1 Introduction

Due to the limitation of oil resources, the issue of increasing the oil recovery factor has always been considered by petroleum engineers. In order to enhance oil recovery in fractured reservoirs, non-miscible injection schemes such as injection of water and dry gas are usually employed. In fractured reservoirs, the injection of miscible gas is completely different from conventional reservoirs. The most important parameter in this case is the MMP, which is influenced by multi-dimensional flow and molecular diffusion. Its amount in fractured reservoirs is higher than that in conventional reservoirs (diffusive mass transfer between matrix and fracture controls miscible injection) [1]. In a non-miscible process,, the displacement and microscopic sweep efficiency are low. In this situation, the oil relative permeability decreases, and more water injection does not produce higher oil production and the water moves around the trapped oil. Miscible displacement can overcome this constraint. In the fully miscible displacement process, the interfacial tension is become zero. In this context, the diffusion of the gas from the fractures into the matrix results more outflow of oil, which delays gas break-through in the fractures, improving displacement and sweep efficiency. A comprehensive investigation of the fractured reservoirs was carried out by Saidi[2]. He noted that the production mechanisms of fractured reservoirs include convection, molecular diffusion, solution gas drive, gravity drainage, matrix–matrix effects, and unbalanced gas–oil gravity drainage. However, the ultimate recovery factor of fractured reservoirs will not be high in the primary and secondary recovery stages. Unlike conventional reservoirs, injection of non-miscible fluids into fractured reservoirs will not result in oil flow towards production wells because non-miscible fluids have a tendency to flow through high permeability fractures. As a result of fluid resistant forces in a matrix with low permeability, only oil in the fracture will be produced. Additionally due to the low permeability of the matrix, the permeability contrast between the matrix and the fracture causes a low ultimate recovery factor for non-miscible injections into this type of reservoir [3, 4]. It should be noted that non-miscible injection causes a difference in fluid composition between matrix blocks and the surrounding fractures. this difference in fluid composition, mass transfer will occur between the fluids present in the fracture and matrix blocks, and molecular diffusion is considered one of the important mechanisms of that produce fractured reservoirs. Due to the fact that injection of miscible gas leads to better recovery of reservoir oil and causes less oil trapping therefore many efforts to improve a miscible gas injection and investigate the miscibility development has done. Furthermore, since most giant oil reserves at middle east are naturally fractured reservoirs, which have a low natural recovery factor, studies on enhanced oil recovery methods, especially the use of miscible gas injection, are important. NFRs are divided into 4 main types [5], The first type of fractured reservoir is one which fractures provides the required porosity and permeability of the system. The reservoir pressure drop is very high, the water and gas cones are rapidly forming, and there is usually a very limited storage capacity for this type of fractured reservoir. The production of these reservoirs increases with the intensity and width of the fractures. The second type of these reservoirs is one in which the permeability is provided by fractures. Due to the weak interaction between matrix and fracture in these reservoirs, an important portion of the matrix oil remains intact. Rate control in the production of these reservoirs is crucial. Additionally, due to the large difference between fracture and matrix permeability, the sweep efficiency under gas and water injection in these reservoirs is not high. The efficiency of this type of reservoir depends on the size and height of the matrix blocks. In the third type of fractured reservoir only a part of the required permeability can be provided by the fracture. The efficiency of secondary recovery methods in these reservoirs is not very high, and their production rate depends on the fracture continuity. A fourth type of reservoir is one in which fractures can only contribute to anisotropy in permeability. Often, these reservoirs are very enclosed and have a much higher skin factor than predicted. The maximum recovery obtains from these kinds of fractured reservoirs.

