1.1. Introduction
Enhanced oil recovery (EOR) with CO
2 injection might be attractive because of the carbon dioxide retention in the reservoir [
1], which provides a positive effect on the feasibility of CO
2 storage and storage capacity obligations regarding the European Union international agreements within the climate change domain (Kyoto protocol from the year 1997 and the Paris climate agreement from the year 2015). Carbon Capture Utilization and Storage (CCUS) comes into focus when the possibilities of CO
2 storage and reduction of storage cost are assessed. Although there are other utilization types, such as the utilization through beverage production or in agriculture, only the CO
2 enhanced oil recovery (CO
2-EOR) has been implemented at a commercial level on an industrial scale [
2,
3,
4]. By injecting CO
2 above the miscibility pressure (or minimum miscibility pressure (MMP)), microscopic displacement efficiency is improved due to viscosity reduction, oil swelling, lower interfacial tension, and a change in the density of oil and brine [
5]. The efficiency of CO
2 storage and CO
2 utilization factors are not easy to determine. Static approximations are easier to implement, which usually leads to the use of statistical distributions and stochastic models [
6,
7,
8], sometimes accompanied by numerical simulation and parameter analysis [
9,
10]. Recently the increasing number of published works have been focused on more complex CO
2-EOR issues, such as injection rates of water and CO
2 (water alternating gas (WAG) ratios), permeability anisotropy, the effect of different simulation cell size, etc. [
11,
12]. Oil recovery, injection cost, and the amount of carbon dioxide permanently stored can be optimized by the application of methods, which include water alternating gas (WAG) injection. Simulation of the WAG process can help establish optimal relation between the stated parameters.
The injection scheme of a typical CO2-EOR process can be classified according to:
CO2 and oil miscibility
miscible
near-miscible
immiscible
injection type
continuous gas injection (CGI)
water alternating gas injection (WAG)
simultaneous water and gas injection (SWAG)
There are no guidelines for the analysis or selection of WAG ratios, well distance, permeability, and time of primary production parameter based on multi-case simulation study as an input. The main reason for the absence of such guidelines, and in general, the reason such analysis has not been performed, is the long run-time of a typical compositional reservoir model and/or high dependence on geological and fluid properties in the case of complex heterogeneous reservoir models.
When CO2-EOR is performed, some of the CO2 retained in the reservoir. Depending on policies, in some cases (for example, the Weyburn Project), it is considered CO2 storage. For that reason, we use the word ‘CO2 retention’ as a synonym for storage. This paper brings a novel approach by a number of variations of the simulation parameters in a conceptual model (i.e., reservoir model and reservoir settings that are similar to real cases but generalized for parameter sensitivity analysis).
CO2 injection into a reservoir can be implemented in miscible and immiscible conditions, and the distinction between the two is defined by the minimum miscibility pressure. If the conditions are miscible, CO2 increases the oil mobility as it is dissolved in oil between the injector and the producer, and if the conditions are immiscible, there is no CO2 dissolution in oil, which means that CO2 flows much faster than oil toward the producers, causing lower oil recovery and higher production of previously injected CO2. The value of the minimum miscibility pressure depends mostly on oil composition and the reservoir temperature, and to determine the exact value of the minimum miscibility pressure, a detailed Pressure-Volume-Temperature (PVT) characterization of oil and the mixture of oil and CO2 is necessary.
1.2. Literature Review
Klinkenberg and Baylé [
13] studied pore size distribution and miscible and immiscible fluid injection and concluded that the pore distribution affects miscible and immiscible displacement differently.
Hall and Geffen [
14] made a mathematical model for saturation pressure, using fluid flow velocity (of liquid and gas), and liquid phase fraction during the two-phase flow. Additionally, pure compounds (methane, propane, butane, etc.) were used in the analysis, and for these compounds, zones of gaseous state, two-phase region, and region of 100% liquid saturation were identified.
Lacey, Draper, and Binder Jr [
15] studied the length of the mixed zone in cores of different diameters. It was concluded that the length of the mixed zone is proportional to the area through which the fluids flow, but this cannot be a rule at the reservoir level.
In the 1960s, different authors studied mixing mechanisms experimentally [
16,
17,
18]. Benham, Dowden, and Kunzman [
16] analyzed the miscibility of rich gases with reservoir fluid by using ternary diagrams with methane, C
2-C
4, and C
5+. They developed a correlation for maximum concentration of methane in miscible conditions as a function of temperature, pressure, the molecular weight of C
5+, and the molecular weight of C
2+.
