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PAPER 2000-01
Minimum Miscibility Pressure from EOS
T. Ahmed
Montana Tech of the University of Montana
This paper is to be presented at the Petroleum Society’s Canadian International Petroleum Conference 2000, Calgary, Alberta, Canada, June 4 – 8, 2000. Discussion of this paper is invited and may be presented at the meeting if filed in writing with the technical program chairman prior to the conclusion of the meeting. This paper and any discussion filed will be considered for publication in Petroleum Society journals. Publication rights are reserved. This is a pre-print and subject to correction.
ABSTRACT
This paper presents a practical and simple procedure for determining the Minimum Miscibility Pressure “MMP” required for the multi-contact miscible displacement of hydrocarbon systems by gas injection. The methodology is based on applying the Peng and Robinson Equation of State; in a modified form, in conjunction with a newly introduced “Miscibility Function”. The mathematical form of the miscibility function is designed to provide with the necessary criteria for predicting the required injection pressure in miscible gas injection. The objective of this paper is to demonstrate how this miscibility function can be used to determine the necessary conditions required for miscible displacement of hydrocarbon systems by gas injection. The validity and the use of the proposed methodology are demonstrated by matching several experimentally measured minimum miscibility pressure values.
INTRODUCTION
The displacement efficiency of crude oil systems by gas injection is highly pressure dependent and miscible displacement is only achieved at pressures greater than a certain minimum. This minimum pressure is called the Minimum Miscibility Pressure “MMP”. Slim-Tube displacement tests are commonly used to determine an MMP for a given crude oil. The minimum miscibility pressure is defined as the pressure of which the oil recovery vs. pressure curve (as generated from the slim-tube test) shows a sharp change in slope, i.e. the inflection point. This minimum miscibility pressure is a strong function of temperature, composition of the crude oil system, and composition of the injection gas. To facilitate screening procedures and to gain insight into the miscible displacement process, many correlations relating the MMP to the physical properties of the oil and the displacing gas have been proposed. Enick, et al
1
pointed out that any correlation should: 1) account for each parameter known to affect the MMP, i.e. temperature, composition of the displacing and displaced fluid; 2) be based on thermodynamic or physical principles that affect the miscibility of fluids, and finally; 3) be directly related to the multiple contact miscibility process. In general, all the published miscibility correlations can be divided into two categories; the first category deals with predicting the minimum miscibility pressure for pure and impure CO
2
; while the other category treats the MMP’s of all other type of gases.
A) PURE AND IMPURE CO
2
MMP:
It is well documented that the development of miscibility in a CO
2
- crude oil displacement process is the result of extraction of some hydrocarbons from the oil by dense CO
2
. Orr and Silva
2
stated that there is considerable evidence that the extraction of hydrocarbons from a crude oil is strongly influenced by the density of CO
2
. Improvement of extraction with the increase in CO
2
density that accompanies increasing pressure accounts for the development of miscibility. The presence of impurities can affect the pressure required to achieve miscible displacement. 1. Orr and Silva2: The authors developed a methodology for determining the MMP for pure and contaminated CO2 - crude oil systems. Orr and Silva pointed out that the distribution of molecular sizes present in a crude oil has a significantly larger impact on the MMP than variations in hydrocarbon structure. The carbon-number distributions of the crude oil system are the only data needed to use the correlation. They proposed the following steps: a) From the chromatographic or the simulated compositional distribution of the crude oil; omit the Methane fraction “C
1
” and all the non-hydrocarbon components from the oil composition. Normalize the weight fractions (w
i
) of the remaining components (C
2
to C
37
). b) Calculate the partition coefficient “k
i
