SPE-28589 Merril and Hartman a Comparison of Equation of State Tuning Methods

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SPE 28589

Sodety

of PetrokurlEn leers

A Comparison of Equation of State Tuning Methods

R.C. Merrill, BP Exploration; K.J. Hartman, Mobil E&P Technical Center; and J.L. Creek,

Chevron Petroleum Technology Co.

SPEMembers

@@@ 19% SocietY of petroleum Engineem, Inc.

E

Thii paper was prepared for prewntaticm at the SPE Wth Annual Technical Conferet?-caand Exhibition held in New Orleats, IA, U.S.A., 2S-28 September 1994.

This paper was aebcted for presentat ion by an SPE Program Commmee following review of infmmetion contelned in en ~act submitted by the authods). Conienf f of the ~-,

= w~t$d,.- .nc .- M@ad by’ tha Soctety o f P etrc4eum E nginecm and am 8ub@t to cormtion by t he

autf cds).

he material, as presented, does ml

necessarily refbti

any poaitbn of the Society of Pen’obum Engineem, itsofficer% o membrs, P8parepreeentedetSPE mwtingnw subjea wpwmak, ,*. - . y . . ... . . . . . ...... ..

.-... LU- ,--

-1. 1=,+*”.i.l.l)uniltOQ~Qf @ S.xbty

d~m E@~. ~~m~k~toan ~dwtia~~~.lllMrM~ my~WX. ~~tititidn~s*kw-m

ofwhen and by WI IOMma WIPW ~ Pm8snted. Wri te Libmrim, SPE, P.O. Sox 83S826, RMwdsIM

,7X 7YX3.W2S, U.S.A. Talex, 162245 SPEUT.

Abstract

Equations of state find widespread use for their

ability to describe a wide variety of reservcm

-.-:-

fiuid behaviour. However, this description is not

usually obtained through

a-priori

predictions.

The parameters of the equation of state (EoS) often

need adjusting (tuning) before yielding usable

reservoir predictions. During tuning, the

parameters of the EoS are adjusted to make the

predictions match a variety of experimental data.

consistency in the application of a technique is

more important than the technique itself.

The co-operative nature of this work serves as a

..----- $..1

:lliie**m*ifin

f p

inhnront ctrrmrrth of

Suuufzaalul Illu=lllallwll 0, sw- .. ...”.”... “.. -..-...

joint ventures. The participating companies have

used this cross-fertilisation to ensure the

technical integrity of their methods.

Introduction

Cubic equations of state (EoS) have found



2

A COMPARISONOF EQUATIONOFSTATETUNINGM~HODS

SPE 28589

~~e .f~aw f

*ha c.irvlnlc, n, *N- an,

,mtinn

fif

~)

UI Ill= mlllplc Uuulu

=Ufuallull WI

state also come into play in certain

circumstances.

Adjusting the parameters to overcome these

limitations is called “tuning” or “characterizing”

an equation of state.

Many methods have been

proposed for this process. Most involve changing

the description of the “heavy end or C7+ portion

of the fluid, while others alter other parameters

(for example see references J213 and others).

More recently, there have been discussions

regarding what sort of data should be used in the

tuning process.4

Our paper has different objectives, and these are

three-fold:

1)

Investigate how three different companies

would approach the tuning process for a

common set of data.

2)

Describe the choices made in the course of

the tuning processes.

3)

Compare the final results of the processes

and decide whether the different

approaches give

radically different

answers for

a-priori

predictions for

which there are no data.

In order to achieve these objectives it was

Data

The data forms the core of any equation of state

tuning process. This study is primarily concerned

with volatile oil data measured as part of a gas

injection study. Table 1 lists the experiments and

the measured quantities available.

During the EoS comparison different philosophies

of data treatment were immediately apparent.

Company A proceeded directly to the tuning step,

expecting that possible problems with the dataset

would be revealed during the tuning. Company B

.- ...4 ----

b: . —--:AA.:--

b.* A-4-

b-n 4..-:--

Spelll

I l lu le m i le w im lue lulg um uat a uc a~i LUI IUIg

the equation of state. Company C used an “extended

EoS” model to assess the data prior to the tuning

step.

Co.

