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CO2oil minimum miscibility pressure model

for impure and pure CO2 streams

Eissa M. El-M. Shokir

Petroleum Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia

Received 15 April 2006; received in revised form 8 December 2006; accepted 14 December 2006

Abstract

CO2 injection processes are among the effective methods for enhanced oil recovery. A key parameter in the design of CO2injection project is the minimum miscibility pressure (MMP), whereas local displacement efficiency from CO2 injection is highly

dependent on the MMP. From an experimental point of view, slim tube displacements, and rising bubble apparatus (RBA) tests

routinely determine the MMP. Because such experiments are very expensive and time-consuming, searching for fast and robust

mathematical determination of CO2oil MMP is usually requested. It is well recognized that CO2oil MMP depends upon the

purity of CO2, oil composition, and reservoir temperature. This paper presents a new model for predicting the impure and pure

CO2oil MMP and the effects of impurities on MMP. The alternating conditional expectation (ACE) algorithm was used to

estimate the optimal transformation that maximizes the correlation between the transformed dependent variable (CO2oil MMP)

and the sum of the transformed independent variables. These independent variables are reservoir temperature (TR), oil compositions

(mole percentage of volatile components (C1 and N2), mole percentage of intermediate components (C2C4, H2S and CO2), and

molecular weight of C5+ (MWC5+)), and non-CO2 components (mole percentage of N2, C1, C2C4, and H2S) in the injected CO2.

The validity of this new model was successfully approved by comparing the model results to the pure and impure experimental

slim-tube CO2oil MMP and the calculated results for the common pure and impure CO2oil MMP correlations. The new model

yielded the accurate prediction of the experimental slim-tube CO2oil MMP with the lowest average relative and average absolute

error among all tested impure and pure CO2oil MMP correlations. In addition, the new model could be used for predicting the

impure CO2oil MMP at higher fractions of non-CO2 components.

2007 Elsevier B.V. All rights reserved.

Keywords: Alternating conditional expectation (ACE); Minimum miscibility pressure (MMP); CO2; Miscible flooding

1. Introduction

MMP, as the name implies, is the minimum pressure

at which the injected gas (CO2 or hydrocarbon gas) can

achieve dynamic miscibility with the reservoir oil

(Stalkup, 1983; Benmekki and Mansoori, 1988; Man-

soori et al., 1989; Jaubert and Wolf, 1998; Wang and

Orr, 2000). An inaccurate prediction of MMP may result

in significant consequences. For example, recommen-

dation for a high operating level of MMP may result in

greatly inflated operation costs as well as occupational

health concerns. On the other hand, if the suggested

MMP is too low, the miscible displacement process

would become ineffective, leading to a high risk of

process failure. Thus, accurate estimation of MMP

would bring significant economic benefits. It is well

recognized that CO2oil MMP depends upon the purity

Journal of Petroleum Science and Engineering 58 (2007) 173185

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of CO2, oil composition, and reservoir temperature.

Various correlations reported in the literature are related

to a unique set of reservoir and fluid conditions; hence,

using of such correlations can lead to an erroneous

estimate of the MMP. From the literature review, pure

CO2oil MMP correlations have been reported inCronquist (1978), Lee (1979), Yellig and Metcalfe

(1980), Holm and Josendal (1982), Orr and Jensen

(1984), Alston et al. (1985), Glaso (1985), Huang et al.

(2003), and Emera and Sarma (2004). On the other

hand, impure CO2oil MMP correlations have been

reported in Kovarik (1985), Alston et al. (1985),

Sebastian et al. (1985), Eakin and Mitch (1988), Dong

(1999), and Emera and Sarma (2005). In addition, pure

or impure CO2oil MMP correlations have been

reported in Johnson and Pollin (1981), Orr and Silva

(1987), Enick et al. (1988), and Yuan et al. (2004).Several methods can be used to measure MMP for an

oilsolvent system. Traditionally, slim tube tests were

conducted for that purpose. The rising bubble apparatus

(RBA) approach was developed in the early 1980s and

is gaining acceptance as an efficient method to measure

MMP (Christiansen and Haines, 1987). An experimen-

tal method, which measures the density of the injection-

gas-rich upper phase in contact with stock tank oil as a

function of pressure was reported for measuring CO2

oil MMP at low temperatures below 50 C (Harmon and

Grigg, 1988). A similar approach was suggested using

the pressure at which the pure solvent achieves liquid-like densities (Orr and Jensen, 1984). This is obtained

by extrapolating the vapour pressure curve of the

solvent. Rao (1997), Gasem et al. (1993), and Rao and

Lee (2002) reported that direct measuring interfacial

tension of an oilsolvent mixture at reservoir conditions

could provide a rapid means of determining MMP.

