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Development and Validation of a New Model for In Situ Foam Generation Using Foamer Droplets Injection

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Abstract

Foam generation and transport in porous media are a proven method to improve the sweep efficiency of a flooding fluid in enhanced oil recovery process and increase the effectiveness of a treatment fluid in well intervention procedures. Foam in the porous media is often generated using surfactant alternating gas or co-injection. Although these operations result in good incremental production, the profit losses could be high due to surfactant retention and lack of water injection facilities in the target fields. One way of reducing foam generation operations expenses is by injecting the surfactant solution disperse throughout the gas phase in a process called “disperse foam.” Core-flooding experimental results have shown that disperse foam techniques reduce the surfactant retention and increase cumulative oil production. This increase means that not only the foam is being generated but also it is blocking the high mobility channels and enhancing the sweep efficiency. Additionally, the operational implementation in field operations is very simple and reduces significantly operational costs of the process. Because few laboratory core-flooding tests and field pilots have been executed using the disperse foam technique, there is a high level of uncertainty associated with the method. Besides, the models reported in the literature do not account for all the associated phenomena, including the surfactant droplets transfer between the gas and liquid phases, and the lamellae stability at low water saturation. For this reason, the development of a mechanistic disperse foam model is key to understand the phenomena associated with “disperse foam” operations. In this work, we use a previous foam mechanistic model to develop a disperse foam model that includes the physicochemical mechanisms of the foaming process a core scale. The model accounts for the foamer mass transference between the gas and liquid phases in a non-equilibrium state with a particle interception model, also accounts for the reversible and irreversible surfactant adsorption on the rock surface in dynamic conditions with a first-order kinetic model, and includes foam generation, coalescence and, transport using a population balance mechanistic model.

Introduction

As the oil saturation in the reservoir is reduced and displacement processes are applied to the reservoir, viscous forces and capillary forces increase. Therefore, flow front fingering generates preferential flow channels and the displacement process becomes inefficient. The preferential flow channels are also generated by reservoir heterogeneities, such as natural fractures and high permeability channels, as well as gravitational segregation when low-density flooding fluids are used, such as recycling gas, nitrogen, flue gas or CO2. Enhanced oil recovery (EOR) foams have proven to be a viable option for increasing oil production in gas flooding projects (Hirasaki 1989; Kovscek and Radke 1993; Blaker et al. 1999; Patil et al. 2018). Foams can block high conductive zones, and they have much higher effective viscosity than the gas, leading to a reduction of viscous fingering and gravity segregation caused by gas injection (Kovscek and Radke 1993; Rossen and Wang 1999; Jamshidnezhad et al. 2010; Luo et al. 2018). As a consequence, foam technology significantly improves the sweep efficiency of recovery projects with gas injection (Hirasaki 1989; Farajzadeh et al. 2012; Li et al. 2012; Zeng et al. 2016).

Most of the EOR foams used in gas injection projects are created in situ using the surfactant alternating gas (SAG) technique: after a well conditioning operation, a liquid foamer solution slug is pumped into the formation; then, gas is continuously injected, generating in situ foam in the most conductive zones of the reservoir contacted with the liquid slug. Although SAG is an effective method for EOR foams generation, one of its major drawbacks relies on the limited contacted volume of the reservoir (Ocampo et al. 2018). Surface equipment and services to pump the liquid surfactant solution are required for SAG field deployments, increasing the operational costs. One alternative to increase the foamer penetration radius and to reduce the operational costs is based on the dispersed foaming technique (Ocampo 2016; Ocampo et al. 2018).

The dispersed foaming technique is based on the injection of foamer droplets carried by a gas stream. The droplets are introduced to the formation and further transferred to the water phase creating a surfactant solution. The combined action of the foamer solution above the critical micelle concentration and an interstitial gas velocity above a threshold value promotes the in situ foam generation. Previous core-flooding evaluations demonstrated that stable blocking foams can be in situ created by the dispersed foamer droplets technique using much lower chemical concentrations than these used in liquid batches injections. These tests also showed that foamer retention rate is two or more orders of magnitude slower when injected in the gas stream than the adsorption loses in the liquid slug injection. The latter implies that higher reservoir volumes can be contacted by the dispersed foaming technique. As a consequence, the foamer droplets can reach deeper zones of the reservoir, overcoming one of the SAG limitations using the gas phase as the carrier fluid (Ocampo et al. 2018). The operative costs and complexity of the deployment operation in fields having gas injection facilities are reduced.