B Cheds

Neither the sixteen stage differential liberation

(DL) nor the separator test data contained gas

gravity data. This made a rigorous mass material

balance check impossible to carry-out. It also

mm-ne=;i-+n~- nhanma in tha ti ininfi etrataau lean

llGuGsallaLGu9 Wtbalayu111111s2uD191e~sbutw~y ~-ww

below). The four stage differential liberation data

did not contain sufficient information to perform a

material balance, but it did have sufficient data to

construct

“Hoffman”

plotss of Ln[KP] vs.

“characterisation factor”. These are similar to

that shown in Figure 11. Hoffman plots are not



SPE28589

R.C. MERRILL, K. J. HARTMAN AND J. L. CREEK

3

“sense-checked” by plotting the data and

comparing to “experience.”

There was nothing

unusual about either the separator or the

differential liberation tests when taken in

isolation, however, when compared to each other

the DL’s GOR was 42% higher than that obtained in

the separator test.

Although large differences

between the DL and separator GOR are not

gn~~mrnon, particularly for volatile oils, this

seemed excessive, particularly for a reported oil

gravity of 43.1 ‘API. The overall gas gravity for

the separator test was “backed-out” using the

empirical relationship provided by McCain:6

~.= (% -0.01357R,7)

(1)

Pinif

This relationship yielded a gravity of 0.55, which

is less than that of methane. On the basis of this

analysis, we decided to omit the separator data

from further consideration. An exception to this

blanket omission was the density of the stock tank

oil.

The reported density of 810 kg/m3 is

consisieni with the C7+ density (837 k@n3)

which was determined by the experimental fluid

characterisation. We decided, therefore, to leave

it in the experimental data-set.

Co.cchras

The laboratory PVT and fluid composition data are

checked with the equation of state to establish the

14.7 to 1,000 psia and 100~50 “F. If the

equation of state predicts a bubble point pressure

for the separator liquid in excess of the separator

pressure

at separator temperature, the

composition is in error or the samples are

mnsidered to be of lesser quality. The calculated

composition of the gas in equilibrium with the

separator liquid at the bubble point pressure of

the separator liquid should agree with the

separator gas composition.

Company C built a 23 component model from the

experimental data. The composition was input and

the simple match of the bubble point pressure

made. Figures 3 and 4 compare the experimental

and estimated results.

The separator test scaled against the volume of

reservoir fluid are shown in Table 2. The gas-oil

ratio agreement is satisfactory. The volumetric

data are not satisfactory. The calculated residual

oil gravity was 42.45 ‘API compared with the

experimental value of 43.1 “APL

The data seem satisfactory ior ine work ai hand.

Note the high uncertainty in the Z values for the

differential and the poor agreement between

predicted and measured volumes for the separator

test.

Equation of State Tuning Methods



4

A COMPARISONOF EQUATIONOFSTATETUNINGMETHODS

SPE 28589

distribution function is fitted to available fluid

imposition data to obtain model parameters

specific to that fluid.

The continuous probability

function is then discretised using a modified

Gaussian quadrature technique to seiect ine besi

lumping scheme for the number of components

specified by the user.

The user can override this

feature and pick the starting carbon numbers of

the lumped fractions.

In this case, we used the C7+ splitting/lumping

package, and tried from two to five C7 +

components. We carried these cases through the

multi-dimension regression step described below.

The two-component C7+ fraction characterisation

had the best match of the static data. It was chosen

for the comparison for that reason, and not because

it had the minimum number of components.

n.----: -- -z *L- n-

rrwpwmrs

rJI uIe U7+ CG~pNK?RiS ii~~ iV3Si~fiWi

using a variation on Twu’s correlation. 14 This

method provides smoothly varying critical

properties for paraffinic hydrocarbon components

with carbon numbers up to about one hundred.

These properties are modified for the aromatic

mntent of the fluid based on molecular weight and

specific gravity.

If no specific gravity data are

supplied, a “typical” distribution is assigned

which assumes increasing aromaticity with

increasing molecular weight.

An aromaticity

factor, A, is defined in the following manner:

Tuning is done with a multi-dimensional

regression scheme.

