Introduction

Tertiary injection processes can potentially recover significant amounts of the initial oil in place (IOIP) left unrecovered after natural drive and secondary waterflooding or gas injection1,2,3,4,5. Numerous experimental and simulation studies have explored the impacts of wettability status, miscibility conditions, vertical heterogeneity, and specifically operational parameters, such as injection pressure, injectant composition, injection rate, well constraints (completion), and injector location, on the performance of tertiary gas injection following secondary waterflooding6,7,8,9,10,11,12,13,14,15,16,17. However, limited research has focused on tertiary gas injection into reservoirs previously subjected to secondary gas injection, despite the frequent use of lean gaseous solvents in field operations to mobilize residual oil recovery after secondary recovery18.

Gas injection offers distinct advantages, particularly in fractured systems, where mass transfer between the fracture and matrix would occur because of molecular diffusion, and in dipping reservoirs with a relatively high vertical permeability, where gravity-assisted gas injection would enhance oil recovery19,20,21,22. Furthermore, carbonate reservoirs, which are typically oil-wet and yield low oil production during conventional recovery processes such as waterflooding, benefit significantly from gas injection, making it a crucial strategy for enhancing oil recovery23,24,25. Importantly, tertiary enriched gas injection after secondary gas injection could not only target residual oil within gas-invaded zones but also might mobilize oil in areas that secondary gas injection may fail to reach effectively.

Laboratory experiments and field observations show that the ultimate displacement efficiency of a gas injection process is highly dependent on the amount of mass transfer/crossflow, capillarity, gas-oil phase behavior, as well as the injection conditions26,27,28,29,30,31. As a hydrocarbon gas mixture is injected into a porous medium containing another mixture of hydrocarbons, a series of complex interactions starts to occur. For instance, during gas-oil displacement, components in the gas dissolve in the oil, and components in the oil are extracted into the gas as local chemical equilibrium is achieved6,32,33. This component exchange is referred to as “compositional effects”. At the same time, interfacial tension between gas and oil can also be substantially lowered because of the component exchange. There are many experimental observations and theoretical evidence representing a significant hydrocarbon film/layer flow at gas/oil interfacial tension (IFT) around 1–3 mN/m, which reflects itself as an increase in hydrocarbon relative permeability34,35,36. As the system achieves miscibility, “compositional effects” and “IFT effects” become the key mechanisms37,38.

Several studies have demonstrated that near-miscible processes yield significantly higher oil recovery than immiscible displacements. Most of this research achieved near-miscibility conditions by increasing the injection pressure7,8, which can reactivate existing natural fractures/faults39, compensate for caprock integrity40, and initiate man-made flow paths, leading to induced seismicity41.

Approaching near miscibility by either (1) choosing an injectant that is strongly soluble in oil, e.g., CO2, which would be highly effective in mobilizing oil through swelling and viscosity reduction23,24,42 or (2) enriching the injected gas with intermediate components, e.g., liquified petroleum gas (LPG) or natural gas liquid (NGL), is rather more attractive compared to pressurizing the injectant from both operational and economical perspectives43. In fact, the process of gas injection at a lower pressure reduces the operational risks associated with the compression of injected gas and lowers the cost associated with delivering a high-density injectant. In addition, some reservoirs are at a pressure lower than the minimum miscibility pressure (MMP) or are experiencing pressure decline, in which a lower-pressure operation may be more feasible37,43,44,45.

Several researchers have conducted coreflood experiments to investigate the influence of gas types and, in turn, miscibility conditions on tertiary oil recovery after waterflooding. Karimaie, et al.23,24, using a fractured carbonate rock core, found that secondary CO2 injection recovered over 70% of the oil, while N2 injection only recovered 15%. This difference was attributed to compositional effects, lower IFT, and potentially oil swelling from CO2. In tertiary injection, CO2 recovered an additional 15.7% of the remaining oil after waterflooding, compared to 11% from N2. Norouzi et al.42 confirmed that water shielding is a major obstacle to tertiary recovery through experiments with CO2 and CH4. They highlighted that miscible gas injection, especially with highly soluble gases like CO2, is crucial for breaking through the water film and achieving effective oil swelling.