Other authors ([
19,
20]) used somewhat different components in the ternary diagram, but oil composition is, in general, divided into components of lower molecular weight, components of the medium, and components of high molecular weight. Such estimates disregard the reservoir heterogeneity (heterogeneity of permeability, pore structures, and fluid saturations), which are mentioned by Deffrenne et al. [
21].
Peaceman and Rachford [
22] proposed a numerical method for the calculation of the 2D miscible displacement. A normal permeability distribution was generated by a random number method, and the model gave results in line with measured experimental data.
The Buckley–Leverett theory was used as a starting point for numerous modifications. Koval [
23] published the most known paper regarding the semi-analytical description of miscible processes, in which a model was given describing solubility as a function of pore volumes injected using the K-factor method for Buckley–Leverett equation extension. He compared the results obtained by the suggested mathematical model with published data and got satisfactory results for heterogeneous systems of the horizontal reservoir in which fluids of different viscosities flow at different velocities—viscous fingering.
Fitch and Griffith [
24] tested alternating water injection to achieve more efficient oil displacement. Simon and Graue [
25] used experimental data regarding solubility, swelling, and CO
2-oil system viscosity and gave a correlation for the prediction of these parameters as a function of oil viscosity and density. Different groups of authors developed more advanced mathematical, i.e., numerical simulation algorithms for CO
2 injection [
26,
27,
28,
29].
Rathmell, Stalkup, and Hassinger [
30] analyzed the relationship between recovery, core length, and injection pressure on 13 m long cores, 5 cm in diameter, with 0.27 porosity and 1D permeability. They assumed that at certain parts of the core, immiscible displacement occurs even when the injection pressure was higher than the MMP. They found that different flow velocities occur due to different oil and CO
2 viscosities, which led to early CO
2 breakthrough and this effect was more pronounced in experiments done on shorter cores. They concluded that oil recovery depends on oil vaporization and higher fractions of swelling.
Teja and Sandler [
31] used the equation of state in which they adjusted the binary interaction coefficients and applied adequate mixing rules to simulate the density of the system/mixture CO
2-oil, swelling factors, and CO
2 solubility in oil at a given temperature.
Wang [
32] designed special equipment for visual detection of miscibility conditions, and he showed that miscible, near-miscible, and immiscible displacement could occur at the same time during the CO
2 injection. Among others, he also states that oil recovery cannot be the only criteria for MMP determination, and he proposed the determination of the optimal portion of CO
2 in a WAG process.
Sigmund, Kerr, and MacPherson [
33] gave a simple correlation for relative permeability determination in a slim-tube simulation model
where k
ro is the relative permeability of the liquid phase, and k
rg is the relative permeability of the gas phase.
Li and Luo [
34] used displacement on core samples and slim-tube experiments to determine a correlation for relative permeabilities determination, which represents input data needed for simulation. They tried to correlate Corey’s exponents and the displacement pressure, but they concluded that relative permeability curves need to be adjusted by matching the simulation model with experimental data.
During WAG injection in water-wet rock, relative permeabilities depend on fluid saturation, saturation history, and the mobility will also depend on the interaction of viscosity, gravity, and capillary pressure [
35]. Measurement of relative permeabilities during the three-phase displacement is usually not performed in a lab; therefore, it is common to measure relative permeabilities of a two-phase system, which is an acceptable input format for most commercial reservoir simulators.
Blunt [
36] and Beygi et al. [
37] reviewed most of so far suggested models for the determination of relative permeabilities of three-phase systems.
Jahangiri and Zhang [
38] modified the second term of the optimization function (given by [
39]) by introducing a mass of the stored CO
2 (concerning overall CO
2 mass storage capacity of the reservoir)
where w
1 and w
2 are weighted for oil recovery and CO
2 storage in the objective function (dimensionless), N
P is cumulative oil recovery (m
3), OIP is oil in place (m
3),
is mass of CO
2 stored (kg)
is the total storage capacity of reservoir (kg).
However, the overall CO
2 storage capacity of the reservoir is an uncertain parameter [
40], and there is still no adequate optimization function for oil recovery and CO
2 sequestration.