A rotational discrimination

method is used to calculate parameter changes in

the non-linear regression so as to minimise the

objeciive of ine

error

funciion. ‘we

simultaneously perturb the regression parameters

and evaluate the Jacobean coefficient matrix

through numerical derivatives.

In this case, three regression parameters were

used. The C

7+

critical properties and acentric

factor were adjusted by regressing on the

aromaticity parameter. All binary interaction

parameters between the light and heavy

hydrocarbon components were varied together,

with the relationship between methane and the

heaviest component controlling.

The shift

parameters of the C7+ components were also

regressed together, so that changes within the C7+

I---., _- .----- -..-.-—-.,-

rracuon were syslemauc.

All of the static data (not the multi-contact data)

were used, with all points having equal weight.

Limited attempts were made with various

weighting schemes, but none significantly affected

the resulting match. The comparison of the tuned

model to the data and the other models is discussed

later.

CO.

B

Equations of State are customarily used to model



SPE 28589

R. C. MERRILL,K. J. HARTMAN AND J. L. CREEK

5

The Twu correlation is used to determine the

critical

properties of the

individual

pseudocomponents. The characterisation factor (as

defined by Whitson) is kept constant for all

-.-, mAAm*mnnnnnte

pmuuwwlllpnlwalk-.

fineaeinnallu /stthnl mh nd in

Ww--r”. .,.., ,- . . ..””~ . ..”. . . .

this case), the Kesler-Lee correlations are used

instead.’ 5

Compositions are @wavs dealt with in weight

fraction. This facilitates changing the C7 +

molecular weight (M. W.) which is used as the

primary tuning parameter. It also permits us to

change the M.W. basis of the fluid.

Many

laboratories report compositions based on n-

alkane M.W., however, for EoS tuning purposes we

usually use the M.W. suggested by Katz and

Firoozabadi.l 6

Binary interaction parameters are determined

using a modified Chueh-Prausnitz relationship:

(3)

The pre-multiplier Ai was set to zero for i2C4.

The exponent “p” was the second tuning parameter.

We normally start our tuning process by

calculating the material balance for each

After the mass and molar properties are matched,

the volumetric are adjusted by altering the shift

parameters of methane and the C6+ components. A

regression is used to match the reported densities.

Thn C -.

naramatnre ~~~ rnlatd by ?h~ fl trmtinn

,,,e “~+ ~-r ”.. ”.”.”

, “,-.”” . “..”,.-..

suggested by Jhaveri and Youngren.

The fit is then tested for internal consistency with

itself and general consistency with the data.

The lack of gas gravity data necessitated an

alteration to our tuning procedure. We could not

use the incremental mass of either the separator

or DL experiments as a guide for our tuning

process. Instead, we replaced the DL mass and

molar properties by the ~ GOR and the

relative volume, both relative to saturated

conditions. There are two reasons for choosing the

-—..---- _l--------- ---

-l .?---

sawralea rererence mnaumns:

1)

The DL process is a reservoir process and

thus should be referenced to reservoir

renditions.

2)

The last stage of a DL process (reduction to

atmospheric pressure) is often difficult to

simulate. Often the bulk of the error in a

fit occurs in this step. In our opinion, it

is unreasonable to bias the rest of the fit to

a point which is not relevant to the

reservoir depletion process.



6


SPE 28589

hypothetical component are optimised. Normally

ine mnsiani composition expansion ciaia wiih iiquia

volumes are the preferred data for regression.

The problem was simplified here by only

optimizing on the hypothetical component Qb

values. The differential liberation data was chosen

because of previous success with volatile oil

samples using these data. Similar results are

obtained regardless of whether the differential

liberation or the constant composition expansion

data are used for regression. The constant

composition expansion are the more reliable data

-,—-- —-

—-. - -,-, :- -_—----- z.-— .L -

-L--- --11

since no ma[erlai IS removeu worn me pnase GWI

during the experiment and the experimental steps

are easier to execute. The optimised f2b values

were mnverted to optimised Tc and Pc values by

solving

ac= Q

RTC 2

c

bc=Q,~

PC=

(5)

and assuming the f2a =

0.45724, that ac and b have

ennetsnt uah mc and finrfinn tha ual I me nf T- and P-

-..”.U. . . .-. ””” u.. ” ....”,..~ ,..” .U, ”w” “, . ~ u..- 8 ~

that

dlOW K2b =

0.07780 for each hypothetical

component.