Fractures reservoirs generally have high initial production rate, but are prone to rapid production decline, early water breakthrough, and problems in reserve calculation. The study of the recovery mechanisms of matrix and fracture systems on a laboratory scale began in 1970. Thompson and Mungan [6] examined an experimental study on gravity drainage in fractured media under conditions of first-miscible contact miscibility. In their study, the displacement velocity was compared with the critical velocity and its effect on oil recovery efficiency. Natural depletion or injection of non-miscible fluids are common strategies in fractured reservoirs. In addition to these common mechanisms, the injection of a rich gas can also be used to improve miscibility conditions and enhance recovery. Firoozabadi and Tan [7] studied the miscible displacement and found that the capillary pressure contrast between the fracture and the matrix is one of the main factors contributing to poor production efficiency. Uleberg and Høier [8] showed that the development of miscibility conditions and increased final recovery can be observed at lower pressures but near MMP using unbalanced gases (gases with a different composition from those in reservoir fluids). However, they also found this effect would be less and the recovery rate would be higher for a miscible injection and for a small block height. The fractured core plug method was used by Shedid to study the effects of fracture on the efficiency of carbon dioxide injection. By using the Slim tube method and experimental correlation, he measured the MMP. As a result of conducting flooding experiments on several cores, he analyzed the effects of fractures on carbon dioxide injection recovery. During the miscible injection process, experimental results show that the amount of oil produced by conventional cores is higher than by fractured cores [9]. The effect of matrix permeability, connate water saturation, and oil viscosity on oil recovery in a matrix-fracture system (MFS method) has been studied by Torabi and Asghari[10]. Based on the results, ultimate recovery at pressures close to or above the MMP does not depend heavily on matrix permeability. In addition, when miscible injection is used, the presence of connate water increases oil recovery. In another study, Torabi and Asghari[11] investigated how matrix permeability, operating pressure, and connate water saturation affected the efficiency of injecting periodic carbon dioxide (Huff and Puff) into the matrix-fracture system. The maximum recovery factor is less than 50% when CO2 is injected into the matrix-fracture system at a pressure lower than MMP. During miscible injection, the permeability effect of the matrix is less than during immiscible injection. In a matrix-fracture system, Torabi et al. [12] investigated the effects of immiscible, near-miscible, and miscible injection of carbon dioxide on increasing oil recovery. These studies found that carbon dioxide injection in near-miscible conditions increased oil recovery (for light oil reservoirs) by up to twice compared to other two methods. It is important to note that one of the problems with miscible injection in fractured reservoirs is a large difference between the mobility of oil and gas, which reduces injection efficiency. Additionally, Chen and Mohanty[13] studied miscible injection of carbon dioxide using a modified core holder and micro consolidation device. According to their findings, the MCM process works better with periodic injection of carbon dioxide. Saeedi [2] proved that the surface tension reduction should not be applied after a certain period of the reservoir production life.

In conventional and one-dimensional systems, miscibility has been studied extensively in recent years and can be measured by experimental and numerical methods. According to these studies, displacement s efficiency is only a function of phase behavior in conventional reservoirs, and fluid properties and rock properties have no significant impact [8]. Due to the structural complexity of fracture reservoirs, this is not as simple as conventional reservoirs. Therefore, it is necessary to study and analyze the conditions that lead to miscibility development in these reservoirs. Displacement in these systems is affected by the interaction between matrix and fracture. Therefore, Understanding the interaction between the fracture and matrix is an important challenge in the design and implementation of a gas injection method.

The purpose of this study is to investigate the injection of different gases in a second type naturally fractured reservoirs and to compare different gas type in terms of final recovery factor and how the miscibility develops. At this study a real naturally fractured reservoir and its history were used, and the production and pressure of the wells and field have been matched. There was at least forty years of production and gas injection history in this field, which made our dynamic model to be valid for future predictions.

In the next section, we present the methodology of research including the reservoir simulation method, MMP calculation and rock and fluid properties. Section 3 shows the results and discussion of the study and last part summarize the conclusion of the research.

2 Simulation

In 1962, the Asmari reservoir was discovered. It began producing in 1966. According to initial reports, the reservoir oil pressure at the datum depth of 2754 m was 4639 psi, which is now about 3900 psi. Since the saturation pressure is 2880 psi, the reservoir is undersaturated. Additionally, the oil formation volume factor is 1.4 bbl/stb and the solution gas–oil ratio is 599 scf/stb. So far, 18 wells have been drilled in the reservoir where 13 of them are production wells. The water oil contact is equal to 2900 m. In 2020, oil with an average rate of 20,600 bbl/day was produced from this reservoir.

2.1 MMP calculation

Development of miscibility in the gas injection process usually occurs in multiple contacts. Especially in real reservoirs where the miscibility is achieved during multiple contacts and goes through condensing/vaporizing process [14, 15]. The first step in determining whether a gas injection is a miscible one or not is to determine the MMP of the injected gas with the reservoir fluid. The minimum miscibility pressure (MMP) of injected gas in the oil phase can be determined by various methods, including laboratory and numerical methods. The MMP can also be determined during the slim tube test based on sudden and significant changes in the ultimate recovery. The composition of the reservoir oil, lean gas, and rich gas as well as the minimum miscibility pressure of different gases is given in Table 1.

Table 1 Composition of reservoir oil, lean gas and rich gas and obtained MMP of different gases
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2.2 Reservoir model simulation

To simulate the effect of injected gases on EOR, a sector model of Asmari reservoir was used, which is shown in Fig. 1. The number of grids in the sector model is 15*17*10. The average permeability of the matrix in the horizontal direction is 0.8 md and in the vertical direction is 0.2 md. The average matrix porosity is 9% and the initial oil saturation is 82%. The permeability of the fractures in the horizontal direction is 230 md. Also, the average porosity of the fractures is 0.5%. Three existing injection wells (P1, P2, P3) and three existing production wells (P4, P5, P6) were used to injection/production study. The relative permeability curves of the water/oil matrix system and the gas/oil matrix system are shown in Fig. 2. Also Fig. 3 shows the normalized capillary pressure diagram.