” for each component from the following equation: Log (k
i
) = 0.761 - 0.04175 C
i
where C
i
is the number of carbon atoms of component i c) Evaluate the weighted-composition parameter “F” from:
Fkw
ii
= ∑
237
d) Calculate the density of CO
2
that is required to achieve miscibility from the following expressions: If the parameter F<1.467, then:
ρ
mmp
= 1.189-0.542F ; For F<1.467 If the parameter F>1.467, then:
ρ
mmp
= 0.42 ; For F>1.467 e) Using the available published CO
2
- pressure density data, find the pressure at the given the reservoir temperature at which the CO
2
density is equal to the required
ρ
mmp
. This pressure is set equal to MMP. A detailed description of Orr and Silva method and its extension is given in reference 2. 2. Extrapolated Vapor Pressure (EVP) Method. Orr and Jensen
3
suggested that the vapor pressure curve of CO
2
could be extrapolated and set equal to the minimum miscibility pressure for low temperature reservoirs (T<120
o
F). This Extrapolated Vapor Pressure (EVP) is conveniently expressed in an equation form by Newittelal
4
, as:
EVP T
= −+
1471091201525537205556.exp... With the extrapolated vapor pressure EVP as expressed in psia and the temperature T in
o
F. Researchers in the Petroleum Recovery Institute
31
suggest equating the MMP with the vapor pressure of CO
2
when the system temperature below the critical temperature “T
c
” of CO
2
. For reservoir temperatures greater than T
c
; they proposed the following expression for estimating the MMP for pure CO
2
: MMP = 1071.82893 10
b
With the coefficient “b” as defined by: b = [2.772-(1519/T)] Where MMP is in psia and T in
o
R. 3. Yellig and Metcalfe
5
: From their experimental study, the authors proposed a correlation for predicting the CO
2
MMP’s that uses the temperature “T” as the only correlating parameter. The proposed expression is given below:
MMP=1833.7217+2.2518055T+.01800674T2-
103949.93/T
Yellig and Metcalfe pointed out that if the bubble point pressure of the oil is greater than the predicted MMP, then the CO
2
MMP is set equal to the bubble point pressure. 4. Alston et al
6
: The authors presented an empirically derived correlation for estimating the MMP’s for pure or impure CO
2
-Oil systems. Alston and co-workers used the temperature T, molecular weight of the pentane-plus of the oil M
C5+
, the mole fraction of the oil intermediate components (C
2
-C
5
, CO
2
, and H
2
S), and the mole fraction of volatile (C
1
and N
2
) oil components as the correlating parameters for developing an expression for estimating the MMP for pure CO
2
- oil systems. The proposed correlation is given by:
MMP = 0.000878 T
1.06
[M
C5+
]
1.78
[X
vol
/X
int
]
0.136
Where: M
C5+
= molecular weight of oil pentane and heavier fractions. X
int
= mole fraction of intermediate oil components (C
2
-C
4
, CO
2
, and H
2
S) X
vol
= mole fraction of the volatile (i.e. C
1
and N
2
) oil components. T = system temperature in
o
F. Contamination of CO
2
by C
1
or N
2
has been shown to adversely affect the MMP. Conversely, the addition of C
2
, C
3
, C
4
, or H
2
S to CO
2
has been shown to have the effect of lowering the MMP. To account for the effects of the presence of contaminants in the injected CO
2
, Alston and co-workers correlated impure CO
2
MMP with the weighted-average pseudo-critical temperature “T
cm
” of the injected gas and the pure CO
2
MMP by the following expression:
cm
T cmimp
T MMP MMP
/893.168
]/8.87[
=
With : T
cm
= [
Σ
w
i
T
ci
] - 459.7 Where: MMP = Pure CO
2
MMP w
i
= Weight fraction of component i in the injection gas T
ci
= Pseudocritical temperature of the injection gas,
o
F. T
i
.= Critical temperature of component i in the injection gas,
o
R. The critical temperatures used in the above expressions are the True Critical Temperature except those of H
2
S and C
2
. The authors assigned a uniform value of 585
o
R for both components. Sebastian et al
7
proposed a similar corrective step that adjusts the pure CO
2
MMP by an amount related to the mole average critical temperature “T
cm
” as follows: MMP
imp
= [C] MMP Where the correction parameter C is given by: C = 1.0 -A [0.0213 - 2.51x10
-4
A + 2.35 A
2
] With A = [T
cm
– 87.89]/1.8 T
cm
=
Σ
y
i
T
ci
Where y
i
is the mole fraction of component i in the injected gas. To give a better fit to their data, the authors adjusted T
c
of H
2
S from 212 to 125
o