Because such experiments are very expensive and

time-consuming, searching or developing a high

accuracy mathematical determination of the CO2oil

MMP is usually requested. Therefore, this paper

presents a new developed model to determine the

pure and impure CO2oil MMP for miscible displace-

ment based on the alternating conditional expectations

algorithm (ACE). The ACE reveals the underlying

statistical relationships among variables corrupted byrandom error. This ACE algorithm presented by

Breiman and Freidman (1985), as other similar non-

parametric statistical regression methods, is intended

to alleviate the main drawback of parametric regres-

sion, i.e., the mismatch of assumed model structure

and the actual data. In non-parametric regression a

priori knowledge of the functional relationship be-

tween the dependent variable Y and independent

variables, X1, X2, Xm, is not required. In fact, one

of the main results of non-parametric regression is

determination of the actual form of this relationship.The objective of this paper is to develop a general

impure and pure CO2oil MMP model that relates

MMP to reservoir temperature, oil compositions, and

CO2 impurities components, compare its efficiency

against the commonly used pure and impure CO2oil

MMP correlations, and investigate the effects of non-

CO2 components on the CO2oil MMP.

2. ACE algorithm

The general form of a linear regression model for p

independent variables (predictors), say X1, X2, , Xp,

Fig. 1. Optimal transformation of the general CO2oil MMP

dependent variable versus the sum of the optimal transformations ofthe independent variables.

Fig. 2. Experimental pure and impure CO2oil MMP versus the

resulted inverse of the optimal transformation of the general CO2oil

MMP dependent variable.

174 E.M.E.-M. Shokir / Journal of Petroleum Science and Engineering 58 (2007) 173185

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and a response variable Y is given by (Breiman and

Freidman, 1985; Wang and Murphy, 2004):

Y b0 Xpi1

biXi e 1

where 0, 1, , p

are the regression coefficients to be

estimated, and is an error term. Eq. (1) therefore

assumes that the response, Y, is a combination of linear

effects of X1, X2, , Xp and a random error component

. Conventional multiple regressions require a linear

functional form to be presumed a priori for the

regression surface, thus reducing the problem to that

of estimating a set of parameters. When the relationship

between the response and predictor variables is

unknown or inexact, linear parametric regression can

Table 1

Experimental CO2oil MMP from different literature sources

Reference Composition of CO2 stream TR C Oil composition Exp.

MMPType of CO2 stream CO2

(%)

H2S

(%)

C1(%)

C2C4(%)

N2(%)

MWC5+ Interm.

(%)

Vol.

(%)

Rathmell et al. (1971) Pure 100 0 0 0 0 42.8 204.10 20.95 17.07 10.35Dicharry et al. (1973) 100 0 0 0 0 54.4 171.20 31.82 29.48 11.00