Grigg et al. 46 conducted several gas-injection corefloods to analyze the effect of pressure on tertiary oil recovery and suggested that the recovery efficiency of gas injection processes can still be high at pressure below the MMP, and observed that CO2, due to its drastic density change when pressure falls below the MMP, is not feasible for near-miscible oil recovery efficiency compared to hydrocarbon gases, which maintain a relatively consistent extraction efficiency even at pressures below the MMP, leading to more sustained oil recovery46,47. They also found that enriching the hydrocarbon gas with intermediate components crucially enhanced oil recovery, especially in near-miscible conditions. Recent experimental studies have highlighted the strong impact of gas composition on tertiary recovery. Coreflood experiments by Ge et al. 48 and Xian et al. 49 showed that modest enrichment with intermediate hydrocarbons can substantially enhance oil recovery compared to lean gases such as N₂ and CH4, with hydrocarbon-enriched gases often outperforming conventional injectants. Complementary carbonate coreflooding and molecular simulation studies have further confirmed that enriched-gas injection induces composition-driven shifts in displacement behavior under near-miscible conditions45. Zick50 also provided experimental observations, supported by equation-of-state predictions, indicating that a combined condensing/vaporizing gas drive makes displacements of oil by enriched gases highly efficient, even though true miscibility is not quite developed46,47. Although the need for further research, including compositional simulations, to fully understand the complex interplay of different recovery mechanisms involved in these processes was also underscored throughout all the aforementioned studies.

Additionally, the use of well-representative gas-oil relative permeability and capillary pressure functions is crucial for accurately modeling fluid displacements11,16,51. Especially in near-miscible tertiary enriched gas injections, the well-established flow functions can play a crucial role in accurately modeling complex fluid displacement. This leads to better predictions of recovery performance, optimization of injection strategies and operational parameters, and a more comprehensive understanding of the complex interplay of different recovery mechanisms. Pratama and Babadagli14,18 focused on improving heavy oil recovery while reducing the environmental impact of tertiary recovery methods by performing a series of Hele-Shaw cell and 2-D porous media experiments using pure and enriched solvents as low greenhouse gas (GHG) and high-efficiency tertiary recovery options in post-steam-assisted gravity drainage (SAGD) applications. Although both studies provide valuable insights into tertiary recovery methods, they lack a discussion on determining gas-oil relative permeability and capillary pressure, especially in tertiary enriched gas injection following a secondary lean gas injection.

This study aims to address these key challenges by experimentally and numerically investigating the gas-oil relative permeability and capillary pressure functions associated with tertiary enriched gas injection, while also evaluating its effectiveness as a recovery strategy after secondary lean gas injection by examining the impacts of key mechanisms__ compositional effects and IFT effects__ on flow behavior at the core scale. By generating reliable flow function data and demonstrating the enhanced oil recovery potential of this tertiary process, the study fills a vital gap in the literature and provides practical insights into improving recovery from gas-invaded reservoirs.

Methodology

In this study, a sample of live oil was prepared by combining crude oil and gas samples from the separator based on the gas-oil ratio (GOR) and formation volume factor (Bo) at reservoir conditions. Table 1 summarizes key properties of the recombined oil. Two gases were synthesized for injection scenarios: (1) lean gas for secondary injection and (2) lean gas enriched with intermediate hydrocarbons for tertiary injection. These gases were synthesized by blending pure components according to the target composition percentages. Detailed compositions of the injection gases are provided in Table 2. In comparison to the lean gas, the enriched gas shows a clear compositional shift, with methane decreasing from 91.58% to 83.20% and the cumulative C₃–C₇ fraction increasing from about 2% to nearly 10%. This enrichment in intermediate hydrocarbons significantly alters the phase behavior by enhancing gas–oil miscibility, strengthening the vaporizing–condensing mechanism, and reducing interfacial tension, thereby improving interface mass transfer and oil recovery efficiency.