Nevertheless, there are key questions about the performance of the new foaming technique at field scale, such as (1) Effective reservoir volume contacted by the foamer; (2) Foamer concentration distribution and loses in the porous rock; (3) Foam generation depth and durability; (4) Foam blocking capacity and strong/weak behavior; (5) Foam generation and stability in low water saturation scenarios; among other questions. A field-scale deployment of the EOR foams generated using the dispersed foaming technique requires an adequate understanding of the underlying phenomena. A rigorous model can help in reducing the risk associated with the use of a new technology. One of the most important elements aspects of the model is the representation of the blocking foam.

Up to date, foam models can be classified into three major approaches: empirical methods, semi-empirical methods and mechanistic or full physics methods. Empirical or semi-empirical models correlate operational variables with gas relative permeability and/or gas viscosity, using a wide range of experimental conditions from laboratory tests and field observations (Ma et al. 2014). The application of these models is restricted, but they are easy to implement. On the other hand, mechanistic approaches are based on the physical mechanisms of the processes. The mechanistic approaches quantify foam texture or bubble density and relate them to foam mobility. Mechanistic models require specific parameters obtained from history matching of experimental/pilot tests and demand more computational time than empirical and semi-empirical models. The major advantage of mechanistic models is the predictive capabilities making more accurate predictions than the empirical and semi-empirical models over a wider region of operative conditions.

We present a new model for simulating the dispersed foaming operation. Section 2 initially introduces the main phenomena of the dispersed foaming technique through the conceptual model. Then, the model transport equations and the constitutive relations are presented. At the end of Sect. 2, the numerical solution strategy for the resulting set of partial differential equations is outlined. The model parameters are adjusted in Sect. 3 using reported experimental data (Ocampo et al. 2018; Ocampo 2016). Additionally, the impact of unknown parameters on the final oil recovery is evaluated through a sensitivity analysis. The simulation of the dispersed foaming technique at well scale and the comparison with SAG are presented in Sect. 4. Main conclusions are highlighted at the end of the paper.

Model Formulation

In the dispersed foaming technique, the foamer solution is dispersed into droplets using a nozzle in the wellhead. The mist travels through the well, reaching the formations opened for injection. Once the foamer droplets are transported into the formation, some of these will be transferred to the liquid phase by an interception mechanism. Consequently, the surfactant concentration in the liquids phases increases as a result of the droplets interception. Depending on the amphiphilic behavior of surfactants, the foamer will be partitioned between the water and oil phases. On the other hand, foamer is adsorbed into the rock matrix. Because the concentrations are initially low the mass transfer mechanism will proceed under non-equilibrium conditions. As soon as the aqueous foamer concentration reaches the critical micelle concentration (CMC), and the interstitial gas and water velocities are adequate, foam generation, transport and coalescence happen as the conventional SAG and co-injection techniques. Finally, the foamer solution is further advected and dispersed in the liquid phases. Main phenomena and mechanisms are summarized in Fig. 1.

Fig. 1
figure1

Disperse foaming mechanisms

The mathematical model is formulated based on the transport and sorption equations for the surfactant, and the foam mechanistic model, coupled to a three-phase flow model. The flow equation for the oleic and gas phase is formulated based on the extended black oil model (Ertekin et al. 2001):

$$ \frac{\partial }{\partial t}\left( {\phi S_{\text{g}} \rho_{{{\text{g}},{\text{sc}}}} b_{\text{g}} + R_{s} \phi S_{\text{o}} \rho_{{o,{\text{sc}}}} b_{\text{o}} } \right) + \nabla \cdot \left( {\rho_{{{\text{g}},{\text{sc}}}} b_{\text{g}} \varvec{u}_{\text{g}} + R_{s} \rho_{{o,{\text{sc}}}} b_{\text{o}} \varvec{u}_{\text{o}} } \right) + \rho_{{{\text{g}},{\text{sc}}}} b_{\text{g}} q_{\text{g}} = 0 $$
(1)
$$ \frac{\partial }{\partial t}\left( {\phi S_{\text{o}} \rho_{{{\text{o}},{\text{sc}}}} b_{o} + R_{v} \phi S_{\text{g}} \rho_{{{\text{g}},{\text{sc}}}} b_{\text{g}} } \right) + \nabla \cdot \left( {\rho_{{o,{\text{sc}}}} b_{\text{o}} \varvec{u}_{\text{o}} + R_{v} \rho_{{{\text{g}},{\text{sc}}}} b_{\text{g}} \varvec{u}_{\text{g}} } \right) + \rho_{{o,{\text{sc}}}} b_{\text{o}} q_{\text{o}} = 0 $$
(2)