Holm and Josendel (1974) 100 0 0 0 0 57.2 182.60 3.48 31.88 13.79

Shelton and Yarborough, 197 100 0 0 0 0 34.4 212.56 10.76 16.78 10.00

Graue and Zana (1981) 100 0 0 0 0 71.1 207.90 13.90 4.40 15.52

Metcalfe (1982) 100 0 0 0 0 32.2 187.77 14.28 10.50 6.90

Metcalfe (1982) 100 0 0 0 0 40.6 187.77 14.28 10.50 8.28

Metcalfe (1982) 100 0 0 0 0 57.2 187.77 14.28 10.50 11.86

Henry and Metcalfe (1983) 100 0 0 0 0 48.9 205.10 22.62 12.50 10.59

Thakur et al. (1984) 100 0 0 0 0 118.3 171.10 28.60 34.20 23.45

Alston et al. (1985) 100 0 0 0 0 67.8 203.81 22.90 31.00 16.90

Alston et al. (1985) 100 0 0 0 0 110 180.60 35.64 32.51 20.21

Alston et al. (1985) 100 0 0 0 0 71.1 221.00 6.99 41.27 23.45

Alston et al. (1985) 100 0 0 0 0 102.2 205.00 9.84 51.28 28.17

Alston et al. (1985) 100 0 0 0 0 80 240.70 8.60 53.36 26.76

Dong et al. (2001) 100 0 0 0 0 59 205.00 11.35 5.45 12.80

Metcalfe (1982) Impure 75 25 0 0 0 40.83 187.8 14.28 10.5 7.53

Metcalfe (1982) 50 50 0 0 0 40.83 187.8 14.28 10.5 6.55

Metcalfe (1982) 90 0 10 0 0 40.83 187.8 14.28 10.5 11.04

Metcalfe (1982) 45 45 10 0 0 40.83 187.8 14.28 10.5 8.83

Metcalfe (1982) 60 20 20 0 0 40.83 187.8 14.28 10.5 14.07

Metcalfe (1982) 67.5 23 10 0 0 58.33 187.8 14.28 10.5 12.41

Metcalfe (1982) 45 45 10 0 0 58.33 187.8 14.28 10.5 10.38

Metcalfe (1982) 60 20 20 0 0 58.33 187.8 14.28 10.5 17.24

Metcalfe (1982) 90 0 0 10 0 48.89 187.27 22.82 34.34 10.07

Metcalfe (1982) 90 0 0 10 0 48.89 187.27 22.82 34.34 9.31

Metcalfe (1982) 80 0 0 20 0 48.89 187.27 22.82 34.34 9.66

Metcalfe (1982) 90 0 0 10 0 65.56 187.27 22.82 34.34 13.04Metcalfe (1982) 80 0 0 20 0 65.56 187.27 22.82 34.34 10.5

Metcalfe (1982) 80 0 20 0 0 40.83 187.8 14.28 10.5 14.83

Metcalfe (1982) 68 22 10 0 0 40.83 187.8 14.28 10.5 10.28

Metcalfe (1982) 40 40 20 0 0 40.83 187.8 14.28 10.5 12.06

Metcalfe (1982) 75 25 0 0 0 58.33 187.8 14.28 10.5 10.35

Metcalfe (1982) 50 50 0 0 0 58.33 187.8 14.28 10.5 8.97

Metcalfe (1982) 90 0 10 0 0 58.33 187.8 14.28 10.5 15.17

Metcalfe (1982) 80 0 20 0 0 58.33 187.8 14.28 10.5 18.74

Metcalfe (1982) 55 25 20 0 0 58.33 187.8 14.28 10.5 16.45

Alston et al. (1985) 92.5 0 7.5 0 0 54.44 185.83 38.4 5.4 10.35

Alston et al. (1985) 90 0 10 0 0 54.44 185.83 40.3 29.3 13.1

Alston et al. (1985) 90.5 0 0 9.5 0 71.11 221 6.99 41.27 18.62

Alston et al. (1985) 95 0 4.9 0 0.1 71.11 207.9 13.9 4.4 16.83

Dong (1999) 90 10 0 0 0 60 200 1.31 0 11.6

Dong (1999) 80 20 0 0 0 60 200 1.31 0 11.4

Dong et al. (2001) 90.1 0 9.9 0 0 59 205 11.35 5.45 16.01

Dong et al. (2001) 89.8 0 5.1 0 5.1 59 205 11.35 5.45 20.51

175E.M.E.-M. Shokir / Journal of Petroleum Science and Engineering 58 (2007) 173185

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yield erroneous and even misleading results. This is the

primary motivation for the use of non-parametric

regression techniques, which make few assumptions

about the regression surface (Freidman and Stuetzle,

1981). These non-parametric regression methods broad-

ly classified into those, which do not transform the

response variable such as generalized additive models,

and those, which do such as the ACE, which is the focus

of this paper. The general form of the non-parametric

ACE algorithm is as following (Breiman and Freidman,

1985; Wang and Murphy, 2004):

hY a Xpi1

/iXi e 2

where is a function of the response variable, Y, and iare functions of the predictors X1, X2, , Xp. Thus, the

ACE model replaces the problem of estimating a linear

function of a p-dimensional variable X= (X1, X2, , Xp)

by estimating p separate one-dimensional functions i,

and using an iterative method. These transformations

are achieved by minimizing the unexplained variance of

a linear relationship between the transformed re-

sponse variable and the sum of transformed predictor

variables. For a given data set consisting of a response

variable Y and predictor variables X1, X2, , Xp, the

ACE algorithm starts out by defining arbitrary measur-

able zero-mean transformations functions (Y), 1(X1), , p(Xp). However, the error variance (