Table 1 Properties of live oil at test conditions.
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Table 2 Lean and enriched gas composition used in coreflooding experiments.
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To simulate formation water, synthetic brine was prepared by dissolving a mixture of salts, including sodium chloride (NaCl), magnesium chloride (MgCl2), calcium chloride (CaCl2), sodium sulfate (Na2SO4), sodium bicarbonate (NaHCO3), and potassium chloride (KCl), in deionized water. At room temperature, the density and viscosity of the prepared brine were 1.1396 g/cm³ and 1.0 cp., respectively. The experiments were conducted in the presence of connate water to replicate in-situ reservoir conditions, acknowledging the ubiquitous presence of water in oil reservoirs. Detailed compositional data for the synthetic brine are provided in Table 3.

Table 3 Ionic composition of synthetic formation brine.
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Four reservoir core samples from a carbonate reservoir in southern Iran were used for the coreflood experiment. The cores, homogeneous and uniform limestone without fractures, were combined into a composite core following the Huppler criterion to minimize capillary end effects. The cores were cleaned using a Soxhlet apparatus with toluene and a methanol/chloroform mixture, then dried and weighed. Porosity was measured with a helium porosimeter and validated via brine saturation. Irreducible water saturation was achieved using the centrifuge technique with brine and dead crude oil, incrementally increasing the rotational speed to 13,000 RPM. Reservoir wettability was restored by aging the cores in dead crude oil at reservoir temperature (107 °C) for four weeks. The properties of the composite core are summarized in Table 4.

Table 4 Petrophysical properties of the composite core used in the study.
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Experimental setup

The coreflood experiments were conducted using a high-pressure, high-temperature (HPHT) coreflood setup designed to replicate reservoir conditions. The apparatus featured a temperature-controlled air oven housing the core holder, injection fluids, and associated components to ensure uniform temperature. Four transfer vessels (TVs) contained the injection fluids: dead crude oil, live oil, dry gas, and enriched gas. Fluid injection was performed using a high-precision double-cylinder pump, with separate cylinders for live oil and other fluids. The core was oriented vertically, with an overburden pressure of 750 psia above the pore pressure applied via a manual hand pump to ensure proper confinement. Differential pressure across the core was measured using two high-accuracy pressure transmitters at the inlet and outlet. A back-pressure regulator (BPR) maintained the outlet pressure and directed the effluent to a separator, where the liquid phase was collected in a graduated cylinder and the gas phase was measured using a gas-metering system. A data acquisition system recorded pressures through a host computer, while gauges monitored transfer vessel pressures. Prior to experimentation, inlet lines and connections were evacuated using a vacuum pump. A schematic of the HPHT coreflood setup is shown in Fig. 1.

Fig. 1
figure 1

Schematic of the coreflooding setup used in the study.

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Experimental procedure

The coreflood experiment was conducted under simulated reservoir conditions (107 °C, 4100 psia) using carbonate core samples. The composite core was assembled by weighing and mounting the cores into a sleeve within the core holder. To prevent trapped air, dead crude oil was dripped onto the cores, and inlet lines were evacuated using a vacuum pump. The injection rate was set at 0.25 cc/min, with a back-pressure regulator maintaining a constant outlet pressure of 4100 psia. Dead crude oil was first injected at 0.1 cc/min, gradually raising the pressure and temperature to reservoir conditions while maintaining a net stress of 750 psia. Once thermal equilibrium was achieved and the pressure drop stabilized after injecting two pore volumes, the injection rate was increased incrementally, and the composite core permeability was calculated using Darcy’s law. Subsequently, live oil was injected at 0.25 cc/min to displace the dead crude oil, with the effluent GOR monitored to confirm full displacement of the dead oil by the live oil. Injection continued until the pressure drop stabilized after three pore volumes. Lean gas was then injected as a secondary recovery agent at a rate of 0.25 cc/min, with pressure drop and production data recorded until oil production ceased. Finally, enriched gas was injected under tertiary recovery conditions at the same rate until additional oil production became negligible. The step-by-step workflow of the experimental procedure is illustrated in Fig. 2.

Fig. 2
figure 2

The flowchart summarizing the experimental procedure used in this study.

