A new empirical correlation of minimum miscibility pressure for produced gas reinjection

Abstract

Minimum miscible pressure is a key parameter to screen and design miscible gas injection projects. The aim of this paper is to establish a correlation with only a few input parameters to easily and accurately predict minimum miscible pressure for the reinjection of produced gas with high acidic components. First, the critical parameters of equation of state for each component of the crude oil were obtained through fitting pressure-volume-temperature (PVT) experimental results. Based on the analytically calculated minimum miscible pressures from mixing-cell method, an empirical correlation for predicting minimum miscible pressure in the displacement of crude oil by produced gas was regressed. Finally, the correlation’s accuracy was tested by comparing the minimum miscible pressures predicted from the new proposed correlation to other previous correlations and 20 experimental slim-tube minimum miscible pressures of 12 oil samples. The results indicate that the analytically calculated minimum miscible pressures from the mixing-cell method have a relative error of 0.5% compared to the slim-tube experiment results, which supports its reliability. Furthermore, the new proposed correlation is observed to be superior in terms of the average relative error being only 6.4% for all the 75 analytically calculated minimum miscible pressures and 20 experimental slim-tube minimum miscible pressures, which is lower than the average relative error obtained from other previous correlations.

Keywords

Minimum miscible pressure empirical correlation mixing-cell method slim-tube experiment produced gas reinjection

Introduction

Gas flooding is regarded as a promising enhanced oil recovery method for oil reservoirs by achieving miscibility (Arne et al., 2000; Chen, 1995; Knut and Lars, 2002; Murty and Al-Khayat, 1989; Teletzke et al., 2005; Zhang et al., 2013). Recently, the most common injection mediums are hydrocarbon (lean gas, enriched gas), CO₂, and N₂ (Chen et al., 2011; Kulkarni and Rao, 2005; Lai et al., 2015; Liu et al., 2019; Meng et al., 2018; Sabyrzhan et al., 2010; Wu et al., 2019). The minimum miscible pressure (MMP) of hydrocarbon injection is always low (Nikolay et al., 2017; Olawale and Hoffman, 2014). CO₂ often is used as injection gas not only because it can achieve miscibility with crude oil at relatively low reservoir pressure, but also because there are potential environmental benefits of reducing the greenhouse effect (Hrvoje et al., 2009; Izgec et al., 2005; Li et al., 2006; Song et al., 2019; Sumeer and Xingru, 2014). N₂ (flue gas) also is used as injection medium because of its low price and extensive source even though it is more difficult to achieve miscibility than CO₂ (Sayegh et al., 1987)_.

The injection gases usually are not miscible upon the first contact with the reservoir crude oil. However, miscibility can be developed gradually with multi-contact by a mass transfer of components between the gaseous and liquid phases (Guo et al., 2010; Johns et al., 1994; Zhu et al., 2015). There are three multi-contact mechanisms (Tang et al., 2004): the vaporizing gas drive (VGD), the condensing gas drive (CGD), and combined condensing/vaporizing drive (CV). In the VGD process, generally referred to as lean gas drive, miscibility develops at the flood front. In the CGD process, commonly referred to as enriched gas drive, miscibility develops at the injection point. In the CV process, miscibility develops at the middle of transition zone (Stalkup, 1987; Tang et al., 2005; Zick, 1986).

MMP is a key parameter to design gas flooding project. It can be calculated by using experimental method, analytical calculation, compositional simulation, and empirical correlation (Ahmed, 1997; Abiodun et al., 2012). The slim-tube experiment is commonly used to determine the MMP for a given crude oil displaced by gas. MMP is often graphically obtained by the inflection point or intersection of two lines that define immiscible and miscible performance regimes on a plot of pressure versus recovery (Yuan et al., 2004). Although slim-tube experiment is the preferred method for testing MMP since both condensing and vaporizing mechanisms can be captured, it is expensive and time-consuming. Analytical calculation and compositional simulation are faster; however, they rely on the accurate fluid characterization by equation of state (EOS). Empirical correlation usually involves simple formulae developed by regressions of slim-tube experimental data. As those correlations are usually derived based on the specific reservoir conditions of crude oil and injection gas, they are limited to oil and injection gas of similar type. Although empirical correlation may be less accurate than other methods, it can quickly predict MMP and screen potential reservoir for miscible gas flooding, particularly when detailed fluid characterizations are not available.