Fig. 1
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Schematic of the simulated sector model

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Fig. 2
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Matrix relative permeability curves a gas/oil system, b water/oil system

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Fig. 3
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Reservoir capillary pressure curves

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3 Results and discussion

3.1 The optimum injection rate

The simulations were performed with different injection rates of 10–60 MMSCF/D to determine the optimum injection rate for used gases. the ultimate recovery factor is calculated for different gas injection rates as well as a natural depletion scenario. According to the Fig. 4, the increasing slope of oil recovery for each gas injection scenario decreases significantly after the break-through time, presumably since most of the fractures containing oil have been drained or saturated with gas and mechanisms such as molecular diffusion has a lower recovery rate. Table 2 provides a summary of the best injection scenarios for each gas, including the recovery percentage and optimum gas injection rate. A flow rate above the optimal flow rate will not significantly increase oil recovery in the gas injection scenarios. The injection pressure was also considered higher than the MMP to reach the miscibility.

Fig. 4
figure 4

Oil recovery factor for different injected gases at optimum injection rate

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Table 2 Comparison of the different gas injection performance
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3.2 Effect of injected gas type on the producing gas–oil ratio

The producing gas–oil ratios of different gas injection is presented in Fig. 5. It shows that the injection of methane and lean gas result in the highest producing gas–oil ratio of the wells. There are also two abnormal rises in GOR is due to the gas breakthrough from fractures to the production wells. Therefore, the richer injected gas and the lower miscibility pressure result in a lower gas–oil ratio due to the better miscibility between the gas and oil. Furthermore, Fig. 6 shows the ratio of cumulative gas production to cumulative gas injection in each case, indicating that the ratio of cumulative gas production to cumulative gas injection will decrease as the injection scenario moves toward miscibility.

Fig. 5
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Producing gas–oil ratio in different gas injection cases

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Fig. 6
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Cumulative gas production to cumulative injection gas ratio in different gas injection cases

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In cases where miscibility is lower (such as methane and lean gas injections), more gas is extracted because less gas dissolves in the oil, as shown in the above figures. In these cases, the gas injection goes through the fractures faster, so the gas production will also increase. When gas is more miscible with oil (such as in a rich gas or carbon dioxide injection scenario), less gas is produced on the surface, and this is exactly the phenomenon clearly illustrated by the diagrams on the figure. In addition, the slimtube simulation results indicate that among the injected gases, the rich gas has the highest amount of intermediate components and the lowest miscibility pressure compared to other gases.

3.3 Investigating the miscibility of different injected gases

Due to fractured reservoirs are complex in nature, there are many ambiguities regarding the development of miscibility. During miscible injection, the most important observed parameters will be surface tension, gas–oil solution ratio, and reservoir oil viscosity. In order to compare the miscibility conditions for each of the studied gases, we have presented the change of these properties in Figs. 7 and 8.

Fig. 7
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Surface tension variation in a particular matrix cell

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Fig. 8
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Variation in reservoir fluid viscosity and gas–oil ratio during injection of different gases at one cell

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Figure 7 shows that during injection of rich gas and carbon dioxide, the surface tension reaches the minimum value compared with injection of lean gas and methane. As a result, rich gas and carbon dioxide are more miscible.

Considering the definition of the miscibility phenomenon, which states that two fluids can dissolve in each other in any proportion, the stability of GOR and decrease in oil viscosity during gas injection are indicators of miscibility. Regarding rich gas injection, a sharp decrease in surface tension between the gas and the reservoir fluid, increasing the solution gas–oil ratio, and reducing the dynamic viscosity of the reservoir fluid during the injection of this gas can improve the miscibility conditions in the reservoir compared to injection of other gases. Based on our study after rich gas, the most desirable miscibility conditions are for the injection of carbon dioxide, lean gas, and methane, respectively. These results are in good agreement with the final recovery of the gas injections.

4 Conclusions

Based on simulations of this real naturally fractured reservoir, the following results were obtained:

The incremental oil recovery at optimum injection rate for methane, carbon dioxide, lean gas, and rich gas is 16.7, 18.8, 17.46, and 19.4%, respectively.

Injection of methane and lean gas at higher rates than the optimum rate, due to low gas solubility in oil causes faster gas breakthrough and leads to lower ultimately oil recovery compared to the optimum injection rate.

For the rich injection, the decrease in surface tension and the increase in solution gas–oil ratio during the injection of rich gas compared to other gases shows that the miscibility condition of this gas is better than others.

Miscibility is difficult to achieve in fractured reservoirs of type 2, and it is necessary to optimize the gas injection rate and pressure continuously to achieve the best miscibility recovery.