2) of a

linear regression of the transformed dependent variable

on the sum of transformed independent variables

(under the constraint, E2(Y)=1) has the following

equation:

e2h;/i; N;/p E hYXpi1

/iXi

" #( )2=Eh2Y

3

ACE algorithm minimizes 2 by holding E2(Y)=1,

E(Y) =E1(X1) ==Ep(Xp)= 0 through a series of

single-function minimizations, involving bivariate con-

ditional expectations. Thus, for a given set functions 1(X1), , p(Xp) minimization of

2 with respect to (Y)

yields the following equation:

hY EXpi1

/iXijY

" #=jjE X

p

i1

/iXi jY

" #jj 4

On the other hand, for a given (Y) minimization of2 with respect to a single function k(Xk) yields the

following equation:

/j;1Xj E hYXp

ipj

/iXi jXk

" #5

The real-valued measurable zero-mean functions i(Xi), i = 1, , p, and (Y) after iterative process of

minimizing 2 are called optimal transformations i(Xi),

i = 1, , p, and (Y) (Breiman and Freidman,

Table 2

Resulting coefficients for all the input parameters

n x A3 A2 A1 A0

1 Oil components TR 2.3660E06 5.5996E04 7.5340E02 2.9182E+00

2 Vol., % 1.3721E05 1.3644E03 7.9169E03 3.1227E01

3 Interm., % 3.5551E05 2.7853E03 4.2165E02 4.9485E02

4 MWC5+ 3.1604E06 1.9860E03 3.9750E01 2.5430E + 01

5 Non-CO2 components C1, % 1.0753E04 2.4733E03 7.0948E02 2.9651E01

6 C2C4, % 6.9446E06 7.9188E05 4.4917E02 7.8383E02

7 N2, % 0 3.7206E03 1.9785E01 2.5014E02

8 H2S, % 3.9068E

06

2.7719E

04

8.9009E

03 1.2344E

01

Fig. 3. Resulted CO2oil MMP from the new ACE-based model versus

the experimental impure and pure CO2oil MMP measurements.


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1985; Wang and Murphy, 2004). In the transformed

space, the response and predictor variables are related as

following:

h

Y Xp

i1/i Xi e

6

where e is the error not captured by the use of the ACE

transformations and is assumed to have a normal dis-

tribution with zero mean. The minimum regression error,

e, and maximum multiple correlation coefficient, are

related by e2 = 1.

3. Factors affecting CO2oil MMP

The main factors affecting CO2

oil MMP arereservoir temperature, oil composition, and purity of

injected gas (Johnson and Pollin, 1981; Alston et al.,

1985; Sebastian et al., 1985; Zuo et al., 1993; Nasrifar

and Moshfeghian, 2004; Yuan et al., 2004; Emera and

Sarma, 2005). The reservoir temperature has a big

impact on CO2oil MMP; as the temperature increases

the MMP increases and vice versa. Rathmell et al. (1971)

reported that the presence of volatile components, like

methane in the crude oil, leads to an increase in CO2oil

MMP while the presence of intermediates C2 to C6 can

reduce the CO2oil MMP. Metcalfe and Yarborough

(1974) argued that any CO2oil MMP correlation shouldtake into consideration the presence of light ends and

intermediates in the crude oil. Alston et al. (1985) in their

experimental slim tube tests proved that the oil recovery

at gas breakthrough is decreased, and CO2oil MMP is

increased by increasing the ratio between the amounts

of volatiles to intermediates in the crude oil composition.

In addition, Alston et al. (1985) stated that molecular

weight of C5+ is better for the correlation purpose than

oil API gravity. In addition, Cronquist (1978) used the

temperature and molecular weight of C5+ as correlation

parameters in addition to the volatile mole percentage ofC1 and N2 in the crude oil.

Furthermore, the presence of non-CO2 (e.g., C1,

H2S, N2, or intermediate hydrocarbons components

(such as C2, C3, and C4)) in the injected gas leads to a

big impact on the CO2oil MMP, either raising or

lowering it depending on the component type. In

general, the presence of H2S, or intermediate hydro-

carbon components in the injected gas decreases the

CO2oil MMP, while the presence of C1 or N2 in the

injected gas substantially increases the CO2oil MMP

(Lake, 1989). Nitrogen from flue gas and C1 from

reinjected CO2 are the large possible contaminants

to CO2 and recycled CO2. The separation of such

components from the injected gas is difficult and

costly. The current trend is to use the flue gas stream as

it is, if such impurities are below certain optimum level

in the injected gas stream. Therefore, the developed

model using the ACE algorithm was designed to reachthe optimal regression between the pure or impure

CO2oil MMP and the reservoir temperature, mole

percentage of oil components (volatiles (C1 and N2),

and intermediate components (C2C4, H2S and CO2)),

MWC5+ , a nd m ol e p er ce nt ag e o f t he n on -C O2components (C1, N2, H2S, and C2C4) in the injected

CO2.

