972 0.8962 0.0587

    27 0.00126 337.8 1074.09 178.16 0.2062 0.8225 0.9014 0.0594

    28 0.00110 349.7 1092.27 173.66 0.2048 0.8478 0.9064 0.0601

    29 0.00096 361.7 1110.04 169.42 0.2034 0.8733 0.9113 0.0608

    30 0.00085 373.7 1127.42 165.41 0.2020 0.8989 0.9160 0.0614

    31 0.00074 385.7 1144.44 161.62 0.2007 0.9247 0.9206 0.0621

    32 0.00065 397.7 1161.12 158.03 0.1995 0.9507 0.9251 0.0627

    33 0.00057 409.7 1177.46 154.62 0.1983 0.9769 0.9295 0.0633

    34 0.00050 421.7 1193.49 151.38 0.1971 1.0034 0.9338 0.0639

    35 0.00044 433.7 1209.22 148.30 0.1960 1.0300 0.9379 0.0645

    36 0.00038 445.7 1224.66 145.36 0.1949 1.0570 0.9420 0.0651

    37 0.00034 457.7 1239.83 142.56 0.1939 1.0842 0.9460 0.0656

    38 0.00029 469.7 1254.74 139.88 0.1929 1.1118 0.9499 0.0662

    39 0.00026 481.7 1269.40 137.31 0.1919 1.1396 0.9537 0.0667 40 0.00023 493.7 1283.82 134.86 0.1909 1.1678 0.9574 0.0672

    41 0.00020 505.7 1298.01 132.50 0.1900 1.1964 0.9611 0.0678

    42 0.00017 517.7 1311.98 130.24 0.1891 1.2253 0.9647 0.0683

    43 0.00015 529.7 1325.74 128.07 0.1882 1.2546 0.9682 0.0687

    44 0.00013 541.7 1339.29 125.99 0.1874 1.2843 0.9716 0.0692

    45 0.00092 656.0 1459.48 109.47 0.1802 1.5921 1.0017 0.0734

    1PLUS FRACTION PSEUDOIZATION

    ---------------------------

    NO. MOL FRAC M. W. TC PC ZC AC GRAV P-R DJK

    (F) (PSIA)