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Simulation model

The experimental processes of lean gas as well as enriched gas (10% NGL + 90% LG) secondary and tertiary injection into a volatile oil-saturated core sample of low permeability were simulated using the CMG/GEM module (CMG 2020). The commercial simulator uses the correlations proposed by Jossi, et al. 52 and Macleod-Sugden53 to calculate viscosity and gas-oil interfacial tension, respectively, throughout the processes, and the PVT behavior of gas and liquid phases during gas injection processes was predicted by the Peng-Robinson EOS54.

Given the shortcomings of analytical and semi-analytical methods—such as not accounting for fluid compressibility, capillary pressure, component exchange, and phase changes—the flow functions (gas-oil relative permeability and capillary pressure) for various injection processes were history matched according to the experimental gas injection data obtained in the laboratory using CMG’s CMOST module (CMG 2020) with the DECE history-matching approach that has been proved to be a reliable and efficient method when it comes to history matching the reservoir engineering problems55.

In this study, experimental data on oil recovery, cumulative gas production, and pressure drop along the core plug were used to simultaneously estimate the gas-oil relative permeability and capillary pressure functions. The pre-defined forms of flow functions are adopted from the LET relative permeability and Gang-Kelkar capillary pressure models56,57, respectively, as outlined below:

$$\:{\text{S}}_{\text{o}\text{D}}=\left(\frac{{\text{S}}_{\text{o}}-{\text{S}}_{\text{o}\text{r}\text{g}}}{1-{\text{S}}_{\text{w}\text{c}\text{o}\text{n}}-{\text{S}}_{\text{g}\text{c}\text{o}\text{n}}}\right)$$
(1)
$$\:{\text{k}}_{\text{r}\text{g}\text{o}}={\text{k}}_{\text{r}\text{g}\text{c}\text{l}}\left(\frac{{\left(1-{\text{S}}_{\text{o}\text{D}}\right)}^{{\text{L}}_{\text{g}\text{o}\text{g}}}\:}{{\left(1-{\text{S}}_{\text{o}\text{D}}\right)}^{{\text{L}}_{\text{g}\text{o}\text{g}}}+{\text{E}}_{\text{g}\text{o}\text{g}}{\text{S}}_{\text{o}\text{D}}^{{\text{T}}_{\text{g}\text{o}\text{g}}}}\right)$$
(2)
$$\:{\text{k}}_{\text{r}\text{o}\text{g}}={\text{k}}_{\text{r}\text{o}\text{g}\text{c}\text{g}}\left(\frac{{\text{S}}_{\text{o}\text{D}}^{{\text{L}}_{\text{g}\text{o}\text{o}}}\:}{{\text{S}}_{\text{o}\text{D}}^{{\text{L}}_{\text{g}\text{o}\text{o}}}+{\text{E}}_{\text{g}\text{o}\text{o}}\left((1-{\text{S}}_{\text{o}\text{D}})^{{\text{T}}_{\text{g}\text{o}\text{o}}}\right)}\right)$$
(3)
$$\:{\text{p}}_{\text{c}\text{o}\text{g}}={\text{p}}_{\text{d}}^{\text{*}}\times\:{\left(\frac{1-{\text{S}}_{\text{g}}-{\text{S}}_{\text{o}\text{r}\text{g}}-{\text{S}}_{\text{w}\text{c}\text{o}\text{n}}}{1-{\text{S}}_{\text{o}\text{r}\text{g}}-{\text{S}}_{\text{w}\text{c}\text{o}\text{n}}-{\text{S}}_{\text{g}\text{c}\text{o}\text{n}}}\right)}^{-{\text{a}}_{\text{g}}}$$
(4)