Many correlations to predict MMP of enriched gas, lean gas, N₂, and CO₂ have been built. Benham et al. (1960) established some graphical correlations based on calculated critical temperatures and pressures of selected fluids system to predict the approximate conditions for a miscible displacement of reservoir fluid by enriched gas. Based on Benham et al.’s data, Glaso (1985) derived MMP prediction correlations for hydrocarbon, CO₂, and N₂ gas miscible flooding as the function of temperature, C₇₊ molecular weight of the oil, C₂–C₆ molecular weight, and C₁ mole percent of the gas. Kuo (1985) established a correlation for the enriched gas which consists of methane and intermediates, such as ethane to butane, based on Peng–Robinson EOS to generate phase envelopes for selected gas/oil systems. Firoozabadi and Aziz (1986) built a correlation for estimating MMP of nitrogen and lean gas based on 13 measured slim-tube experimental data. Eakin and Mitch (1988) established a correlation of MMP based on 102 measured data with rising bubble apparatus. Several CO₂ MMP correlations have been published. Yelling and Metcalfe (1980), Metcalfe (1982), Alston et al. (1985), Sebastian et al. (1985), Dong and Huang (2000), Yuan et al. (2004), Shokir (2007), Johns et al. (2009), Zhang et al. (2016), and Lai et al. (2017) established different MMP correlations for pure CO₂ and impure CO₂. Rutherford (1962) found that miscibility between reservoir oil and displacing gas is a function of the pseudocritical temperature of the injected fluid. Jacobson (1972) found this to be true if the critical temperature of H₂S and CO₂ was adjusted slightly by multiplying a factor of 0.85. Glaso (1990) established a correlation for estimating the MMP of nitrogen based on 18 measured MMP data. Yurkiw and Flock (1994) evaluated 15 MMP correlations for rich gas, lean gas, and nitrogen and their results support the applicability of EOS-based methods for accurate MMP predictions.

Produced gas (PG) reinjection is an effective developing method and has been applied in many oilfields (Chen et al., 2017a, 2017b; Kassenov and Kaliyev, 2016; Li et al., 2016; Zakaria, 2011). The PG is usually a mixture of CO₂, H₂S, C₁, and C₂–C₆. There are a fairly large number of reservoirs where the molecular percentages of acid gas components (CO₂, H₂S) are high in the PG (Xu et al., 2015; Zhang et al., 2016). The developed correlations may not be applicable for the prediction of MMP of the PG with high acidic gas components. Therefore, this paper intends to establish a correlation to easily and accurately predict MMP for the reinjection of PG with high acidic gas components. First, the critical parameters of the EOS for each component of the crude oil were obtained through fitting pressure-volume-temperature (PVT) experimental results. On this basis, an empirical correlation for predicting MMP in the displacement of crude oil by PG was regressed. Finally, the correlation accuracy was tested by comparing the MMPs predicted from the new proposed correlation to the ones in other previous correlations and 20 experimental slim-tube MMPs.

Proposed correlation for MMP

MMP calculation using analytical method

Based on its characterization, the crude oil (A) of oilfield K in Kazakhstan, with high H₂S and CO₂ content, was divided into nine pseudo-components. In oilfield K, the PG was reinjected into the reservoir to maintain the reservoir pressure and enhance oil recovery. The composition of oil A and PG is given in Table 1. The C₂₀₊ fraction of the crude oil has a density of 907 kg/m³. The reservoir temperature of oilfield K is 212°F. The parameters of the EOS were adjusted using Eclipse PVTi (developed by Schlumberger) to match the laboratory’s PVT data. Molecular weight of the plus fraction was adjusted to match the oil density. The critical parameters of the EOS for each component after adjustment are presented in Table 1.

Table 1.

The pseudo-composition of crude oil and produced gas and the critical parameters of EOS.