    --- -------- ------ -------- -------- ------- ------- ------- -------

    1 0.04640 108.8 585.69 411.09 0.2609 0.3200 0.7533 0.0387

    2 0.08054 187.5 790.04 283.80 0.2411 0.5033 0.8239 0.0485

    3 0.01507 387.4 1138.35 165.63 0.2067 0.9360 0.9243 0.0626

    ---------------------------------------------------------------------

    AVG 0.14200 183.0 760.23 312.85 0.2643 0.4893 0.8290 0.0493

    PLUS PROPERTIES WRITTEN TO UNIT 22

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    1

    **************************************************************************

    * *

    * DDDDDD EEEEEEE SSSSS KK KK TTTTTTTT OOOOO PPPPPP *

    * DD DD EE SS SS KK KK TT OO OO PP PP *

    * DD DD EE SS KK KK TT OO OO PP PP *

    * DD DD EEEEE SSSSS KKKK TT OO OO PPPPPP *

    * DD DD EE SS KK KK TT OO OO PP *

    * DD DD EE SS SS KK KK TT OO OO PP *

    * DDDDDD EEEEEEE SSSSS KK KK TT OOOOO PP *

    * *

    * PPPPPP VV VV TTTTTTTT *

    * PP PP V V TT *

    * PP PP VV VV TT *

    * PPPPPP V V TT *

    * PP VVVV TT *

    * PP VV TT *

    * PP VV TT *

    * *

    * PHASE BEHAVIOUR PROGRAM *

    * *

    * COPYRIGHT 1984, 1985, 1986, 1987, 1988 *

    * 1989, 1990, 1991, 1992, 1993 *

    * 1994, 1995, 1996, 1997 *

    * LANDMARK GRAPHICS CORPORATION *

    * ALL RIGHTS RESERVED *

    * *

    * VERSION 4.0 CREATED 01 JUN 1997 *

    * ** LL AAAAA N NN DDDDDD M M AAAAA RRRRRR KK KK *

    * LL AA AA NN NN DD DD MM MM AA AA RR RR KK KK *

    * LL AA AA NNN NN DD DD M M M M AA AA RR RR KK KK *

    * LL AAAAAAA NN N NN DD DD M MM M AAAAAAA RRRRRR KKKK *

    * LL AA AA NN NNN DD DD M M AA AA RR RR KK KK *

    * LL AA AA NN NN DD DD M M AA AA RR RR KK KK *

    * LLLLLLL AA AA NN N DDDDDD M M AA AA RR RR KK KK *

    * *

    * GGGGG RRRRRR AAAAA PPPPPP HH HH IIII CCCCC SSSSS *

    * GG GG RR RR AA AA PP PP HH HH II CC CC SS SS *

    * GG RR RR AA AA PP PP HH HH II CC SS *

    * GG RRRRRR AAAAAAA PPPPPP HHHHHHH II CC SSSSS *

    * GG GGG RR RR AA AA PP HH HH II CC SS *

    * GG GG RR RR AA AA PP HH HH II CC CC SS SS *

    * GGGGG RR RR AA AA PP HH HH IIII CCCCC SSSSS *

    * *

    ***************************************************************************

    1 *********************************************

    * * * D E S K T O P - P V T *

    * *

    * PHASE BEHAVIOUR PROGRAM *

    * *

    * VERSION 4.0 *

    * *

    * COPYRIGHT 1984, 1985, 1986, 1987, 1988 *

    * 1989, 1990, 1991, 1992, 1993 *

    * 1994, 1995, 1996, 1997 *

    * LANDMARK GRAPHICS CORPORATION *

    * ALL RIGHTS RESERVED *

    * *

    *********************************************

    SEQUENCE

    NUMBER CARD IMAGES OF THE INPUT DATA

    -------- ---------------------------------------------------------------------

    X C ------------------------------

    X C DESKTOP-PVT EXAMPLE PROBLEM #1

    X C GOOD OIL #8 - REGRESSION

    X C VOLATILE OIL EXAMPLE

    X C ------------------------------

    X C

    X C

    X C -------------------------

    X C REGRESSION VARIABLES ARE:

    X C (1) OMEGA C8

    X C (2) OMEGB C8

    X C (3) OMEGA C14

    X C (4) OMEGB C14

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    X C (5) OMEGA C30

    X C (6) OMEGB C30

    X C (7) DJK C1-C8

    X C (8) DJK C1-C14

    X C (9) DJK C1-C30

    X C (10) OMEGA C1

    X C (11) OMEGA C1

    X C -------------------------

    X C

    1 R REGRESS

    2 R VARIABLE MIN INIT MAX

    3 R 1 .7 1. 1.3

    4 R 2 .7 1. 1.3

    5 R 3 .7 1. 1.3

    6 R 4 .7 1. 1.3

    7 R 5 .7 1. 1.3

    8 R 6 .7 1. 1.3

    9 R 7 .7 1. 1.3

    10 R 8 .7 1. 1.3

    11 R 9 .7 1. 1.3

    12 R 10 .7 1. 1.3

    13 R 11 .7 1. 1.3

    X C

    14 R IMAX IPRINT H TOL1 TOL2 TOL3

    15 R 20 0 X X X X

    X C

    16 R COMP MW TC PC ZC ACENTRIC OMEGAA OMEGAB

    17 R C1 X X X X X 10 11

    18 R C8 X X X X X 1 2

    19 R C14 X X X X X 3 4 20 R C30 X X X X X 5 6

    X C

    21 R DJK C1

    22 R C8 7

    23 R C14 8

    24 R C30 9

    X C

    25 R ENDREG

    X C

    X C ----------------------------------------

    X C INITIALIZE AFTER SPLIT OF HEAVY FRACTION

    X C ----------------------------------------

    X C

    1 EOS PR

    2 COMPONENTS

    3 CO2 C1 C2 C3 NC4 NC5 C6 C8 C14 C30

    4 PROPERTIES

    5 COMP MW TC PC ZC ACENTRIC OMEGAA OMEGAB

    6 C8 108.82 585.69 411.09 0.26093 0.32000 X X 7 C14 187.49 790.04 283.80 0.24105 0.50331 X X

    8 C30 387.42 1138.35 165.63 0.20672 0.93601 X X

    X C

    9 DJK C1

    10 C8 0.038665

    11 C14 0.048547

    12 C30 0.062598

    X C

    13 ENDEOS

    X C

    X PVTFILE

    X C

    X C -------------------

    X C SATURATION PRESSURE

    X C -------------------

    X C

    14 PSAT

    15 COMPOSITION 0.0584 0.5043 0.0965 0.0875 0.0589 0.0295 0.0229

    16 0.046396 0.080535 0.015069 17 TEMP F 276

    18 BPEXP PSIG 4375

    X C

    X C --------------

    X C PHASE ENVELOPE

    X C --------------

    X C

    19 ENVELOPE

    20 COMPOSITION 0.0584 0.5043 0.0965 0.0875 0.0589 0.0295 0.0229

    21 0.046396 0.080535 0.015069

    22 TEMP F -100 800 10 600 800 10

    23 PSAT PSIG 2000 6000 2000 100 300 100

    X C

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    X C --------------

    X C LIQUID DENSITY

    X C --------------

    X C

    X C NOTE: LIQUID DENSITY DATA IS GIVEN IN THE REPORT

    X C IN THE CONSTANT COMPOSITION EXPANSION TEST.

    X C

    24 LIQDEN

    25 COMPOSITION 0.0584 0.5043 0.0965 0.0875 0.0589 0.0295 0.0229

    26 0.046396 0.080535 0.015069

    27 TEMP 276 F

    28 PRES PSIG 6000 4375

    29 DEXP GM/CC .4924 .4530

    X C

    X C ------------------------------

    X C CONSTANT COMPOSITION EXPANSION

    X C ------------------------------

    X C

    X C NOTE: XLIQ IS USED BECAUSE DATA IS DEFINED AS

    X C LIQUID VOLUME AT PRESSURE RELATIVE TO

    X C VOLUME AT SATURATION PRESSURE.