4. Developing impure and pure CO2oil MMP model

As mentioned before, the ACE algorithm wasapplied to correlate the pure or impure CO2oil MMP

to the independent variables of reservoir temperature,

mole percentage of oil components, molecular weights

of the heavy fractions (C5+), and mole percentage of

CO2 impurities components. The experimental data that

were used to develop and validate the new model are

presented in Table 1. These experimental data were used

as reported in the literature without any modification or

manipulation and they have different miscibility criteria

and experimental conditions. This is contrary to the

approach of Alston et al. (1985), who interpreted the

data to satisfy their experimental miscibility criteria(90% recovery at solvent breakthrough).

A graphical user interface program, GRACE (Xue

et al., 1997), was used to derive a general pure or impure

CO2oil MMP model. Fig. 1 shows the resulted optimal

transformation of the general CO2oil MMP dependent

Fig. 4. The resulted pure CO2oil MMP from the new ACE-based

model versus the calculated pure CO2oil MMP from Cronquist

(1978), Lee (1979), Yellig and Metcalfe (1980), Alston et al. (1985),Glaso (1985), and Emera and Sarma (2004) correlations.


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Table 3Comparison of the pure CO2oil MMP resulted from the new ACE-based model to the calculated pure CO2oil MMP from different literature correlat

Reference Exp. pure CO2oil MMP,

MPa

ACE based Emera and

Sarma (2004)

Alston et al.

(1985)

Glaso (1985) Cronquist

(1978)

Model Model Model Model Model

MPa Error

(%)

MPa Error

(%)

MPa Error

(%)

MPa Error

(%)

MPa Erro

(%)

Rathmell et al. (1971) 10.35 10.27 0.75 10.35 0.04 10.09 2.52 10.01 3.31 8.33 19

Dicharry et al. (1973) 11.00 10.66 3.13 10.28 6.51 8.99 18.29 11.39 3.51 9.77 11

Holm and Josendel (1974) 13.79 14.23 3.22 14.92 8.22 14.31 3.79 17.32 25.63 11.07 19

Shelton and Yarborough (1977) 10.00 10.13 1.31 9.83 1.72 10.17 1.73 8.69 13.09 6.96 30

Graue and Zana (1981) 15.52 15.16 2.29 14.97 3.56 13.60 12.36 14.76 4.92 12.83 17

Metcalfe (1982) 6.90 7.29 5.62 7.36 6.64 7.05 2.16 8.19 18.72 5.60

18Metcalfe (1982) 8.28 8.74 5.53 8.82 6.49 8.26 0.28 9.44 14.05 7.01 15

Metcalfe (1982) 11.86 11.51 2.95 11.80 0.52 10.67 10.01 11.92 0.46 9.77 17

Henry and Metcalfe (1983) 10.59 10.73 1.36 11.18 5.52 10.65 0.57 11.10 4.84 9.27 12

Thakur et al. (1984) 23.45 23.30 0.66 22.09 5.80 17.93 23.54 20.44 12.85 21.70 7

Alston et al. (1985) 16.90 16.66 1.41 16.32 3.45 15.38 8.99 13.60 19.56 14.57 13

Alston et al. (1985) 20.21 20.65 2.19 21.37 5.72 17.82 11.84 19.11 5.47 21.07 4

Alston et al. (1985) 23.45 22.19 5.39 22.15 5.55 22.57 3.75 23.61 0.67 18.09 22

Alston et al. (1985) 28.17 27.65 1.84 28.15 0.07 26.50 5.92 25.18 10.61 26.17 7

Alston et al. (1985) 26.76 27.06 1.11 27.75 3.71 29.20 9.11 24.24 9.44 25.01 6

Dong et al. (2001) 12.80 13.07 2.13 12.96 1.27 12.07 5.73 12.52 2.16 10.61 17

ARE 0.25 0.65 5.37 0.85 15

AARE 2.55 4.05 7.54 9.33 16

Standard deviation of error 3.11 4.25 7.26 7.18 9

Correlation coefficient 0.998 0.993 0.967 0.970 0

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Table 5

Comparison of CO2oil MMP estimated from the new ACE-based model to the experimental slim tube CO 2oil MMP, and to the calculated CO2oil MMP from different literature correlations

References Type

of CO2

stream

CO2 H2S C1 C2

C4

N2 TR MWC7+ Interm. MWC5+ C2

C6

Vol. Exp.