WAG injection can increase oil mobility, increase the displacement efficiency and the oil recovery, but the usual problem of a WAG process is the reduced displacement efficiency due to water blockage of CO
2-oil contact [
41], and that is the main reason why it is crucial to design the injection process correctly. Christensen, Stenby, and Skauge [
41] gave an overview of 59 WAG projects. The expected recovery increase in some fields (South Swan, Slaughter Estate, Dollarhide, and Rangely Weber) is up to 20 %. Most of the WAG projects started in the tertiary phase of the exploitation. In other words, only recent WAG projects in the North Sea have started in the earlier exploitation phase. Eighty percent of projects are performed under miscible conditions, and the ratio of water and gas injection is mostly 1:1. Usual problems of a WAG process have been described, such as injectivity reduction, early water and gas breakthrough, corrosion, different temperatures of injected phases, hydrates formation, etc.
As a CO
2-EOR process can be classified as immiscible, near-miscible, and miscible, the same classification may be applied to the WAG process. The water is used to maintain the reservoir pressure above the MMP, and to prevent the early breakthrough of CO
2 to the production wells. Near miscible or immiscible WAG injection implies three-phase flow for which, no matter the longtime application of WAG processes in the world, there is still no complete understanding of changes in fluid composition which happen during such flow [
41]. Extensive experimental and simulation research results have been published related to the mechanisms of displacement in the WAG process and water and gas injectivity [
42,
43,
44,
45,
46,
47,
48,
49,
50,
51,
52]. Relative permeability models with different conditions of wettability for a three-phase system were developed along with hysteresis models necessary for the simulation of displacement in a WAG process [
36,
37,
48,
53,
54,
55,
56,
57,
58,
59,
60].
Within the ESCOM (Evaluation System for CO
2 Mitigation) project [
61], numerous numerical simulations of hypothetical reservoirs were performed to define a mathematical model that would help to estimate the additional recovery and amount of CO
2 retained in the reservoir. Different analyses identified the most important parameters, after which sensitivity analyses of these parameters were performed.
The amount of CO
2 retained in the reservoir as part of the CO
2-EOR project will become important in the EU if trading with European emission allowances (EUA) will be possible on the emission market, EU emissions trading system (EU ETS). Vulin et al. [
62] investigate development of EU ETS, historical EUA price volatility, and trends correlated with price movements of natural gas, coal, and oil to forecast long-term EUA price probability using momentum strategy and geometric Brownian motion. Same as oil price, EUA price is influenced by policy, but some dependency on natural gas price and consumption was detected.
Sustainable development is based on finding the balance between industry growth and the environment, i.e., generating the lowest amount of damage while operating industrial activities efficiently.
To prove that CO2-EOR represents a feasible, mature, and clean carbon capture utilization and storage (CCUS) option, it is crucial to single out the most economically favorable option that can be applied considering the parameters crucial for CO2-EOR operations. Earnings of a CO2-EOR storage project come from oil production and avoided CO2. Avoided CO2 refers to the amount of CO2 retained in the reservoir during the EOR project, and this volume of CO2 can be considered as allowance and therefore used for trading in the EU ETS. Price of EUA on EU ETS can be observed as possible additional income besides oil production and on the other side highest costs are related to transport and injection of CO2 in CCUS projects.
Macintyre [
63] examine different processes, instrumentation, material, and operating considerations connected to the design of CO
2 compression, dehydration, and injection and concluded that the additional cost of corrosion prevention measures for CO
2 injection is insignificant compared to the total implementation costs of the Joffre EOR project, which was the first miscible CO
2-EOR project in Canada. He provided a real p-h diagram for the Joffre EOR project that requires only three stages of CO
2 compression up to 130 bar.
McCollum and Ogden [
64] gave some recommendations and examples of how to calculate compression and pumping power requirements emphasizing lower power requirements for pumping when the CO
2 liquefies, i.e., for pressure and temperature conditions above CO
2 critical values, including the Capital costs (CAPEX) estimation for pumping and compression phase of CO
2 transport and injection.
Habel [
65] observed the difference between reciprocating and centrifugal compressors for onshore CO
2 CCUS applications with a recommendation for assessment of the required number of stages in case of centrifugal compressors that have many advantages over reciprocating compressors for flows over 12 kg/s and outlet pressure up to 250 bar.
Desai [
66] made some general observations and challenges in the case of CO
2 compression, including steps that can help companies to estimate their CO
2 compressor requirements.