    X C

    30 CCEXP

    31 COMPOSITION 0.0584 0.5043 0.0965 0.0875 0.0589 0.0295 0.0229

    32 0.046396 0.080535 0.015069

    33 TEMP 276 F

    34 BUBPT 4375 PSIG

    35 PRES VREL XLIQ ZG

    36 6000 0.9200 X X

    37 5000 0.9613 X X 38 4500 0.9909 X X

    39 4375 1.0000 1.000 X

    40 4328 1.0052 X X

    41 4300 X .651 X

    42 4267 1.0117 X X

    43 4230 1.0158 X X

    44 4150 X .570 X

    45 4059 1.0368 X X

    46 3960 X .530 X

    47 3709 1.0883 X X

    48 3408 1.1472 X X

    49 2688 1.3595 X X

    50 1962 1.7834 X X

    51 1271 2.7310 X X

    52 951 3.6866 X X

    X C

    X C -------------------------

    X C CONSTANT VOLUME DEPLETION

    X C ------------------------- X C

    53 CVDEP

    54 COMPOSITION 0.0584 0.5043 0.0965 0.0875 0.0589 0.0295 0.0229

    55 0.046396 0.080535 0.015069

    56 TEMP 276 F

    57 BUBPT 4375 PSIG

    58 PRES 4375 3700 3000 2200 1400 700

    59 CO2 .0584 .0632 .0661 .0686 .0695 .0696

    60 C1 .5043 .6053 .6226 .6337 .6263 .5813

    61 C2 .0965 .0996 .1011 .1043 .1089 .1154

    62 C3 .0875 .0827 .0824 .0836 .0883 .1024

    63 C6 .0229 .0142 .0121 .0128 .0107 .0130

    64 MW C8 C30 183 138 129 120 115 116

    65 ZGAS X .893 .858 .860 .892 .939

    66 VPROD X .08753 .19629 .35179 .52727 .69232

    67 SLIQ X .501 .450 .414 .376 .333

    X C

    X C ------------------

    X C SURFACE SEPARATION X C ------------------

    X C

    68 SEP

    69 COMPOSITION 0.0584 0.5043 0.0965 0.0875 0.0589 0.0295 0.0229

    70 0.046396 0.080535 0.015069

    71 TEMP 276 F

    72 BUBPT 4375 PSIG

    73 DNSAT .4530 GM/CC

    74 TSTD 80.

    75 PSTD 0.

    76 BO 2.852

    77 PRES TEMP GORSP GORST SVF GRVG

    78 385. 80. X 2187. X X

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    79 50. 80. X 294. X X

    80 0. 80. X 173. X X

    X C

    81 END

    1NONLINEAR REGRESSION DATA

    -------------------------

    CONTROL VARIABLES

    -----------------

    IMAX IPRINT H TOL1 TOL2 TOL3

    ---- ------ ------- ------- ------- -------

    20 0 0.2000 0.0010 0.0010 0.0100

    INITIAL VALUES OF REGRESSION VARIABLES

    -----------------------------------------

    VARIABLE MINIMUM INITIAL MAXIMUM

    -------- ------- ------- -------

    1 0.7000 1.0000 1.3000

    2 0.7000 1.0000 1.3000

    3 0.7000 1.0000 1.3000

    4 0.7000 1.0000 1.3000

    5 0.7000 1.0000 1.3000

    6 0.7000 1.0000 1.3000

    7 0.7000 1.0000 1.3000 8 0.7000 1.0000 1.3000

    9 0.7000 1.0000 1.3000

    10 0.7000 1.0000 1.3000

    11 0.7000 1.0000 1.3000

    REGRESSION VARIABLE ASSIGNMENTS

    -------------------------------

    COMPONENT ACENTRIC OMEGA OMEGA

    NO. NAME MW TC PC ZC FACTOR A B PCHOR VSHFT

    --- ------ ---- ---- ---- ---- -------- ----- ----- ----- ------

    1 CO2 0 0 0 0 0 0 0 0 0

    2 C1 0 0 0 0 0 10 11 0 0

    3 C2 0 0 0 0 0 0 0 0 0

    4 C3 0 0 0 0 0 0 0 0 0

    5 NC4 0 0 0 0 0 0 0 0 0

    6 NC5 0 0 0 0 0 0 0 0 0 7 C6 0 0 0 0 0 0 0 0 0

    8 C8 0 0 0 0 0 1 2 0 0

    9 C14 0 0 0 0 0 3 4 0 0

    10 C30 0 0 0 0 0 5 6 0 0

    THERE ARE NO REGRESSION VARIABLES CORRESPONDING TO MOLE FRACTIONS.