Components	Oil A composition (mol%)	Produced gas (PG) composition (mol%)	Molecular weight (g/mol)	Pc (psi)	Tc (°F)	Acentric factor
H₂S	14.69	17.42	34.08	1296	212	0.1
CO₂	4.12	4.92	44.01	1072	88	0.23
C₁	49.36	59.03	16.04	667	−117	0.01
C₂	7.32	8.7	30.07	708	90	0.1
C_3–4	7.22	8.05	49.81	592	280	0.17
C_5–6	3.04	1.72	77.11	473	438	0.26
C_7–10	6.5	0.16	113.34	392	879	0.34
C_11–20	5.34	0	190.08	280	898	0.51
C₂₀₊	2.41	0	437.91	177	1177	0.8

EOS: equation of state.

As slim-tube experiment is expensive and time-consuming, we used the mixing-cell method to calculate MMP. The mixing-cell method is that a series of PVT cells are interconnected and initially filled with oil and the gas is mixed in the upper cell at a trial pressure and the equilibrium phases are calculated assuming that complete mixing occurs within the cell (Abiodun et al., 2012; Tadesse et al., 2012). The mixing-cell method, by multiple contacts of equilibrium gas and oil with fresh gas and oil to find the key tie, has the advantage of high precision and quick calculating speed. The MMP of oil A displaced by PG is 4038 psi as determined by the mixing-cell method. Compared to the slim-tube experiment result of 4060 psi, a relative error of 0.5% supports the reliability and correctness of the mixing-cell method. Based on the original reservoir fluid, two oil and four gas samples are virtually manufactured by changing the components’ composition, as shown in Table 2. The analytical MMPs of oils A, B, and C displaced by gases PG, A, B, C, and D at temperatures 90, 150, 212, 270, and 330°F are calculated by the mixing-cell method. The results are presented in Table 3.

Table 2.

Composition of different reservoir fluids and injection gases.

Components	Oil A	Oil B	Oil C	Gas PG	Gas A	Gas B	Gas C	Gas D
Components	(mol%)	(mol%)	(mol%)	(mol%)	(mol%)	(mol%)	(mol%)	(mol%)
H₂S	14.69	9.73	11.14	17.42	4.25	8.5	12.76	21.26
CO₂	4.12	2.73	3.12	4.92	1.2	2.4	3.6	6
CH₄	49.36	32.69	37.42	59.03	90	80	70	50
C₂	7.32	4.85	5.55	8.7	2.12	4.25	6.37	10.62
C_3–4	7.22	14.73	5.47	8.05	1.96	3.93	5.89	9.82
C_5–6	3.04	6.2	2.3	1.88	0.46	0.92	1.38	2.29
C_7–10	6.5	13.26	7	0	0	0	0	0
C_11–19	5.34	10.89	14	0	0	0	0	0
C₂₀₊	2.41	4.92	14	0	0	0	0	0

Table 3.

Comparison of MMPs estimated from correlations to analytical calculated MMPs.