where \(\:{\text{S}}_{\text{o}\text{r}\text{g}}\), \(\:\text{L}\), \(\:\text{E}\), \(\:\text{T}\), \(\:{\text{k}}_{\text{r}\text{g}\text{c}\text{l}}\), \(\:{\text{k}}_{\text{r}\text{o}\text{g}\text{c}\text{g}}\), \(\:{\text{p}}_{\text{d}}^{*}\), \(\:{\text{a}}_{\text{g}}\) are the parameters used in the history matching processes. Additionally, \(\:{\text{S}}_{\text{w}\text{c}\text{o}\text{n}}\)​ is assumed to remain constant at the irreducible water saturation level, while \(\:{\text{S}}_{\text{g}\text{c}\text{o}\text{n}}\)​ and \(\:{\text{S}}_{\text{g}\text{c}\text{r}\text{i}\text{t}}\)​ are set to zero. In addition, it is noteworthy that the ignorance of water-oil flow functions in the study is because the processes of gas injection were conducted at irreducible water saturation, where the water phase is totally immobile. The LET relative permeability model was adopted due to its versatility and proven suitability for history matching. With three tuning parameters, this correlation allows independent control over curve shape across different saturation ranges, making it highly flexible for accurately reproducing displacement behavior53. For capillary pressure, the Gang–Kelkar model was selected because of its ability to capture both spontaneous and forced imbibition characteristics and to reliably represent capillary pressure curves derived from production data during history matching56,57.

Furthermore, the Betté’ model (Coats 58; Betté et al. 59) available in CMG/GEM was employed to account for the mechanism of IFT effects by interpolating between immiscible (initial \(\:{\text{k}}_{\text{r}\text{o}\text{g}}\) and \(\:{\text{k}}_{\text{r}\text{g}\text{o}}\)) and miscible hydrocarbon relative permeabilities (\(\:{\text{k}}_{\text{r}\text{h}}\)) using a weighting function (\(\:{\text{f}}_{{\text{k}}_{\text{r}}}\)), detailed in the Eqs. (5–9). When the gas/oil IFT (\(\:{{\upsigma\:}}_{\text{g}\text{o}}\)) drops below the threshold IFT (\(\:{{\upsigma\:}}_{\text{g}\text{o}}^{\text{*}}\)), the oil and gas relative permeabilities, \(\:{\text{k}}_{\text{r}\text{o}\text{t}}\)​ and \(\:{\text{k}}_{\text{r}\text{g}\text{t}}\) respectively, are adjusted, otherwise they remain the same as their initial values. According to the Eq. (8), smaller values of the weighting factor \(\:{\text{f}}_{{\text{k}}_{\text{r}}}\) strengthens the influence of IFT on relative permeabilities. A similar approach was taken to adjust oil/gas capillary pressure values when (\(\:{{\upsigma\:}}_{\text{g}\text{o}}\le\:{{\upsigma\:}}_{\text{g}\text{o}}^{\text{*}}\)), although the exponent (\(\:{\text{n}}_{{\text{p}}_{\text{c}}}\)) used in weighting factor (\(\:{\text{f}}_{{\text{p}}_{\text{c}}}\)) is different, leading to independent adjustment of capillary pressure due to the IFT effects, as can be seen in the Eq. (9).

$$\:{\text{k}}_{\text{r}\text{h}}=0.5({\text{k}}_{\text{r}\text{o}\text{g}\text{c}\text{g}}+{\text{k}}_{\text{r}\text{g}\text{c}\text{l}})$$
(5)
$$\:{\text{k}}_{\text{r}\text{g}\text{t}}={\text{f}}_{{\text{k}}_{\text{r}}}{\text{k}}_{\text{r}\text{g}\text{o}}+\left(1-{\text{f}}_{{\text{k}}_{\text{r}}}\right){\text{k}}_{\text{r}\text{h}}\left(\frac{{\text{S}}_{\text{o}}}{1-{\text{S}}_{\text{w}}}\right)$$
(6)
$$\:{\text{k}}_{\text{r}\text{o}\text{t}}={\text{f}}_{{\text{k}}_{\text{r}}}{\text{k}}_{\text{r}\text{o}\text{g}}+\left(1-{\text{f}}_{{\text{k}}_{\text{r}}}\right){\text{k}}_{\text{r}\text{h}}\left(\frac{{\text{S}}_{\text{o}}}{1-{\text{S}}_{\text{w}}}\right)$$
(7)
$$f_{{k_{r} }} = \left\{ {\begin{array}{*{20}l} {1,} \hfill & {\sigma _{{go}} > \sigma _{{go}}^{*} } \hfill \\ {\left( {\frac{{\sigma _{{go}} }}{{\sigma _{{go}}^{*} }}} \right)^{{n_{{k_{r} }} }} ,} \hfill & {\sigma _{{go}} \le \sigma _{{go}}^{*} } \hfill \\ \end{array} } \right.,\;f_{{p_{c} }} = \left\{ {\begin{array}{*{20}l} {1,} \hfill & {\sigma _{{go}} > \sigma _{{go}}^{*} } \hfill \\ {\left( {\frac{{\sigma _{{go}} }}{{\sigma _{{go}}^{*} }}} \right)^{{n_{{p_{c} }} }} ,} \hfill & {\sigma _{{go}} \le \sigma _{{go}}^{*} } \hfill \\ \end{array} } \right.$$
(8)
$$\:{\text{p}}_{\text{c}\text{o}\text{g}\text{t}}={\text{f}}_{\text{p}\text{c}}{\text{p}}_{\text{c}\text{o}\text{g}}$$
(9)