    BINARY INTERACTION COEFFICIENTS

    -------------------------------

    1 2 3 4 5 6 7 8 9 10

    1

    2 0

    3 0 0

    4 0 0 0 5 0 0 0 0

    6 0 0 0 0 0

    7 0 0 0 0 0 0

    8 0 7 0 0 0 0 0

    9 0 8 0 0 0 0 0 0

    10 0 9 0 0 0 0 0 0 0

    PARAMETERS D AND E FOR VOLUME SHIFT PARAMETER CALCULATION

    D E

    0 0

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    K-COEFFICIENT OF PEDERSEN ET AL. VISCOSITY CORRELATION

    K-COEFFICIENT REGRESSION VARIABLE

    ------------- -------------------

    k(1) 0

    k(2) 0

    k(3) 0

    k(4) 0

    k(5) 0

    k(6) 0

    k(7) 0

    BINARY INTERACTION COEFFICIENTS FOR COMPUTING PSEUDO-

    CRITICAL TEMPERATURE OF PEDERSEN ET AL. VISCOSITY CORRELATION

    ------------------------------------------------------------------

    1 2 3 4 5 6 7 8 9 10

    1

    2 0

    3 0 0

    4 0 0 0

    5 0 0 0 0

    6 0 0 0 0 0

    7 0 0 0 0 0 0

    8 0 0 0 0 0 0 0

    9 0 0 0 0 0 0 0 0

    10 0 0 0 0 0 0 0 0 0

    1EQUATION OF STATE: PENG-ROBINSON

    COMPONENT PROPERTIES

    --------------------

    COMPONENT MOLE TC PC CRITICAL ACENTRIC OMEGA OMEGA PCHOR

    NO. NAME WEIGHT DEG F PSIA Z-FACTOR FACTOR A B

    -- ------ ------- -------- -------- -------- -------- -------- -------- -------

    1 CO2 44.01 87.90 1070.90 0.2742 0.22250 0.45724 0.07780 49.6

    2 C1 16.04 -116.60 667.80 0.2890 0.01260 0.45724 0.07780 71.0

    3 C2 30.07 90.10 707.80 0.2850 0.09780 0.45724 0.07780 111.0

    4 C3 44.10 206.00 616.30 0.2810 0.15410 0.45724 0.07780 151.0

    5 NC4 58.12 305.70 550.70 0.2740 0.20150 0.45724 0.07780 191.0

    6 NC5 72.15 385.70 488.60 0.2620 0.25240 0.45724 0.07780 231.0

    7 C6 84.00 463.00 468.30 0.2698 0.23130 0.45724 0.07780 271.0

    8 C8 108.82 585.69 411.09 0.2609 0.32000 0.45724 0.07780 351.0

    9 C14 187.49 790.04 283.80 0.2411 0.50331 0.45724 0.07780 591.9

    10 C30 387.42 1138.35 165.63 0.2067 0.93601 0.45724 0.07780 1236.7

    NUMBER OF VOLATILE COMPONENTS: 10

    BINARY INTERACTION COEFFICIENTS

    -------------------------------

    1 2 3 4 5 6 7 8 9 10

    1

    2 0.1500

    3 0.1500 0.0000

    4 0.1500 0.0000 0.0000

    5 0.1500 0.0200 0.0100 0.0100

    6 0.1500 0.0200 0.0100 0.0100 0.0000

    7 0.1500 0.0298 0.0100 0.0100 0.0000 0.0000

    8 0.1500 0.0387 0.0100 0.0100 0.0000 0.0000 0.0000

    9 0.1500 0.0485 0.0100 0.0100 0.0000 0.0000 0.0000 0.0000

    10 0.1500 0.0626 0.0100 0.0100 0.0000 0.0000 0.0000 0.0000 0.0000

    k-COEFFICIENT OF THE PEDERSEN ET AL. VISCOSITY CORRELATION----------------------------------------------------------

    NO. K-COEFFICIENT

    ----- ---------------

    k(1) 0.9746020E+01

    k(2) 0.1808340E+02

    k(3) 0.4126660E+04

    k(4) 0.4460550E+02

    k(5) 0.9765440E+00

    k(6) 0.8181340E+02

    k(7) 0.1564990E+05

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    BINARY INTERACTION COEFFICIENTS FOR THE

    PEDERSEN ET AL. VISCOSITY CORRELATION

    ---------------------------------------

    1 2 3 4 5 6 7 8 9 10

    1

    2 0.0000

    3 0.0000 0.0000

    4 0.0000 0.0000 0.0000

    5 0.0000 0.0000 0.0000 0.0000

    6 0.0000 0.0000 0.0000 0.0000 0.0000

    7 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

    8 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

    9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

    10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

    CORRELATION OF SOLUBILITY OF CO2 IN WATER

    -----------------------------------------

    Rsw(pure water) = A*P*( 1 - B*sin(C*P/(C*P+1) )

    A = A0 + A1*T + A2*T**2 + A3*T**3 + A4*T**4

    B = B0 + B1*T + B2*T**2 + B3*T**3 + B4*T**4

    C = A0 + C1*T + C2*T**2 + C3*T**3 + C4*T**4

    log( Rsw[brine]/Rsw[pure water] ) = S0 * S * T**S1

    where Rsw in scf/stb

    P in psia

    T in degree F

    S in weight percent solid

    A0 A1 A2 A3 A4

    1.1630599 -16.6303997 111.0730515 -376.8592529 524.8891602

    B0 B1 B2 B3 B4

    0.9650900 -0.2725500 0.0923400 -0.1008300 0.0997900

    C0 C1 C2 C3 C4

    1.2803000 -10.7566004 52.6962204 -222.3948822 462.6725464

    S0 S1

    -0.0280370 -0.1203900

    CORRELATION OF DENSITY OF CO2 SATURATED WATER

    ----------------------------------------------

    Den(lb/cu ft) = Den,1atm(lb/cuft) + 0.001 * D1 * Rsw(scf/stb)