F. 5. National Petroleum Council (NPC): The NPC proposed an empirical correlation that provides rough estimates of the pure CO2 MMP’s. The correlation uses the API gravity and the temperature as the correlating parameters as shown below: Gravity (
o
API) MMP (psi) <27 27 to 30 >30 4,000 3,000 1,200 Reservoir Temperature Correction T (
o
F) Additional Pressure (psi) <120 120 to 150 150 to 200 200 to 250 0 +200 +350 +500 6. Enick-Holder-Morsi
1
: Enick and co-authors presented a set of working graphs for estimating the MMP for CO
2
-crude oil systems. The graphs are divided into four categories:
ã
Pure CO
2
-Stock Tank oil MMP prediction graph
ã
Three correction graphs to account for CO
2
impurities
ã
Two graphs that are designed to account for CO
2
gaseous components
ã
A correction graph to account for the temperature dependency of CO
2
impurities and live-oil gases The authors reported an average reported predicted MMP/actual MMP ratio of 1.09; with a standard deviation of 19% 7. Croquist
32
: The author proposed an empirical equation that was generated from regression fit on 58 data points. Croquist characterizes the miscibility pressure as a function of T, molecular weight of the oil pentanes-plus fraction, and the mole percentage of methane and nitrogen. The correlation has the following form:
MMP=15.988 T
A
With: A = 0.744206+0.0011038 M
C5+
+ 0.0015279 Y
cl
Where: T = Reservoir temperature,
0
F Y
cl
= sum of the mole% of methane and nitrogen
B) Lean-Gas and Nitrogen Miscibility Correlations:
High pressure Lean gases and N
2
injection have been successfully used as displacing fluids for EOR projects and also widely used in gas cycling and pressure maintenance. Firoozabadi and Aziz
8
documented the successful use of Lean gas and N
2
as high-pressure miscible gas injection in several oil fields. 1. Firoozabadi and Aziz: The authors proposed a generalized correlation that can predict MMP for N
2
and Lean gases. They used the concentration of oil intermediate components, temperature, and the molecular weight of C
7+
as the correlating parameters. The authors define the intermediates as C
2
- C
5
, CO
2
, and H
2
S components. The correlation has the following form: MMP = 9433 - 188x10
3
F + 1430x10
3
F
2
with F = I/(M
c7+
T
2.5
) where I = concentration of intermediates , i.e. C
2
-C
4
, CO
2
, and H
2
S, mol% T = temperature,
o
F M
c7+
= molecular weight of C
7+
2. Hudgins - Liave - Chung
9
: The authors performed a comprehensive laboratory study of N
2
miscible flooding for enhanced recovery of light crude oil. They stated that the reservoir fluid composition, especially the amounts of C
1
through C
5
fractions, is the major determining factor for miscibility. For pure N
2
, the authors proposed the following expression: MMP = 5568 e
-R 1
+ 3641 e
-R 2
With: R
1
= 792.06 [C
2
- C
5
]/W R
2
= 2.158x10
6
[C
1
]
5.632
/W where: W = M
c7+
T
0.25
T = temperature,
o
F C
1
= mole fraction of methane C
2
- C
5
= mole fraction of C
2
-C
5
3. Glaso
10
: The author investigated the effect of reservoir fluid composition, displacement velocity, column length of the slim-tube, and temperature on slim-tube oil recovery with N
2
. Glaso used M
c7+
, T in
o
F, and the mole percent methane and intermediates (C
2
- C
6
) in his correlation. He proposed the following relationships: For API<40 MMP = 80.14 + 35.35 H + 0.76 H
2
where:
HMTCC
C
=
+ −
7088011260641033....
/[()()]
For API>40 MMP = -648.5 + 2619.5 H - 1347.6 H
2
where:
HMTCCC
C
= −
+
7048025260121042....
/[()()]
EQUATION OF STATE APPROACH
The usefulness of the PREOS has been tested
11,12
with limited success in predicting the phase behavior and MMP's of simulated reservoir fluids. Firoozabadi and Aziz
8
compared the PREOS prediction results with available experimental data and concluded that the EOS in general overestimates the MMP. Lee and Reitzel
13
observed a similar trend and attributed the deviation to inaccuracies in establishing critical points and to a lack of suitable data to fine tuning the PREOS. Creek and Sheffield
14
investigated the formation of a CO
2
rich second “liquid phase in mixtures of CO
2
and Permian Basin reservoir fluids. The authors stated that they were unable to adjust the parameters of the EOS to match the experimentally generated phase envelope. They attributed that to the inability of cubic equations of state to model the behavior of molecules like CO
2
. A modified version of the Redlich-Kwong equation of state (RKEOS) has reportedly been used successfully to model the phase

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