Results and discussion

This section presents the results of cumulative gas production, oil recovery, and pressure drop from compositional simulations of the coreflooding experiments, and history-matched gas-oil relative permeability and capillary pressure functions, along with their adjusted parameters, are also provided. Additionally, to comprehensively evaluate the prevailing oil mobilization mechanisms during the tertiary gas injection, the ternary diagrams and pseudo-component production throughout the coreflooding experiments are analyzed.

Production results and the history-matched flow functions

The experimental as well as compositional simulation results of cumulative gas production, oil recovery, and pressure drop from coreflooding experiments, including secondary lean gas injection, secondary continuous enriched gas injection (10% NGL + 90% DG), and secondary lean gas injection followed by tertiary enriched gas injection (10% NGL + 90% DG) are illustrated in Figs. 3 and 4. A comparison of the ultimate oil recovery factors indicates that tertiary enriched gas injection increases the oil recovery from 73% at the end of secondary lean gas injection to 85%, aligning closely with the recovery achieved through secondary enriched gas injection. This improvement is attributed to both compositional and IFT effects, which become more active upon the initiation of tertiary enriched gas injection. The detailed analyses of the reasons behind how tertiary enriched gas injection would trigger the rigorous interplay of these mechanisms, leading to a significant enhanced oil recovery, are provided in sections ‎3.2 and ‎3.3.

Fig. 3
figure 3

Comparison of experimental and history-matched (a) oil recovery, (b) pressure drop along the core, and (c) cumulative gas production for secondary lean gas injection followed by tertiary enriched gas (10% NGL + 90% DG) injection.

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Fig. 4
figure 4

Comparison of experimental and history-matched (a) oil recovery, (b) pressure drop along the core, and (c) cumulative gas production for secondary continuous enriched gas (10% NGL + 90% DG) injection .

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As shown in Figs. 3 and 4, the DECE history matching technique achieved a strong alignment with the experimental production and pressure drop data. The history-matched gas-oil relative permeability and capillary pressure, used by the compositional simulator to accurately predict experimental production and pressure drop data for secondary lean gas injection, secondary continuous enriched gas injection, and tertiary enriched gas injection following secondary lean gas injection, are presented in Figs. 5 and 6, and Fig. 7 respectively. Additionally, the history-matched parameters for gas-oil relative permeability, capillary pressure, and IFT effects models are detailed in Table 5. The comparison of flow functions across various injection schemes reveals that enriching the injectant with intermediate components results in more linear gas-oil relative permeabilities, a reduction in gas-oil capillary pressure, as well as \(\:{\text{S}}_{\text{o}\text{r}\text{g}}\). Although the injectant composition in tertiary enriched gas injection matches that of secondary enriched gas injection, the resulting flow functions differ significantly due to variations in saturation history and oil mobilization mechanisms, which will be discussed in detail in sections ‎3.2 and ‎3.3. These differences highlight the inadequacy of flow functions from secondary gas injection for simulating tertiary enriched gas injection, underscoring the need for re-determination of relative permeability and capillary pressure functions tailored to tertiary gas injection processes.

Fig. 5
figure 5

Comparison of history-matched (a) gas-oil relative permeabilities and (b) capillary pressure functions for secondary lean gas injection.