    D1 = 5.80000

    IDEAL GAS STATE ENTHALPY COEFFICIENTS

    -------------------------------------

    H* = A + B*T + C*(T**2) + D*(T**3) + E*(T**4) + F*(T**5)WHERE THE UNITS ARE

    H* - BTU / LB-MOLE

    T - DEGREES RANKIN

    COMPONENT

    NO NAME A B C D E F

    -- ------ ---------- ---------- ---------- ---------- ---------- ----------

    1 CO2 0.210E+03 0.504E+01 0.445E-02 -0.117E-05 0.153E-09 -0.578E-14

    2 C1 -0.112E+03 0.917E+01 -0.472E-02 0.679E-05 -0.245E-08 0.312E-12

    3 C2 -0.631E+00 0.796E+01 -0.752E-03 0.879E-05 -0.387E-08 0.548E-12

    4 C3 -0.325E+02 0.761E+01 0.415E-02 0.950E-05 -0.472E-08 0.702E-12

    5 NC4 0.432E+03 0.573E+01 0.156E-01 0.301E-05 -0.244E-08 0.381E-12

    6 NC5 0.196E+04 -0.202E+00 0.318E-01 -0.623E-05 0.590E-09 -0.142E-13

    7 C6 0.000E+00 0.242E+01 0.343E-01 -0.477E-05 0.000E+00 0.000E+00

    8 C8 0.000E+00 0.392E+01 0.447E-01 -0.629E-05 0.000E+00 0.000E+00

    9 C14 0.000E+00 0.297E+01 0.741E-01 -0.974E-05 0.000E+00 0.000E+00

    10 C30 0.000E+00 0.111E+03 0.215E+00 -0.360E-04 0.000E+00 0.000E+00

    PVT PROPERTIES FORMATTED FOR SIMULATOR INPUT HAVE BEEN WRITTEN TO UNIT 22

    1SATURATION PRESSURE CALCULATION

    -------------------------------

    COMPONENT MOLE FRACTION

    --------- -------------

    CO2 0.05840

    C1 0.50430

    C2 0.09650

    C3 0.08750

    NC4 0.05890

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    NC5 0.02950

    C6 0.02290

    C8 0.04640

    C14 0.08054

    C30 0.01507

    TEMPERATURE SATURATION PRESSURE (PSIG ) DEN AT PSAT (LB/FT3) Z-FAC AT PSAT

    DEGREES F DATA CALC TYPE DATA CALC DATA CALC

    ----------- -------- -------- ---- -------- -------- ------ ------

    276.00 4375.000 3919.877 BP 0.0000 28.5103 0.0000 0.8891

    1CALCULATED COMPOSITIONS:

    ------------------------

    P = 3919.9 ZZ = 0.58400E-01 0.50430E+00 0.96500E-01 0.87500E-01 0.58900E-01

    0.29500E-01 0.22900E-01 0.46396E-01 0.80535E-01 0.15069E-01

    ZY = 0.85827 YY = 0.64949E-01 0.60176E+00 0.98682E-01 0.81770E-01 0.49343E-01

    0.22724E-01 0.16209E-01 0.27810E-01 0.34297E-01 0.24527E-02

    ZX = 0.88908 XX = 0.58400E-01 0.50430E+00 0.96500E-01 0.87500E-01 0.58900E-01

    0.29500E-01 0.22900E-01 0.46396E-01 0.80535E-01 0.15069E-01

    KV = 0.11121E+01 0.11933E+01 0.10226E+01 0.93451E+00 0.83774E+00

    0.77032E+00 0.70783E+00 0.59941E+00 0.42586E+00 0.16276E+00

    1PHASE ENVELOPE CALCULATION

    --------------------------

    COMPONENT MOLE FRACTION

    --------- -------------

    CO2 0.05840 C1 0.50430

    C2 0.09650

    C3 0.08750

    NC4 0.05890

    NC5 0.02950

    C6 0.02290

    C8 0.04640

    C14 0.08054

    C30 0.01507

    TEMPERATURE SATURATION PRESSURE (PSIG )