We find that volatile oil data are difficult to fit

is even more striking when the relative volume is

-,.... —

—. . . .—-—.

alsplayeci in iis more usual Iormal Figure )j.

The underlying cause of this improvement in the

volumetric fit is due to the treatment of density.

The densities predicted by model A are

significantly less than those predicted by either

model B or model C. The residual density of this fit

is 772 kg/m3, for the B and C the values are 864

kg/m3 and 838 kg/m3. It should be recalled that

a residual oil density was not reported, however

the stock tank density from the separator test was

810 kg/m3.

The initial reservoir densities of all

three equations are similar, but the density

changes far more rapidly during depletion for

modelsB and C.

A second reason (largely dwarfed by the density

effect) lies in the mass of gas liberated in the last

(lowest pressure) DL step. Model A liberates

approximately 30% more gas than either Models B

Qrc.

At reasonable reservoir conditions (>500 psia),

the models give similar depletion behaviour, as

illustrated in the first figures of this series.

Turning io ine aeiaiiea composiiionai aaia oi ine

4 stage differential liberation, we see that all

equations yield similar K-values over the entire

pressure range measured (Figures 10 and 11).



SPE28589

R. C. MERRILL, K. J. HARTMAN AND J. L. CREEK 7

Table 3.

It should be remembered that both

Models B and C discounted this data.

Discussion

The three models were developed using remarkably

similar procedures, despite the independent nature

of the work. As a consequence, the models have

very similar critical property trends, as shown in

Figures 16 and 17. The largest differences occur

in the selection of the C7+ pseudocomponents. The

Semi-continuous thermodynamic approach seems

to be widely implemented, although each

implementation has minor variations.

These

techniques result in the selection of properties

with similar trends.

The single most important difference in tie modeis

.

is in the treatment of the experimental densities.

This is reflected in the Pen610ux shift parameters.

Co. B had the largest, and these were obtained by

regressing SXlieiyagjairiSiCMWty CHa. Ca. A% “w~ie

the smallest, and were obtained during a general

regression which included all the data points and

two other regression parameters (aromatidty and

binary interaction parameters).

All three models capture the decrease in volume

and release of gas when viewed from a reservoir

perspective.

However, models B and C fail to

capture the behaviour when viewed from a more

interesting; Co. C remariieo on ine size of Co. A and

Co. B’s parameters, whilst A and B were suqxised

by the smallness of Co. C’s. To some extent, it is

believed that the larger methane interaction

coefficients used by Co. B compensate for the

lowered molecular weight of the fluid.

Corrskferations 0/ Fit

Company A felt that good matches were obtained for

the DL and the CCE data. The separator match of

GOR, formation volume factor and stock tank

density shows the compromise that the regression

routine made with these three diverging data

points. Since all points had equal weight, and there

were more relative volume data, that data was then

weighted more heavily than the separator data.

The MCV experiment was not regressed against.

-–– —.,,. L-

rosslrxy, me compromise iii density fiiaich caused

by regressing against the separator data may have

influenced the liquid volumes predicted for the

MCV. The overall match was acceptable, although

if +hie t., cwa

*~~@m s. atsa

hnwina nnlw a einaln

1111= WGI= 6

uaaG, llavlvl~ vtlr~ u otll~mw

fluid sample would have been regarded as risky,

especially considering the volatile nature of the

fluid.

Companies B and C were disappointed in the

“goodness” of their respective fits.

Company B was concerned with the validity of the

separator test. The “sensibility check” revealed



a


SPE 28589

This is not consistent with the unusual gas gravity

calculated from the mass material balance

equation. This leads to the possibility that the feed

composition is incorrect. Feed compositions are

usually determined via a ‘singie stage fiash”,

where the overall composition is determined by

mathematically recombining the liquid and vapour

compositions.

An error in this step would be

difficult to detect but would lead to the observed

inconsistencies between the EoS predictions and

laboratory measurements.

Equation (1) can be used to back-calculate any of

the parameters.

All of the EoS models predict a

surface gas gravity of =0.73. If one uses this

value to back-calculate the stock tank gravity, one

obtains a density of 735 kg/m3.