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Fig. 6
figure 6

Comparison of history-matched (a) gas-oil relative permeabilities and (b) capillary pressure functions for enriched gas (10% NGL + 90% DG) injection.

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Fig. 7
figure 7

Comparison of history-matched (a) gas-oil relative permeabilities and (b) capillary pressure functions for tertiary enriched gas (10% NGL + 90% DG) injection following secondary lean gas injection.

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Table 5 History matched parameters of the relative permeability (LET), capillary pressure, and IFT effects models in secondary and tertiary gas injection processes.
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Ternary diagrams

As shown in Fig. 8, the composition paths of the gas phase, oil phase, and overall mixture at a specified grid block (0.5 × L away from the injector grid, where L is the length of the porous medium) throughout the processes of secondary lean gas injection, secondary continuous enriched gas (10% NGL + 90% DG) injection, and secondary lean gas followed by tertiary enriched gas (10% NGL + 90% DG) injection are analyzed.

During secondary lean gas injection, the oil phase composition evolves primarily parallel to (CH4− = 0) axis, with intermediate components (C2–C12) being evaporated into the gas phase, and heavy components (C13+) contributing more to the oil phase. The ultimate overall fluid composition indicates that a significant portion of the oil remains, highlighting the limited efficiency of the lean gas injection process. However, throughout the secondary continuous enriched gas injection, the overall fluid composition predominantly approaches gas phase composition, implying that the overall mixture contains a negligible amount of the oil phase, suggesting a satisfactory efficiency for the secondary continuous enriched gas injection process. More interestingly, as can be seen in Fig. 8, despite the processes in which miscibility conditions are achieved by pressurizing, in the core-plug compositional simulations in which miscibility is approached by enrichment of the injectant, the miscibility conditions are not immediately achieved in the early stage of the process46,47.

Following the compositional paths in tertiary enriched gas injection shows that the onset of tertiary flooding causes compositional paths to change course as the oil phase composition mainly progresses parallel to the axis (CH4− = 0) with an increase in intermediate components (C2 to C12), signifying the dissolution of intermediate components from the gas phase into the oil phase. Therefore, a combined condensing/vaporizing gas drive makes the displacement of oil by the enriched gas highly efficient47. Ultimately, the trajectory of the overall fluid composition toward the gas phase indicates that the final mixture contains only a negligible fraction of the oil phase. This outcome reflects the high efficiency of the tertiary enriched gas injection process in recovering residual oil after secondary gas drive.

Fig. 8
figure 8

Composition paths of the gas phase, oil phase, and overall mixture at midlength (0.5 L) throughout (a) secondary lean gas injection, (b) enriched gas (10% NGL + 90% DG) injection, and (c) secondary lean gas injection followed by tertiary enriched gas (10% NGL + 90% DG) injection. (The start and end points of the processes are marked in the figures).

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Component production

In order to compare the relative dominance of the prevailing oil mobilization mechanisms and the extent to which near-miscibility is achieved, the production of a heavy pseudo-component throughout the processes of secondary lean gas, followed by tertiary enriched gas (10% NGL + 90% DG) injection, and secondary continuous enriched gas (10% NGL + 90% DG) injection is displayed in Figs. 9 and 10, respectively. The left, middle, and right columns represent the moles of the pseudo-component in the injector well, whole core, and producer well, respectively. It should also be noted that all the processes were conducted at a constant rate with the pressure of 4200 psi and temperature of 107 °C, and the moles of the pseudo-component are calculated under standard conditions for the left and right columns and under reservoir conditions for the middle column.

C12 + heavy pseudo-component

As illustrated in Figs. 9 and 10, in the left column, due to the absence of the C₁₃⁺ in the composition of injectants, the molar amount of the pseudo-heavy component remains consistently zero; therefore, the C₁₃⁺ pseudo-component appearing in the gas phase, either in the core or the producer sector, has to be traced back to the oil phase. In the middle column, comparing secondary injection processes, as near-miscibility is approached by enrichment, more component exchange due to compositional effects as well and IFT effects causes the ultimate moles of C₁₃⁺ in the oil phase to decrease and the molar content of C₁₃⁺ in the gas phase to increase, suggesting more C₁₃⁺ of the oil phase is vaporized into the gas phase and eventually is produced, manifesting itself through a greater production of the pseudo-component in the right column.