Oil	Injection gas	T (°F)	Analytical MMP (psi)	Abbas MMP (psi)	Kuo MMP (psi)	Glaso MMP (psi)	Eakin MMP (psi)
A	A	90	4408	3327	3972	5646	3774
A	A	150	5091	3541	4648	9986	4012
A	A	212	5291	3740	5962	14,470	4225
A	A	270	5335	3897	7864	18,664	4400
A	A	330	5397	4036	10,786	23,004	4559
A	B	90	3959	3327	3246	3094	3599
A	B	150	4528	3541	3798	5505	3830
A	B	212	4878	3740	4873	7996	4037
A	B	270	5008	3897	6427	10,327	4206
A	B	330	5001	4036	8815	12,737	4361
A	C	90	3294	3327	2574	1827	3447
A	C	150	3950	3541	3011	3165	3670
A	C	212	4392	3740	3863	4548	3869
A	C	270	4618	3897	5095	5841	4032
A	C	330	4689	4036	6988	7179	4182
A	PG	90	2843	3327	1923	1248	3306
A	PG	150	3550	3541	2251	1950	3518
A	PG	212	4038	3740	2887	2675	3709
A	PG	270	4302	3897	3808	3353	3865
A	PG	330	4433	4036	5223	4054	4007
A	D	90	2143	3327	1451	1121	3208
A	D	150	2855	3541	1697	1534	3412
A	D	212	3402	3740	2177	1962	3594
A	D	270	3750	3897	2872	2362	3743
A	D	330	3957	4036	3939	2775	3880
B	A	90	4627	3345	3987	5646	3774
B	A	150	5117	3572	4665	9986	4012
B	A	212	5380	3777	5984	14,470	4225
B	A	270	5539	3937	7893	18,664	4400
B	A	330	5616	4078	10,826	23,004	4559
B	B	90	3709	3345	3258	3094	3599
B	B	150	4280	3572	3812	5505	3830
B	B	212	4631	3777	4890	7996	4037
B	B	270	4855	3937	6450	10,327	4206
B	B	330	4969	4078	8847	12,737	4361
B	C	90	2980	3345	2583	1827	3447
B	C	150	3624	3572	3022	3165	3670
B	C	212	4056	3777	3877	4548	3869
B	C	270	4272	3937	5114	5841	4032
B	C	330	4331	4078	7014	7179	4182
B	PG	90	2372	3345	1931	1248	3306
B	PG	150	3065	3572	2259	1950	3518
B	PG	212	3568	3777	2898	2675	3709
B	PG	270	3860	3937	3822	3353	3865
B	PG	330	3996	4078	5242	4054	4007
B	D	90	1739	3345	1456	1121	3208
B	D	150	2455	3572	1704	1534	3412
B	D	212	2999	3777	2185	1962	3594
B	D	270	3339	3937	2882	2362	3743
B	D	330	3535	4078	3953	2775	3880
C	A	90	4831	4965	6091	4231	4937
C	A	150	5464	5355	7128	7454	5312
C	A	212	5655	5611	9143	10,784	5651
C	A	270	5928	5785	12,060	13,900	5930
C	A	330	5890	5927	16,540	17,123	6188
C	B	90	4095	4965	4978	2686	4478
C	B	150	4728	5355	5825	4740	4829
C	B	212	5136	5611	7472	6862	5146
C	B	270	5388	5785	9855	8848	5409
C	B	330	5478	5927	13,517	10,902	5651
C	C	90	3548	4965	3946	1775	4077
C	C	150	4308	5355	4618	3084	4404
C	C	212	4711	5611	5923	4437	4700
C	C	270	5034	5785	7813	5702	4945
C	C	330	5198	5927	10,716	7012	5172
C	PG	90	2796	4965	2950	1237	3697
C	PG	150	3595	5355	3451	2035	3998
C	PG	212	4127	5611	4427	2861	4271
C	PG	270	4437	5785	5840	3633	4498
C	PG	330	4669	5927	8009	4431	4707
C	D	90	2430	4965	2224	1024	3426
C	D	150	3244	5355	2603	1557	3706
C	D	212	3811	5611	3339	2107	3961
C	D	270	4090	5785	4404	2622	4172
C	D	330	4369	5927	6040	3155	4367

MMP: minimum miscible pressure.

The new correlation of MMP

The MMPs of oils A, B, and C displaced by gases PG, A, B, C, and D at temperatures 90, 150, 212, 270, and 330°F are also calculated by currently used correlations (shown in Appendix 1), and the results are presented in Table 3. Figure 1 shows the comparison between the analytically calculated MMPs and the predicted MMPs from several currently used correlations. As shown, the MMP predicted by correlations varies significantly. The maximum (average) relative error for the 75 analytically calculated MMPs is 104.3% (22%) for Abbas correlation, 180.8% (32.7%) for Kuo correlation, 326.2% (61.7%) for Glaso correlation, and 84.5% (11.9%) for Eakin correlation. Although Eakin correlation is the most reliable among these four correlations, it is still not sufficiently accurate; in some cases, the relative errors are over 1400 psi. Thus, a new correlation is required to predict MMPs for PG reinjections.

Figure 1.

Comparison of analytical calculated MMPs with predicted MMPs from currently used correlations. (a) Abbas correlation, (b) Kuo correlation, (c) Glaso correlation, and (d) Eakin correlation. MMP: minimum miscible pressure.