MMP

ACE based model Yuan et al. (2004) Emera and

Sarma (2004)

Alston et al.

(1985)

Correlation Correlation Correlation

(%) (%) (%) (%) (%) (C) (%) (%) (%) MPa MMP

MPa

Error

(%)

MMP

MPa

Error

(%)

MMP

MPa

Error

(%)

MMP

MPa

Error

%

Eakin and Mitch

(1988)

Pure 100 0 0 0 0 82.2 281 20.59 261.64 26.09 6.74 21.35 19.22 0.10 18.61 0.13 23.10 0.08 23.24 0.0

Eakin and Mitch

(1988)

100 0 0 0 0 115.6 281 20.59 261.64 26.09 6.74 25.31 25.50 0.01 16.51 0.35 31.20 0.23 31.34 0.2

Alston et al.

(1985)

100 0 0 0 0 112.2 220 28.10 213.50 28 32.70 24.15 25.06 0.04 21.35 0.12 27.59 0.14 28.11 0.

Harmon and Grigg

(1988)

100 0 0 0 0 104.4 1 73 24.10 153.96 27.05 42.71 22.00 23.06 0.05 19.51 0. 11 1 7. 76 0.19 14.02 0.

Harmon and

Grigg (1988)

100 0 0 0 0 76.7 224 5.17 217.67 7.4 39.63 20.69 22.39 0.08 23.97 0.16 23.97 0.16 24.24 0.

Harmon and

Grigg (1988)

100 0 0 0 0 54.4 1 90 29.43 168.39 37.12 29.73 11.78 10.97 0.07 9.73 0. 17 10 .20 0.13 8.83 0.2

Harmon and

Grigg (1988)

100 0 0 0 0 81.1 220 16.78 198.40 26.78 9.82 15.97 15.89 0.00 1 8.60 0.16 17.00 0.06 15.19 0.0

ARE 0.04 7.95 5.05 0.0

AARE 4.98 17.18 14.39 18.9

Standard deviation

of error

0.06 0.18 0.16 0.2

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Metcalfe (1982) Impure 80 0 0 20.00 0 48.89 200 22.82 187.27 26.39 34.34 7 .93 7.94 0.001 17.58 1.22 7.90 0.004 7.61 0.0

Metcalfe (1982) 80 0 0 20.00 0 65.56 200 22.82 187.27 26.39 34.34 12.88 12.01 0.07 1 6.06 0.25 12.66 0.02 13.53 0.0

Metcalfe (1982) 80 0 20 0.00 0 40.83 206 14.28 187.80 24.44 10.50 14.83 14.82 0.00 19.28 0.30 14.85 0.00 21.30 0.4

Sebastian et al. (1985) 81 0 19 0.00 0 41.25 240 17.01 223.00 23.62 16.48 19.42 18.02 0.07 20.59 0.06 7.90 0.28 17.44 0.

Eakin and

Mitch (1988)

75 0 0 25.00 0 115.56 216 42.44 187.88 40.76 32.99 16.79 16.15 0.04 18.50 0.10 17.64 0.05 17.10 0.0

Eakin and

Mitch (1988)

90 0 0 10.00 0 82.22 281 20.59 261.64 26.09 6.74 16.66 16.80 0.01 22.96 0.38 17.30 0.04 17.28 0.0

Eakin and

Mitch (1988)

91.183 0 0 8.14 0 82.22 281 20.59 261.64 26.09 6.74 19.07 17.24 0.10 2 2.45 0.18 17.43 0.09 17.31 0.0

Eakin and

Mitch (1988)

90 0 0 10.00 0 115.56 281 20.59 261.64 26.09 6.74 21.31 23.07 0.08 19.62 0. 08 2 0. 51 0.04 20.49 0.0

Eakin and

Mitch (1988)

75 0 0 25.00 0 115.56 281 20.59 261.64 26.09 6.74 18.86 19.71 0.05 24.30 0.29 17.47 0.07 16.94 0.

Eakin and

Mitch (1988)

91.183 0 0 8.14 0 115.56 281 20.59 261.64 26.09 6.74 22.76 23.52 0.03 19.26 0. 15 20 .67 0.09 20.53 0.

