Keywords

1 Introduction

CO2 miscible flooding has become one of the most widely applied non-thermal EOR techniques [1,2,3]. The process development efforts have also been escalated, partly due to an increasing global awareness of the detrimental effects of industrial flue gases on the environment [4, 5]. Industrial flue gas from power plants, which contains high CO2 concentrations, is an attractive option. However, extracting CO2 from the industrial flue gas will increase project costs due to requiring expensive gas separation facilities. And it is often the remaining low percentages of non-CO2 component gases (H2S, SO2, N2, CO, and O2) that are more difficult and costly to remove [6,7,8,9]. A promising cost-effective process is thus to inject flue gas directly.

One important consequence is the need to understand the effects of the impurities (non-CO2 gases) on minimum miscibility pressure (MMP), which is critical to the design and implementation of a flue gas flooding. A lot of effort has been made toward investigating the effects of contaminants in CO2, i.e., H2S, SO2, N2, and C1-C4 on MMP [9,10,11,12,13,14,15,16]. In general, the existence of H2S, SO2, and C2-C4 or intermediate hydrocarbons can decrease the CO2-MMP, while the presence of methane or N2 in CO2 can substantially increase the CO2-MMP.

Although O2 and carbon monoxide are the most common components in flue gas, a few studies has been reported on the effect of O2 and carbon monoxide on CO2-MMP [16, 17]. Therefore, the objective of this study is to investigate systematically the effect of non-CO2 component gases, i.e., H2S, SO2, N2, CO, and O2, on MMP in detail. In this work, slim tube experiments of effect of O2 concentration in CO2 on MMP are carried out on the model oil (n-C5H12/n-C16H34) and Jiangsu crude oil with three types of gases having various O2 contents. To verify the accuracy of our algorithm determining MMP, the experimental results and the case published in the literature are compared with the MMPs calculated by using a new multiple-mixing-cell model with a tie-line length for determining the MMP [18,19,20,21]. And then the MMPs of model oils with non-CO2 components are predicted.

2 Experiment

2.1 Materials

The crude oil samples with a viscosity of 12.3 mPa·s at 50 °C, studies are from Block L6 in the Jiangsu Oilfield, China. The model oil is a mixture of n-C5H12/n-C16H34 with a mole fraction ratio of 0.43/0.57. The n-pentane and n-hexadecane were purchased from Sinopharm Chemical Reagent Co. Ltd. And used without further treatment. The CO2 gas (99.5%) and O2 contaminated gases (94.81% and 90.01% CO2) were purchased from Linde Industrial Gas (China), and used without further purification or adjustment.

2.2 Slime Tube Apparatus and Procedure

The slim-tube tests for determining oil recovery by displacing hydrocarbon fluids with pure CO2 or contaminated CO2 gases were conducted in a coiled, stainless tube of 0.46 cm ID packed with 50/70-mesh glass beads. The column length of the tube was 14.6 m. The porosity of the slim-tube column was 35.3% and the permeability 11.0 Darcy. The pore volume of the slim tube was 86.0 cm3.

Both the reservoir fluid and the injection gas were transferred to the slim tube from vessels with a floating piston; the piston was activated with distilled water driven by a high-pressure Syringe pump. A backpressure regulator was placed close to the slim-tube outlet to control the system pressure.

Prior to each run, the apparatus is carefully cleaned with toluene followed by distilled acetone and dried with N2 at a temperature of 100 °C. And then the slim tube is heated to the operating temperature. The oil sample is injected into the slime tube at the desired operating pressure to saturate the slim tube. The gas is injected into the slim tube to displace oil using a positive displacement pump at a rate of 12.0 cm3/h. The following data are collected during the slim-tube experiment: the pore volume of injected gas, the volume of oil produced, and the volume of gas produced. Data are taken every ten minutes. The experiments continued until 1.2 PV of gas was injected into the slim tube. The recovery of oil plotted vs. different displacement pressures at 1.2 PV CO2 gas injected determined the MMP at the prevailing temperature.

In this work, the MMPs of six systems were measured, which are the model oil (a mixture of 43/0.57n-C5H12/n-C16H34) and Jiangsu crude oil with three types of gases having various O2 contents (pure CO2, 5.19 mol% O2, and 9.99 mol% O2). The experiments are conducted at five different pressures for each system. The operating temperatures used are 50 °C for the model oil and 60 °C for the Block L6 crude oil, respectively.

3 Multiple-Mixing-Cell Modeling

In this paper, a multiple-mixing-cell model is used in order to compute key tie length and then the MMP. The multiple-mixing-cell model is a discrete model of a continuous gas injection process in the slim tube experiment. A packed slim tube is discretized into a series of constant volume cells and the continuous gas injection process is discretized into a series of constant volume batches (shown in Fig. 1).