    DEGREES F ESTIMATE COMPUTED TYPE

    ----------- -------- -------- ------

    -100.00 ** NONE FOUND **

    -90.00 ** NONE FOUND **

    -80.00 ** NONE FOUND **

    -70.00 2000.000 842.706 BUBPT

    -60.00 ** NONE FOUND ** -50.00 ** NONE FOUND **

    -40.00 2000.000 1221.923 BUBPT

    -30.00 2000.000 1362.726 BUBPT

    -20.00 2000.000 1505.560 BUBPT

    -10.00 4000.000 1647.812 BUBPT

    0.00 4000.000 1787.778 BUBPT

    10.00 4000.000 1924.407 BUBPT

    20.00 4000.000 2057.060 BUBPT

    30.00 4000.000 2185.349 BUBPT

    40.00 4000.000 2309.043 BUBPT

    50.00 4000.000 2428.013 BUBPT

    60.00 4000.000 2542.194 BUBPT

    70.00 4000.000 2651.565 BUBPT

    80.00 4000.000 2756.138 BUBPT

    90.00 4000.000 2855.942 BUBPT

    100.00 4000.000 2951.023 BUBPT

    110.00 4000.000 3041.434 BUBPT

    120.00 6000.000 3127.238 BUBPT

    130.00 6000.000 3208.498 BUBPT 140.00 6000.000 3285.283 BUBPT

    150.00 6000.000 3357.661 BUBPT

    160.00 6000.000 3425.703 BUBPT

    170.00 6000.000 3489.477 BUBPT

    180.00 6000.000 3549.052 BUBPT

    190.00 6000.000 3604.495 BUBPT

    200.00 6000.000 3655.872 BUBPT

    210.00 6000.000 3703.248 BUBPT

    220.00 6000.000 3746.685 BUBPT

    230.00 6000.000 3786.243 BUBPT

    240.00 6000.000 3821.982 BUBPT

    250.00 6000.000 3853.959 BUBPT

    260.00 6000.000 3882.228 BUBPT

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    CO2 0.05840

    C1 0.50430

    C2 0.09650

    C3 0.08750

    NC4 0.05890

    NC5 0.02950

    C6 0.02290

    C8 0.04640

    C14 0.08054

    C30 0.01507

    TEMPERATURE PRESSURE LIQUID DEN (GM/CC ) ---- Z-FACTOR ----

    DEGREES F PSIG DATA CALC DATA CALC

    ----------- -------- -------- --------- -------- --------

    276.00 6000.000 0.4924 0.5079 0.00000 1.22203

    4375.000 0.4530 0.4704 0.00000 0.96307

    1CONSTANT COMPOSITION EXPANSION

    ------------------------------

    COMPONENT MOLE FRACTION

    --------- -------------

    CO2 0.05840

    C1 0.50430

    C2 0.09650

    C3 0.08750

    NC4 0.05890

    NC5 0.02950

    C6 0.02290 C8 0.04640

    C14 0.08054

    C30 0.01507

    SATURATION PRESSURE: NEWTON-RAPHSON

    FLASH CALCULATIONS: NEWTON-RAPHSON

    VISCOSITY CORRELATION: LOHRENZ, BRAY AND CLARK

    TEMPERATURE = 276.00 DEGREES F

    OBSERVED PSAT = 4375.00 PSIG (BUBPT)

    CALCULATED PSAT = 3919.88 PSIG (BUBPT)