Interestingly, switching the injection scheme from secondary lean gas to tertiary enriched gas injection enhances component exchange due to compositional effects. This shift can also reduce the IFT to values below the critical threshold, leading to a decrease in residual oil saturation. Consequently, more target oil becomes available for component exchange, extraction from volatile oil, and eventual recovery under near-miscible conditions. Following the onset of tertiary enriched gas injection after secondary lean gas injection, the C₁₃⁺ content in the oil decreases more rapidly, transitioning into the gas phase. Consequently, a comparison of the ultimate recovery reveals that tertiary enriched gas injection following secondary lean injection achieves a comparable recovery of C₁₃⁺ compared to secondary continuous enriched gas injection, suggesting a reliable, efficient enhanced oil recovery (EOR) method.

Fig. 9
figure 9

C13+ pseudo-component molar content in the injector, core, and producer sectors throughout secondary lean gas injection followed by tertiary enriched gas (10% NGL + 90% DG) injection.

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Fig. 10
figure 10

C13+ pseudo-component molar content in the injector, core, producer sectors throughout secondary continuous enriched gas (10% NGL + 90% DG) injection.

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Summary and conclusions

This study investigates the effectiveness of tertiary enriched gas injection following secondary lean gas injection for residual oil recovery as a relatively unexplored enhanced oil recovery method in previous research. To address this, a series of experiments involving injecting lean gas followed by enriched gas in volatile oil-saturated carbonate core samples was conducted. The CMG/GEM compositional module was employed to simulate the experiments, and the DECE history matching technique was applied to match experimental data on oil recovery, cumulative gas production, and pressure drop. For the first time, gas-oil relative permeability and capillary pressure functions for the tertiary enriched gas injection following secondary lean gas injection were simultaneously determined. The following conclusions can be drawn,

  • Tertiary enriched-gas injection increased the ultimate oil recovery factor from 73% (after secondary lean-gas flooding) to 85%, representing a significant increase in oil recovery. This demonstrates that enrichment can effectively mobilize residual oil left behind after secondary lean-gas injection.

  • Compositional and interfacial tension (IFT) effects were found to strongly influence flow behavior and relative permeability during tertiary enriched-gas injection. The derived gas–oil relative permeability and capillary pressure functions for tertiary enriched-gas injection differ substantially from those obtained in secondary gas floods, reflecting the impact of saturation history and altered fluid interactions. As a result, flow functions from secondary gas injection are inadequate for accurately simulating tertiary processes.

  • This study demonstrates, for the first time, the simultaneous derivation of gas–oil relative permeability and capillary pressure functions for tertiary enriched-gas injection following secondary lean-gas injection, and highlights the need for dedicated experimental characterization or model calibration to capture history-dependent multiphase flow behavior in tertiary injection scenarios.

  • Ternary diagram trajectories and component production analyses revealed that the dominant recovery mechanism during tertiary enriched-gas injection is a combined vaporizing–condensing gas drive, enhanced by increased intermediate hydrocarbon transfer and interfacial tension reduction.

  • These findings show that tertiary enriched-gas injection could be a technically promising strategy for enhancing residual oil recovery in reservoirs that have previously undergone secondary lean-gas injection, particularly under reservoir conditions where increasing injection pressure to achieve miscibility is not operationally or economically feasible. This approach is best suited for reservoirs containing volatile to intermediate oils, where the addition of intermediate hydrocarbon components to the injection gas can significantly enhance mass transfer and reduce interfacial tension. In contrast, its effectiveness diminishes for heavy oils with limited volatile fractions.

  • Overall, this work fills a key gap in the literature by providing experimental cases and history-matched flow functions for tertiary enriched-gas injections and by illustrating the underlying oil-mobilization mechanisms under these specific reservoir and operational constraints. These insights provide a stronger basis for reliable modeling and design of tertiary hydrocarbon-gas recovery strategies.