Eakin and Mitch

(1988)

77.95 0 0 20.35 0 115.56 281 20.59 261.64 26.09 6.74 21.69 20.67 0.05 2 3.38 0.08 17.80 0.18 16.98 0.2

Eakin and Mitch

(1988)

90 10 0 0.00 0 115.56 281 20.59 261.64 26.09 6.74 24.04 24.90 0.04 19.62 0.18 23.94 0.00 24.39 0.0

Eakin and Mitch

(1988)

75 25 0 0.00 0 115.56 281 20.59 261.64 26.09 6.74 23.38 23.69 0.01 24.30 0.04 23.23 0.01 23.77 0.0

Eakin and Mitch

(1988)

30 0 45.7 20.00 4.3 82.22 216 42.44 187.88 40.76 32.99 34.38 34.95 0.02 15.19 0.56 153.00 3.45 20310.07 589.7

Eakin and Mitch

(1988)

30 0 45.7 20.00 4.3 82.22 281 20.59 261.64 26.09 6.74 27.52 30.65 0.11 38.04 0.38 148.45 4.39 19705.23 715.0

ARE 0.19 19.00 5.30 0.9

AARE 4.47 25.42 6.69 9.7

Standard deviation

of error

0.06 0.35 0.09 0.

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variable versus the sum of the optimal transformations

of the independent variables. The linear regression

between these dependent and independent variables is

shown in Eq. (7).

h

CO2 oil MMP X/1 TR /2 Vol: /

3 Interm: /

4 MWC5

zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{oil components

f/5 C1 /6 C2 C4 /

7 N2 /

8 H2Sg

zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{NonCO2 components7

Fig. 2 shows the experimental measurements of the

pure and impure CO2oil MMP versus the resulted

inverse of the optimal transformation of the general

CO2oil MMP dependent variable, whereas the inverseoptimal transformation yielded a final impure or pure

model in the following form:

General CO2 oil MMP

0:068616 z3 0:31733 z2 4:9804 z 13:432 8

where

z

X8

n1

zn; and 9

zn A3nx3n A2nx

2n A1nxn A0n 10

where, the values of the coefficients A3, A2, A1, and A0

are listed in Table 2.

Fig. 3 shows a perfect match between the predicted

MMP from the new model versus the experimental

impure and pure CO2oil MMP.

5. Validation of the new model

Firstly, to test the ability of the developed CO2oil

MMP model to reproduce the experimental observation,

it was tested against the literature pure CO2oil MMP

correlations. Although nearly all of the data sets used in

building this new model were also used in building the

other early correlations, especially Emera and Sarma

(2004) correlation, the new model yields the accurate

CO2oil MMP estimation. As shown in Fig. 4, Emera

and Sarma (2004), and Alston et al. (1985) correlations

provide a closer match to the new model.

Table 3 shows that the average relative error (ARE),

average absolute relative error (AARE), and the standard

deviation of error for the new model are 0.25%, 2.55%, and

3.11% respectively. In the second orderEmera and Sarma

(2004) correlation gives an ARE equal to 0.65%, AARE

equal to 4.05%, and standard deviation of error equal to

4.9%. Finally, Alston et al. (1985) give an ARE equal to

5.37%, AARE equal to 7.54, and standard equal to

8.55%. In the decreasing order of accuracy, Glaso (1985),

Cronquist (1978), Yellig and Metcalfe (1980), and Lee

(1979) correlations came in sequence order.

Secondly, the resulted impure CO2oil MMP values

from the new model were compared to the commonly

used impure CO2oil MMP correlations (Emera and

Sarma, 2005; Dong, 1999; Alston et al., 1985; Sebastian

et al., 1985; Kovarik, 1985), as shown in Table 4. From

this table, the new model yields the lowest ARE equal to

0.142%, lowest AARE equal to 3.3%, and lowest

standard deviation of error equal to 4.67%. Fig. 5 showsthat the new model presents the optimum match with the

experimental data. Also, Emera and Sarma (2005)

correlation is a closer match to the new model; however,

Sebastian et al. (1985) and Alston et al. (1985) come in

the third and fourth order, respectively.