As for other correlations, we selected four input parameters for predicting MMP: temperature, molecular weight of heptane plus in the oil, molecular weight, and molecular percentage of intermediates (C₂–C₆, CO₂, and H₂S) in the gas. We found a good fit for the analytically calculated MMPs as shown in Figure 2. The equation for fit is

p_{m} = 13155 {(\frac{1000 y_{C_{2 +}}}{M O_{_{C_{7 +}}}^{^{1.25}} \cdot M G_{_{C_{2 +}}}^{0.5} \cdot T^{0.7}})}^{2} - 14665 (\frac{1000 y_{C_{2 +}}}{M O_{_{C_{7 +}}}^{^{1.25}} \cdot M G_{_{C_{2 +}}}^{0.5} \cdot T^{0.7}}) + 6042.2

(1)

where p_m is the MMP (psi); T is the temperature (°F); MO_C₇₊ is the molecular weight of heptane plus in the oil; MG_C₂₊ is the molecular weight of intermediates defined by C₂–C₆, CO₂, and H₂S in the displacing gas; and y_C₂₊ is the molecular percentage of intermediates in the displacing gas (mol%).

Figure 2.

The new proposed correlation based on analytical calculated MMPs. MMP: minimum miscible pressure.

Figure 3.

Comparison of analytical calculated MMPs with predicted MMPs from the new developed correlation. MMP: minimum miscible pressure.

The maximum relative error and the average relative error of the new proposed correlation for the 75 analytically calculated MMPs are 19.5 and 4.8%, respectively. The correlation coefficient of the new correlation is 0.9514. Figure 3 and Figure 4 shows the comparison of the analytically calculated MMPs and the predicted MMPs from the newly developed correlation. As shown, the new proposed correlation is superior to the other four correlations.

Figure 4.

Comparison of experimental slim-tube MMPs with predicted MMPs from currently used correlations. (a) Abbas correlation, (b) Kuo correlation, (c) Glaso correlation, and (d) Eakin correlation. MMP: minimum miscible pressure.

Verification of the new correlation

There are some published data providing the results of slim-tube experiments with 12 oil samples (shown in Table 4) which were used to test the accuracy of the new correlation. The new proposed correlation and the other four correlations predicted the slim-tube MMPs. The results are presented in Table 4. Figures 4 and 5 compare the experimental slim-tube MMPs with the predicted MMPs of the developed and currently used correlations. The maximum (average) relative error for the 20 experimental slim-tube MMPs is 246% (80%) for Abbas correlation, 155% (29%) for Kuo correlation, 161% (50%) for Glaso correlation, 120% (30%) for Eakin correlation, and 32% (14%) for the new proposed correlation. This illustrates that the new proposed correlation is more accurate than all other correlations in predicting MMP.

Table 4.

Comparison of MMPs estimated from correlations to slim-tube MMPs.

Reference	T (°F)	MO _C ₇₊ (g/mol)	C₁+N₂ (mol%)	y _C ₂₊ (mol%)	MG _C ₂₊ (g/mol)	Slim-tube MMP (psi)	Abbas MMP (psi)	Kuo MMP (psi)	Glaso MMP (psi)	Eakin MMP (psi)	MMP from equation (1) (psi)
Glaso (1985)	210	231	73.3	26	39.05	5100	4849	5171	5679	4138	4575
Lee and Reitzel (1982)	217	193	86.6	13	36.20	4902	4835	6249	8775	4147	5062
Lee and Reitzel (1982)	215	204	86.6	13	36.20	5076	4950	6510	8613	4310	5117
Lee and Reitzel (1982)	222	191	86.6	13	36.20	5497	5507	6194	9440	4133	5064
Firoozabadi and Aziz (1986)	200	209	83.2	15	37.25	5800	5609	5795	7433	4118	4983
Firoozabadi and Aziz (1986)	225	250	90.3	10	33.52	6000	6011	9936	11,955	5305	5505
Deffrenne et al. (1961)	250	197	64.8	35	37.16	3700	3511	4844	4319	3928	3991
Deffrenne et al. (1961)	250	197	60.0	40	30.00	3400	3511	5600	4580	3966	3566
Deffrenne et al. (1961)	250	197	80.0	20	30.00	3600	3511	9169	8177	4261	4663
Meltzer et al. (1965)	258	190	91.7	8	42.40	5400	5343	6882	14,097	4349	5521
Shelton and Yarborough (1977)	105	243	32.9	67	36.43	2000	5383	991	1155	2371	2118
Frimodig et al. (1983)	130	183	69.1	31	40.13	3400	3847	2681	2781	3313	3301
Kuo (1985)	132	302	65.0	35	44.00	3880	9166	3999	3020	3454	4276
Kuo (1985)	132	302	62.4	38	44.00	3650	9166	3729	2756	3288	4164
Kuo (1985)	132	302	54.3	46	44.00	2916	9166	2938	2063	2814	3835
Kuo (1985)	170	215	53.1	47	38.14	2400	5906	2447	2312	3469	3173
Kuo (1985)	206	215	53.1	47	38.14	2680	6038	2841	2768	3595	3442
Metcalfe (1982)	105	206	20.0	80	39.00	1754	5020	–	–	3298	2027
Metcalfe (1982)	135	206	10.0	90	39.00	1505	5213	–	–	3317	1975
Metcalfe (1982)	135	206	20.0	80	39.00	1800	5213	–	–	3396	1965