    OBSERVED Z-FACTOR AT PSAT = 0.0000

    CALCULATED Z-FACTOR AT PSAT = 0.8891

    OIL DENSITY AT PSAT = 0.4567 GM/CC

    GAS DENSITY AT PSAT = 0.3288 GM/CC

    PRES REL. VOLUME LIQ VOL FRAC LIQ MOLE FRAC------- --------------- --------------- ---------------

    PSIG DATA CALC DATA CALC DATA CALC

    ------- ------ ------ ------ ------ ------ ------

    6000.0 0.9200 0.8991 0.0000 0.8991 0.0000 1.0000

    5000.0 0.9613 0.9386 0.0000 0.9386 0.0000 1.0000

    4500.0 0.9909 0.9638 0.0000 0.9638 0.0000 1.0000

    4375.0 1.0000 0.9709 1.0000 0.9709 0.0000 1.0000

    4328.0 1.0052 0.9737 0.0000 0.9737 0.0000 1.0000

    4300.0 0.0000 0.9753 0.6510 0.9753 0.0000 1.0000

    4267.0 1.0117 0.9773 0.0000 0.9773 0.0000 1.0000

    4230.0 1.0158 0.9796 0.0000 0.9796 0.0000 1.0000

    4150.0 0.0000 0.9846 0.5700 0.9846 0.0000 1.0000

    4059.0 1.0368 0.9905 0.0000 0.9905 0.0000 1.0000

    3960.0 0.0000 0.9972 0.5300 0.9972 0.0000 1.0000

    3709.0 1.0883 1.0310 0.0000 0.8338 0.0000 0.8034

    3408.0 1.1472 1.0847 0.0000 0.7258 0.0000 0.6657

    2688.0 1.3595 1.2817 0.0000 0.6033 0.0000 0.4938

    1962.0 1.7834 1.6740 0.0000 0.5286 0.0000 0.3834

    1271.0 2.7310 2.5538 0.0000 0.4666 0.0000 0.2963 951.0 3.6866 3.4459 0.0000 0.4363 0.0000 0.2573

    PRES OIL Z-FACTOR GAS Z-FACTOR OIL DENSITY GAS DENSITY

    ------- --------------- --------------- --------------- ---------------

    PSIG DATA CALC DATA CALC DATA CALC DATA CALC

    ------- ------ ------ ------ ------ ------ ------ ------ ------

    6000.0 0.0000 1.2220 0.0000 0.0000 0.0000 0.5079 0.0000 0.0000

    5000.0 0.0000 1.0636 0.0000 0.0000 0.0000 0.4866 0.0000 0.0000

    4500.0 0.0000 0.9833 0.0000 0.0000 0.0000 0.4738 0.0000 0.0000

    4375.0 0.0000 0.9631 0.0000 0.0000 0.0000 0.4704 0.0000 0.0000

    4328.0 0.0000 0.9555 0.0000 0.0000 0.0000 0.4690 0.0000 0.0000

    4300.0 0.0000 0.9509 0.0000 0.0000 0.0000 0.4682 0.0000 0.0000

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    4267.0 0.0000 0.9456 0.0000 0.0000 0.0000 0.4673 0.0000 0.0000

    4230.0 0.0000 0.9396 0.0000 0.0000 0.0000 0.4662 0.0000 0.0000

    4150.0 0.0000 0.9266 0.0000 0.0000 0.0000 0.4638 0.0000 0.0000

    4059.0 0.0000 0.9118 0.0000 0.0000 0.0000 0.4611 0.0000 0.0000

    3960.0 0.0000 0.8956 0.0000 0.0000 0.0000 0.4580 0.0000 0.0000

    3709.0 0.0000 0.8733 0.0000 0.8440 0.0000 0.4770 0.0000 0.2989

    3408.0 0.0000 0.8433 0.0000 0.8303 0.0000 0.4989 0.0000 0.2636

    2688.0 0.0000 0.7462 0.0000 0.8184 0.0000 0.5393 0.0000 0.1936

    1962.0 0.0000 0.6158 0.0000 0.8298 0.0000 0.5746 0.0000 0.1336

    1271.0 0.0000 0.4575 0.0000 0.8618 0.0000 0.6080 0.0000 0.0829

    951.0 0.0000 0.3701 0.0000 0.8842 0.0000 0.6245 0.0000 0.0612

    PRES OIL VISCOSITY GAS VISCOSITY SURF TENS

    ------- --------------- --------------- -----------

    PSIG DATA CALC DATA CALC DYNE/CM

    ------- ------ ------ ------ ------ -----------

    6000.0 0.0000 0.0850 0.0000 0.0000 0.0000E+00

    5000.0 0.0000 0.0754 0.0000 0.0000 0.0000E+00

    4500.0 0.0000 0.0705 0.0000 0.0000 0.0000E+00

    43