This is

significantly less than the reported value of

810 kg/m3.

With the separator data in question, and

deliberately omitted from some of the fits, the

final results must be judged on the basis of the

reservoir information. On this basis, there is

little to choose between the models. Model A

provides a slightly better match to the volumetric

depletion data whilst models B and C perform a bit

better for the volumetric contact data.

A-Priori Displacement Study

the measured bubble

Doint.

Similar critical

–

volume vs. molecular weight relationships were

used for all three models and the Lohrenz-Bray -

Clark correlation was used to predict viscosity.20

Pressure drop profiies for the three cases were

very similar. Figure 18 shows the recovery in

pore volumes produced and the associated gas/oil

ratio at standard conditions. Figure 19 shows the

mole fraction of C7+ components in the produced

vapour phase (Yc7+) at reservoir conditions. The

figures are divided into regions 1,2,3 and 4.

Region 1 runs from O pore volumes injected (PVI)

to gas breakthrough. This occurs at 0.49 PVI for

the A and B models and slightly later, 0.53 PVI,

for the C model. For all three cases, production

after breakthrough consists almost entirely of

fluid which is vapour at reservoir conditions and

liquid at stock tank conditions.

The first shoulder (0.50 to 0.85 PVI) in the GOR

and YC7+ curves is Iabelled Region 2. It is the

result of equilibrium conditions between the

injected methane and the initial reservoir fluid.

Model B shows a somewhat different equilibrium

balance with Yc7+= 0.069 vs. 0.052 for the A and

C models.

Region 3 (0.85 to 1.20 PVI) on Figures 18

and 19 is a smooth extraction of the remaining

C2-C6 components from the liquid phase. This

extraction takes place very smoothly for all three



SPE28589

R.C. MERRILL,K. J. HARTMAN AND J. L. CREEK

9

give very similar results. The breakthrough for

Co. C was delayed by 0.04 PVI. Contrarily, in

n ..-..I 0 e.-

m-.+ eimilnr Iettandsrd

dh(?~ irIS~~~@~ D i31 IU u UIG IIIW w I IIICU I~,CU WA w

condition recoveries, and GORS ) or A and C are

most alike (Yc7+ in Region 2).

7L. . -

- . .- ,

,i*e

“ II, ~a~~

I IIGW I GSult= cer:mgy

~~p ~@Qn~

fQr

field-scale simulation of gas injection into volatile

oils.

Field-scale compositional simulations

frequently require minimisation of the number of

components.

Premature recovery may be

predicted with a model that has too few C7+

components. It is suggested that sensitivity studies

be conducted prior to ensure that the required

detail is maintained.

If slim tube data are

available, the EoS should be confirmed.

Conclusions

This work has provided information regarding the

current state of the art in equation of state tuning,

by illustrating and comparing tuning methods

three different companies. The following points

era al nr.

al~ ~leal.

1)

~)

The equation of state tuning process is

highly dependent upon high quality data.

When even one item of suspect data is

included it can bias the entire fit.

M- c, -f tha

=Ainipantc rslid q~n ~~

IWun= WI 111=p=, .Iwl ----- .-, O=-

7)

The

effect of different C7 +

characterisations was clearly seen during

an

CL..

~-Q~~O~~

D~~di 2ik r Q 2

S i ll iu

displacement. - - “ “ ““ “

data may be

sensitivities to

Qrnps.

Tuning to actual slim tube

necessary, as well as

number and type of C7+

Acknowledgements

The authors gratefully acknowledge the permission

of B.P. Exploration, Chevron, and Mobil to present

this work.

We also acknowledge the crucial role played by

Heriot-Watt University (Edinburgh, Scotland) for

providing both the data and the forum for this

exercise.

Symbols and Abbreviations

Bo

Pstk

Pinit

Y

v

MW

~

Formation volume factor, rb/stb

m---:... -$ bk- -*-.-L += Ir Al

~hdfis

Uel Iblly VI ~1= ~LuGm

LanmVII, UIDw,. .

Density of the reservoir oil, Ibm/f@.

Gas gravity (Air=l .0)

pseudo-molar volume, g/gmol, eqn 2

molecular weight

siope in equation 2



10


SPE 28589

1.