where ϕ is porosity, S is phase saturation, ρ is fluid density, b is the inverse of the formation factor volume, u is the phase velocity, q is well production–injection term, Rs is the dissolved gas in the oleic phase and Rv is the volatilized gas–oil ratio. Subscripts sc indicates standard conditions and g and o denotes gas and oil, respectively.

A key element of the proposed model is the transport of the surfactant in the droplets transported by the gas phase and aqueous and oil phases. In addition, surfactant adsorption occurs. Considering that surfactant concentration in liquid phases is initially zero and gradually increases as foamer droplets collide, mass transfer rate between phases is slow. Therefore, the assumption of local equilibrium does no longer hold in the dispersed foaming technique. The surfactant transport equations are presented in Eqs. (5)–(8), respectively, for the droplets in gas phase, aqueous phase and oleic phase:

$$ \frac{\partial }{\partial t}\left( {\phi S_{\text{g}} \rho_{{{\text{g}},{\text{sc}}}} b_{\text{g}} c_{\text{sg}} } \right) + \nabla \cdot \left( {\rho_{{{\text{g}},{\text{sc}}}} b_{\text{g}} \varvec{u}_{\text{g}} c_{\text{sg}} } \right) + c_{\text{sg}} \rho_{{{\text{g}},{\text{sc}}}} b_{\text{g}} q_{\text{g}} = - \dot{m}_{{{\text{s}},{\text{g}} \to {\text{o}}}} - \dot{m}_{{{\text{s}},{\text{g}} \to w}} $$
(3)
$$ \frac{\partial }{\partial t}\left( {\phi S_{\text{w}} \rho_{{w,{\text{sc}}}} b_{\text{w}} X_{\text{sw}} } \right) + \nabla \cdot \left( {\rho_{{{\text{w}},{\text{sc}}}} b_{\text{w}} \varvec{u}_{\text{w}} X_{\text{sw}} } \right) + X_{\text{sw}} \rho_{{w,{\text{sc}}}} b_{\text{w}} q_{\text{w}} = \dot{m}_{{{\text{s}},{\text{g}} \to {\text{w}}}} - \dot{m}_{{{\text{s}},{\text{w}} \to {\text{o}}}} - \dot{m}_{{{\text{s}},{\text{w}} \to {\text{r}}}} $$
(4)
$$ \frac{\partial }{\partial t}\left( {\phi S_{\text{o}} \rho_{{{\text{o}},{\text{sc}}}} b_{\text{o}} X_{\text{so}} } \right) + \nabla \cdot \left( {\rho_{{o,{\text{sc}}}} b_{\text{o}} \varvec{u}_{\text{o}} X_{\text{so}} } \right) + X_{\text{so}} \rho_{{o,{\text{sc}}}} b_{\text{o}} q_{\text{o}} = \dot{m}_{{{\text{s}},g \to o}} + \dot{m}_{{{\text{s}},{\text{w}} \to o}} - \dot{m}_{{{\text{s}},o \to {\text{r}}}} $$
(5)

where csg represents the surfactant droplets dispersion ratio (chemical solution volume/gas volume), Xsw and Xso represent the surfactant concentration in water and oil phases and s is the surfactant mass transfer rate between phases.