Finally, to test and validate the accuracy of the new

model, MMPs were calculated for 22 systems not used in

building the model for pure and impure CO2 displacements

of crude oils. The new model successfully predicted the

experimental slim-tube CO2oil MMP, with high accuracy,

for presence of different non-CO2 components up to 70mol

%,andupto45.7mol%ofC1 in the injected CO2 stream (asshown in Table 5). On the other hand, all the tested impure

CO2oil MMP correlations failed in predicting the MMP's

values for the last two systems in Table 5, due to the higher

content of methane in the injected CO2. However, Yuan et

al. (2004) correlation is strictly limited for methane content

in the injected CO2 up to 40mol.%, and the other

correlations are limited for methane content up to 23mol

%. From Table 5, although the last two systems were not

considered in the error calculation for all the compared

correlations, the new model yields the accurate prediction

of the experimental slim-tube CO2oil MMP for all thetested systems with the lowest average relative and average

absolute error among all tested impure and pure CO2oil

MMP correlations.

6. Sensitivity analysis

@Risk (2005) software was used to demonstrate the

sensitivity analysis of the new model and the depen-

dence of the dependent variable (CO2oil MMP) on

each of the independent variables. The results of the

sensitivity analysis (shown in Fig. 6) are based on the

rank correlation coefficient that calculated between the


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output variable (CO2oil MMP) and the samples for

each of the input distributions. The higher the

correlation between any input variable and output

variable means higher significant influence of that

input in determining the output's value. From Fig. 6, it is

obvious that the reservoir temperature has the majorimpact on the CO2oil MMP, and as the temperature

increases the CO2oil MMP increases which confirms

with all published correlations. Also, the effects of oil

compositions on the predicted MMP confirms with all

published correlations whereas increasing MWC5+ or

volatiles mole percent leads to an increase in CO2oil

MMP. On the other hand, any increase in the mole

percent of the intermediate components (C2C4, H2S,

and CO2) causes a decrease in the CO2oil MMP. In

addition, the existence of non-CO2 components such as

H2S and hydrocarbon components (C2 to C4) in the CO2stream has a positive impact on the MMP, whereas they

contribute to the decrease in MMP. In contrast, the

existence of non-CO2 components such as C1 and N2 in

the CO2 stream has a higher negative impact on the

MMP, because they cause a higher increase in the CO2

oil MMP.

7. Conclusions

A new model has been developed to predict the

impure and pure CO2oil MMP. A comparison between

its predicted values against experimental data, and thewidely used impure and pure CO2oil MMP correla-

tions has been carried out. Based on the results of this

new model, the following conclusions are drawn:

1. The new CO2oil MMP model yields the accurate

prediction with the lowest average relative and

average absolute error among all tested impure andpure CO2oil MMP correlations.

2. The effects of CO2 impurities components on the

CO2oil MMP are in the following order in terms

of their impact: N2, C1, hydrocarbon components

(C2C4) , and H2S. Whereas C1 and N2 have a

higher negative impact on the MMP, H2S and

hydrocarbon components (C2C4) have a positive

impact on the MMP.

3. The new CO2oil MMP model can be used to predict

the impure CO2oil MMP with high accuracy for

methane content in the injected CO2 stream up to

45.7mol%, and different non-CO2 components (e.g.,

C1, N2, H2S, and C2C4) up to 70%.

4. The new model is strictly valid only for C1, N2,

H2S, and C2C4 contents in the injected CO2stream.

5. The new model can be used as an effective tool to

estimate the MMP for initial design of economical

CO2-miscible flooding project.

Nomenclature

Interm. Intermediates components, C2C4, H2S, andCO2, %

MMP Minimum miscibility pressure, MPa

MWC5+ Molecular weight of C5+ fraction

TR Reservoir temperature, C

Vol. Mole percentage of the volatiles (C1 and N2), %

X, X1, , Xp Independent or predictor variables

Y Dependent or response variable

e ACE regression error

Gaussian random noise

E() Mathematical expectation

() Transformation for dependent variable

() Optimal transformation for dependent variable

Fig. 6. Sensitivity analysis of the new CO2oil MMP model and the

dependence of CO2oil MMP on each of the independent variables.

Fig. 5. The resulted impure CO2oil MMP from the new ACE-based

model versus the calculated impure CO2oil MMP from Alston et al.

(1985), Sebastian et al. (1985), Kovarik (1985), Dong (1999), andEmera and Sarma (2005) models.


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i() Transformation for independent variable

i() Optimal transformation for independent variable

Average relative error, ARE, %:

ARE 100N

XN1

ycalculated

ymeasuredymeasured

Average absolute relative error, AARE, %:

AARE 100

N

XN1

jycalculatedymeasuredymeasured j

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