Coats, K. H. and Smart, G. T., “Applicationof a

Regression Based EoS PVT Program to Laboratory

Data,” SPE Reservoir Engineering, May 1984, 277-

299.

2.

Pedersen, K. S., Thomassen, P. and

Fredenslund, Aa., “Thermodynamics of Petroleum

Mixtures Containing Heavy Hydrocarbons. 1. Phase

Envelope Calculations by Use of the Soave-Redlich-

Kwong Equation of State,” Ind. Eng. Proc. Des. Dev.,

B, 1964,946-54.

3.

Whitson, C. H., ‘Characterizing Hydrocarbon

Plus Fractions:

SPEJ, 23, 1983 663-64.

4.

Merrill, R. C. and Newley, T. M. J., “A

Systematic Investigation into the Most Suitable Data

for the Development of Equations of State for

Petroleum Reservoir Fluids.” Fluid Phase Equil, 82,

1993, 101-110.

5

Hoffman,A. E., Crump,J. S. and Holcott,C. R.

“Equilibrium Constants for a Gas CondensateSystem”,

Tians. AIME (1953) 198,1-10.

6. McCain, W. D., Ih,e Pro- of Petr-

-, 2nd cd., Pennwell Books, 1990, p 318.

7.

Chien, M.C.H. and Monroy, M. “Two New

of State to Improve Volumetric Predictions,’ SPE

13118, presented at the 59th Annual SPE Meeting,

Sept 16-19, 1984.

13.

Whitson, C. H., Anderson, T. F. and Sareide,

l., “C7+ Characterisation of Related Equilibrium Fluids

using the Gamma Distribution,” in

G7+ Fractim

CharacterIs@

.

Chorn and Mansoori, ads., Taylor

& Francis, (New York, 1989), 35-56.

14

Twu, C. H.,

“An Internally Consistent

Correlation for Predicting the Critical Properties and

Molecular Weights of Petroleum and Coal-Tar Liquids,”

Fluid Phase Equilibria, 16,

137-150.

15.

Kesler, M. G. and Lee, B. L, “Improve

Prediction of Enthalpy Fraction, ”

Hydrocarbon

Processing, 55, 1976 153-8.

16.

Katz, D. L. and Firoozabadi, A. “Predicting

Phase Behaviour of Condensate/Crude-Oil Systems

Using Methane Interaction Coefficients,” J. Pe Tech.

Nov. 1978) 1649-1655, Trans AIME, 265.

17

Ikhranc R A and Rant+lnr .Q I

“Tha I lea nf a

““,,,”, ”, , . . . ., . ...” v-. .-.-., -. . . . . . . . -“-

. . .

Semicontinuous Description to Model the C7+ Fraction

in Equation of State Calculations”, SPE Reservoir

Engineering, 1041(August 1988).



SPE28589

11

1)

2)

3)

4)

5)

6)


Table 1

Data Used for Comparison

Reservoir Fluid Composition

Mole fractions, component densities, component

molecular weights.

Constant Composition Expansion:

Relative Volumes (V/Vsat), liquid saturations,

saturation pressure, saturation density.

Differential Liberation

Solution gas-oil ratio, Relative oil volume, Total

relative volume, Gas Z-Factor.

Four Stage DL:

Vapour compositions, equilibrium vapour and liquid

volumes, equilibrium gas density.

Forward contact experiment:

Equilibrium vapour and fiquid compositions, volumes,

and densities (4 contacts with methane).

Backwards contact experiment

same as (5). (3 contacts with methane).

For the CCE and DL experiments, the values are reported vs. depletion pressure. In the

contact experiments the values are reported vs. contact number and for the separator test

the values are either by stage oroverall.

In a backward contact experiment, the oil from the previous contact is brought into contact

with fresh gas.

In the forward contact experiment, the gas from a previous contact is

brought into contact with fresh oil.

These processes are meant to simulate the front and

back regions of a displacement front.

Table 2

CompanyC ChecksVs. SeparatorExperiment

Pressure

Temperature Rs

Expt Rs so Expt BO

psia

“F SCF/RESBBL SCF/RESBBL VoO/[RESBBL] Vo/V[RESBBL]



12

A COMPARISONOF EQUATIONOFSTATETUNINGM~ODS

N

N

0

N

0

0

Gas-Oil Ratio, Rs SCF/STB

gog~ -

0

“~

SPE 28589




. -

by”’’’-”’’”’”’””.