Fig. 1.
figure 1

Schematic diagram of cell-to-cell simulation

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By assuming constant temperature and pressure in each cell, no physical dispersion among cells, no capillary force in each cell and among cells, and perfect mixing in each cell, this multiple-mixing-cell model is converted into a pure thermodynamic P/T flash calculation. A block-algebra simultaneous flash algorithm coupled with the Peng-Robinson (PR) cubic equation of state (EOS) is used in this work. The binary interaction parameters (kij) used and the parameters of the model are given in Table 1. We also set kij’s involving O2, H2S, SO2 and CO to zero.

Table 1. Binary interaction parameters [22]
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The parameters of our multiple-mixing-cell model are listed in Table 2. The total number of cells (Nc) is chosen to ensure that a steady-state compositional path of the process can be achieved. The cell volume, gas oil ratio (GOR), and fraction flow function do not affect the determination of the key tie lines, thus they do not affect the MMP calculation. The total batch number of gas injection can be calculated from.

Table 2. Parameters of the multiple-mixing-cell model
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$$ N_{b} = N_{c} \frac{1.2}{GOR} $$
(1)

Where the value of 1.2 is an extensively accepted criterion; i.e., the required amount of gas injected for oil recovery calculation from the slim tube experiment is 1.2 PV.

A multi-contact miscibility process is controlled by a sequence of (nc − 1) key tie lines: the initial tie line, the injection tie line, and (nc − 3) crossover tie lines, where nc is the number of components [19, 22,23,24,25,26,27,28]. The MMP is defined as the lowest pressure at which one of the key tie lines becomes a critical tie line. There are many criteria that can be used to determine the MMP, but Zhao et al. found that zero key tie-line length is a robust criterion for this purpose [18]. Since all of the key tie lines can be robustly found through our multiple-mixing-cell model, our MMP calculation can be robustly based on the determination of tie-line length (TL), which is defined as

$$ TL = \sqrt {\sum\limits_{i} {\left( {x_{i} - y_{i} } \right)^{2} } } $$
(2)

where xi and yi are the equilibrium mole fractions of component i in the liquid and vapor phases, respectively. At the MMP, the tie-line length of one of the key tie lines reaches zero.

The calculation procedure of the gas displacement process in the slim tube experiment is summarized as follows [18,19,20,21]:

In a first step, the program simulates a number of cells of equal volume in a series. All the cells contain initially the same fluid (the reservoir oil). A specified amount of gas is added to cell 1. After mixing of the injected gas and the cell fluid, assuming perfect mixing, vapor fraction in the cell (v) can be determined from a P/T flash calculation. If v ≥ 1, the mixture is at or above its dew point and the total gas volume must be larger than the cell volume. The excess gas is then moved into cell 2. If v ≤ 0, the mixture is at or below its bubble point. The excess oil is moved into cell 2. If 0 < v < 1, the mixture is in the two-phase region. The excess fluid moved from cell 1 to cell 2 is determined by the fractional flow function, i.e., Eq. (3).

$$ \left\{ \begin{aligned} f_{g} = \frac{{S_{g}^{2} /\mu_{g} }}{{S_{g}^{2} /\mu_{g} + (1 - S_{g} )^{2} /\mu_{o} }} \hfill \\ f_{o} = \frac{{(1 - S_{g} )^{2} /\mu_{o} }}{{S_{g}^{2} /\mu_{g} + (1 - S_{g} )^{2} /\mu_{o} }} \hfill \\ \end{aligned} \right. $$
(3)

The liquid saturation (So) is defined as

$$ S_{o} = \frac{{V_{l} }}{{V_{l} + V_{v} }} $$
(4)

where Vl and Vv are volumes of liquid and vapor phases after flash calculation, respectively.

In a second step, the excess volume formed in cell 2 is transferred to cell 3 and so on until production is obtained from the last cell. When one batch calculation has been completed, a new injection into cell 1 can take place and the cell to cell transfer calculation is resumed. If all key tie lines on current pressure are located, the calculation of next pressure should be processed.

It is important to mention that although the multiple-mixing-cell model [17] is somewhat similar to a one-dimensional compositional flood simulator, it offers an important advantage over the latter, i.e., the determination of key tie lines, and thus the MMP is not affected by the size of the mixing cell and the numerical dispersion induced by GOR and fractional flow. As also previously explained, the total number of cells we choose: as long as the steady-state compositional path can be achieved, all of the key tie lines can be determined.