MMP: minimum miscible pressure.

Figure 5.

Comparison of experimental slim-tube MMPs with predicted MMPs from the new developed correlation. MMP: minimum miscible pressure.

In order to improve the accuracy of prediction, the 75 analytical calculated MMPs and 20 experimental slim-tube MMPs from displacement tests reported in the literatures were regressed to obtain a new correlation (shown in Figure 6) as follows

p_{m} = 13483 {(\frac{1000 y_{C_{2 +}}}{M O_{_{C_{7 +}}}^{^{1.25}} \cdot M G_{_{C_{2 +}}}^{0.5} \cdot T^{0.7}})}^{2} - 15285 (\frac{1000 y_{C_{2 +}}}{M O_{_{C_{7 +}}}^{^{1.25}} \cdot M G_{_{C_{2 +}}}^{0.5} \cdot T^{0.7}}) + 6092.4

(2)

Figure 6.

The new proposed correlation based on analytical calculated MMPs and experimental slim-tube MMPs. MMP: minimum miscible pressure.

The new correlation incorporating the slim-tube MMPs has the average relative error of 4.6% for the 75 analytical calculated MMPs, of 11% for the 20 experimental slim-tube MMPs and of 6.4% for all 95 MMPs (shown in Figure 7). The correlation coefficient of the new correlation is 0.9244. It should be pointed out that the new proposed correlation is based on the characteristics of 15 oil samples and therefore it is limited to oils of similar type. In other words, the new proposed correlation is limited to the conditions of MO _C ₇₊ ranging from 183 to 302 g/mol, MG _C ₂₊ ranging from 30 to 44 g/mol, the molecular percentage of C₁ ranging from 10 to 91.7%, the molecular percentage of CO₂ ranging from 0 to 45%, the molecular percentage of H₂S ranging from 0 to 45%, and the reservoir temperature ranging from 90 to 330°F.

Figure 7.

Comparison of analytical calculated MMPs and experimental slim-tube MMPs with predicted MMPs from the new developed correlation. MMP: minimum miscible pressure.

Conclusions

An empirical correlation for predicting MMP in the displacement of crude oil by PG was regressed based on 75 analytical calculated MMPs from mixing-cell method and 20 experimental slim-tube MMPs. The following conclusions can be summarized from the results of this work:

Good agreement between the analytically calculated MMP from the mixing-cell method and the results of the slim-tube experiment, with a relative error of 0.5% indicates that the analytically calculated MMPs with a wide range of temperatures and reservoir fluids can be used to develop an empirical correlation.

The new proposed correlation with an average relative error of 6.4% for all the 75 MMPs shows its accuracy. The proposed correlation’s predictions are more precise than other previous correlations.

The new proposed correlation is limited to the conditions of MO _C ₇₊ ranging from 183 to 302 g/mol, MG _C ₂₊ ranging from 30 to 44 g/mol, the molecular percentage of C₁ ranging from 10 to 91.7%, the molecular percentage of CO₂ ranging from 0 to 45%, the molecular percentage of H₂S ranging from 0 to 45%, and the reservoir temperature ranging from 90 to 330°F.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Major Projects of China (2017ZX05030).

ORCID iD

Congge He

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