,

I

Q/..

;;:

I:*

lWAd - Z



2.8

4.0 1

EIpt

o ti, A

0 rxE

O

A ti c

. :

. 8

t

.

b I

3.0

2.0

2.2

4

>

D

8

1.0

-1

0

-2.0

-3,0

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.0

-5,0

-40 -3.0

-3.0

-1,0 0.0

1.0 2.0

3.0

C4mrac erisat ionFactor: b (1/ 1.-1 / T)

o

1275

2550

31025

5100

Pressure, peia

N

-1

N

Flgura 1 0. Four Staga D.L.:2S MPa K-v alues vs . c omponent

Figur4 9.

D if fe renti al L ibe ra ti on “ Fo rma ti on Vo lu me f ac tor

—.

Eapt

““”’

o

&.A

8*

e

0 CQ. e

***

BB

A Cac p

n

45

4.0

ErotVepouf

—Cc. A

—tie

---cc. c

EXF4

Lquid

—Ca. A

—CO. B

- - - C

40

2.0

35

30

0.0

~ 25

20

-4.0

15

J.

-6.0

10

5

-8.0

3.0

.2.0

-1.0

0.0

1.0

2.0

3.0

C4mracter iserbn Factor: b (l/T--l/T)

1 2 3

4

C on l ao l N um be r

Flgura

12. Forward Contacte, Phaee Maes

FIgUra 11. FourStep D.L: 4MPe KIvalbaaw6.coImponafd



N

-4

u

0.60

}

‘- —-. _=

-—-— -—

--4

—.-—.—--

.55

D

ExprVepow

—Cc. A

—CQB

---ac

Exps1.iqui4

—Ce. A

—can

---sac

.

.

.35

5

_ —.

,.--=--= --

e--- ---

-.

e----

- ~-----

0.30 --

025

&—

1-

1

2

3

4

COnSWS Number

Flguro 13. Forward Contact Experiment, Phase Densitiee

0.70

0.40

‘~ 0.40

0.30

0.20

0.10

1

2

3

COIIWI Nuntmr

F19UWIS.

Backward Contact Experiment,

PlhaeeDenaitiee

70

Contact Number

Figure 14. Backwards Contec te, Phaa a

MaSS

b.

m

A

s’

r

CO A

(%8

0

100

200

300

400

500

600

Molesulw

Wsieht

Figure 16. EoS Perametere, Critical Temparatura

Cn

2

M

m

ul

m

a

>

E



30

20

10

000 4..~ o

200 300

400 500 Soo

Mol*cular Wdghl

Figure 17:

Acent ri c F ac II or and C ri ti ca l Pr essu re

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0.00

[’r “~ ‘ ““’’’”’”’”’’”’”’”; — Co.A

1

2 \3

4

— -CO B

----. CO C

. .

L

. .

‘1.

\

&

— —

- .

7

f . . . , . , . - t ~,

. . . - - - - -- - - - -- - - -- - - - -- -

1

1

2

3

4

5

Pore Vdumss Injaded

Fiaure 19: Vsmorisad C-

at

Raaarvoironditions

,.

I

1 1 1

1

1 2 3 4

r

/

——.

-- -_... r_...

-.= .— -

. -5

J

1

.,..:]

—- Co. A

— -CO. B

---- . CO C

1

I

1 2 3 4 5

a

&e V dumm- I nj au ad

Figure 18: ProductiontS2andardondtions

o.a

g 0,5

8

.s

0.4

0.3

0.2

.:

~ 0.1

I

1 I

4

. . . . . . . . . .- --------- . . . . . . . . .. . . . . . -

.— —— —— ..-

1

2 3

Pc4e Voluma6 lr-IJaasd

Figure20: ProductiontReservoirCondidona

——

—– Co.

—

.4%.0

----. CO.

——

L—

4 s

I&

, 07

10’

10>

SPE-28589 Merril and Hartman a Comparison of Equation of State Tuning Methods

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Transcript of SPE-28589 Merril and Hartman a Comparison of Equation of State Tuning Methods