4 Results and Discussion

4.1 Slim Tube Experiments

To interpret the experiments, oil recovery factors (ORF) at 1.2 pore volume (PV)s of injected gas are often plotted as a function of injection pressure. The MMP criteria were used to determine MMP as the pressure when ORF is 90% or 95%. Figure 2 shows plots of ORF versus injection pressure for the model oil with three different gas injections at 50 °C. When ORF is 95%, the MMPs of the model oil with pure CO2 is 10.72 MPa. This is in better agreement with that for the same system reported in the literature [29], indicating that the MMP determined in our slim tube experiment is reliable. As expected, the MMP varied depending on the criterion used. The results in Table 3 and Fig. 2 show that a slim tube oil recovery criterion of 90% will usually yield MMPs lower than that from 95% criterion. The results indicated that the effect of O2 impurity in CO2 is to increase the MMP.

Fig. 2.
figure 2

ORF versus injection pressure for the model oil with three different gas injections at 50 °C. (a) pure CO2, (b) 5.19 mol% O2 in CO2 gas, (c) 9.99 mol% O2 in CO2 gas

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Table 3. Slim tube experimental MMP
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Figure 3 shows plots of ORF versus injection pressure for the Jiangsu crude oil with three different gas injections at 60 °C. The MMPs for these systems are also summarized in Table 1. Similar to the model oil, O2 impurity in CO2 increases the MMP for the Jiangsu crude oil.

Fig. 3.
figure 3

ORF versus injection pressure for the Jiangsu crude oil with three different gas injections at 60 °C. (a) pure CO2, (b) 5.19 mol% O2 in CO2 gas, (c) 9.99 mol% O2 in CO2 gas

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4.2 Multiple-Mixing-Cell Modeling

4.2.1 Validity of the Algorithm

In this study, the accuracy of our algorithm determining MMP was verified and compared with a case. The required oil and gas composition of the case was taken from the published literature [23]. The case is a six-component oil consisting of 20% CH4, 5% CO2, 5% C4H10, 40% C10H22, 10% C14H30, and 20% C20H42 with pure CO2 as the injection gas. The tie-line length calculations are illustrated in Fig. 4. For this six-component system, there are five key tie lines and the crossover tie-line1 reaches zero at the MMP. As noted in the figure, the calculation is stopped at a pressure close to the MMP; the length of the crossover tie-line1 would be exactly zero at the MMP. This is due to the common difficulty encountered when one tries to do flash calculation in the critical region. We determine the MMP to be 16.02 MPa by extrapolation, which is in excellent agreement with the calculated MMP (16.4 MPa) reported in the literature [23].

Fig. 4.
figure 4

Key tie-line lengths in the simulation of a six-component oil with pure CO2 as the injection gas at 71.1 °C. crossover tie-line1 becomes a critical tie line at 16.02 MPa.

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The MMPs of model oils with O2-contaminated CO2 are then predicted. As showed in Fig. 5, MMP was determined to 11.76 MPa and 13.24 MPa by extrapolation, respectively, which are found to be reliable within the experimental error (4.18%–3.06%) in Table 4. This indicates our modeling has higher accuracy to determine MMP.

Fig. 5.
figure 5

Key tie-line length versus injection pressure for the model oil with three different gas injections at 50 °C. (a) 5.19 mol% O2 in CO2, (b) 9.99 mol% O2 in CO2. crossover tie-line becomes a critical tie line at 11.76 MPa and 13.24 MPa, respectively.

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Table 4. Comparison of measured and calculated MMPs for model oil
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4.2.2 Effect of Non-CO2 Components on MMP

In this study, the MMPs of model oils with non-CO2 components (N2, H2S, O2, CO, and SO2) are predicted. Table 4 summarizes our predictions. The content of N2, CO and O2 in CO2 increases the MMP, and the effect of H2S and SO2 in CO2 is to decrease the MMP. This is because an improvement in the solubility of contaminated CO2 in the model oil due to the higher critical temperatures of H2S and SO2 than that of CO2. On the other hand, the existence of the components (i.e., N2, CO and O2) with lower critical temperatures causes a reduction in solubility of contaminated CO2 in the model oil and has the opposite effect. From our prediction, the effect of impurity in CO2 stream on MMP is found to N2 > CO > O2 > H2S > SO2 in order, as depicted in Fig. 6.

Fig. 6.
figure 6

MMPs for model oils with impurity in CO2 gases at 50 °C.

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5 Conclusion

In this study, lab experiments of effect of O2 concentration in CO2 on MMP are carried out on the model oil (n-C5H12/n-C16H34) and Jiangsu crude oil with three types of gases having various O2 contents. The results indicated that the MMPs for these oils increase with increasing O2 contents in CO2 gas. The experimental results and the case are also supported by our modeling work using a new multiple-mixing-cell model, which is found to be a robust and more accurate method for determining the MMP. The calculation results indicated that MMPs decrease favorably as the H2S and SO2 contents in CO2 stream increase, and increase unfavorably as an increase of O2, CO and N2 impurity in the CO2 streams, and the effect of impurity in CO2 stream on MMP is found to N2 > CO > O2 > H2S > SO2 in order.