Because foamer droplets interception to the aqueous phases increases water saturation, the equation of the water phase is modified by adding the mass transfer term, as follows:

$$ \frac{\partial }{\partial t}\left( {\phi S_{\text{w}} \rho_{{w,{\text{sc}}}} b_{w} } \right) + \nabla \cdot \left( {\rho_{\text{w,sc}} b_{\text{w}} \varvec{u}_{\text{w}} } \right) + \rho_{{w,{\text{sc}}}} b_{\text{w}} q_{\text{w}} = \dot{m}_{{w,g \to {\text{w}}}} $$
(6)

The water transport equation in the droplets phase is:

$$ \frac{\partial }{\partial t}\left( {\phi S_{g} \rho_{g,sc} b_{g} c_{wg} } \right) + \nabla \cdot \left( {\rho_{g,sc} b_{g} \varvec{u}_{g} c_{wg} } \right) + c_{wg} \rho_{g,sc} b_{g} q_{g} = - \dot{m}_{w,g \to w} $$
(7)

The sorbed surfactant equation on the porous rock accounts for the mass transfer from/to the oleic and aqueous phases, as follows:

$$ \frac{\partial }{\partial t}\left( {\left( {1 - \phi } \right)\rho_{\text{r}} N_{{{\text{s}},{\text{r}}}} } \right) = \dot{m}_{s,w \to r} + \dot{m}_{s,o \to r} $$
(8)

where Nsr the surfactant adsorption in the rock.

Foam characteristics are modeled using the lamella population balance method (LPBM) (Falls et al. 1988; Patzek 1985, 1988; Kovscek and Radke 1994). Here, foam texture is represented by a lamella concentration which is estimated using a population balance equation. Changes in foam texture are defined by lamella generation and coalescence dynamics. The method allows for an effective tracking of the foam texture and a good description of stationary and transient flows. The LPBM equation has a conservative form, similar to the multiphase flow equations, simplifying the coupled numerical solution. According to the LPBM, a fraction of the created foam can be transported through the reservoir and the remaining one is trapped. Depending on the operative conditions foam generation and destruction can occur simultaneously. In addition, the LPBM allows for injected or produced foams through the wells. The population equation can be expressed as follows (Kovscek and Radke 1994):

$$ \frac{\partial }{\partial t}\left( {\phi (S_{\text{f}} n_{\text{f}} + S_{\text{t}} n_{\text{t}} )} \right) + \nabla \cdot \left( {\varvec{u}_{\text{g}}^{f} n_{\text{f}} } \right) - \phi S_{\text{g}} \left( {r_{\text{g}} - r_{\text{c}} } \right) + \dot{q}_{\text{f}} = 0 $$
(9)

where n denotes number of lamellas per unit of volume (lamella texture), rc in the lamella coalescence rate and rg is the lamella generation rate. Subscripts f and t denotes flowing and trapped foam.

Constitutive Equations

The non-equilibrium process happening in the disperse foam method involves different mass transfer mechanisms. Water and surfactant transfer rate form the foamer droplets to the liquid phases depends on the droplets concentration and velocity as well (Walmsley et al. 1996). The water and surfactant rate from the droplets to the aqueous phase can be described using the interception model:

$$ \dot{m}_{{w,g \to {\text{w}}}} = K_{\text{wg}}^{\text{int}} c_{wg} \rho_{\text{g}} V_{\text{g}} \varphi S_{\text{g}} $$
(10)
$$ \dot{m}_{{{\text{s}},g \to {\text{w}}}} = K_{\text{sg}}^{\text{int}} c_{\text{sg}} \rho_{\text{g}} V_{\text{g}} \varphi S_{\text{g}} $$
(11)

where Kint is the kinetic interception coefficients and V is the interstitial velocity. The surfactant dissolution between oleic and aqueous phases can be expressed as follows:

$$ \dot{m}_{{{\text{s}},w \to {\text{o}}}} = K_{s,w \to o}^{\text{dis}} \left( {X_{\text{s,o}}^{\text{eq}} - X_{\text{s,o}} } \right) $$
(12)

where Kdis is the kinetic diffusion coefficient from aqueous phase to oleic phase, X is the surfactant mass fraction in oil and superscript eq denotes equilibrium conditions. The linear driving force model is used to represent adsorption and desorption rate:

$$ \dot{m}_{{{\text{s}},{\text{p}} \to {\text{r}}}} = K_{\text{s,r}}^{\text{ads}} \left( {N_{\text{s,r}}^{\text{eq}} - N_{\text{s,r}} } \right) $$
(13)

where Kads is the kinetic sorption coefficient, and subscripts r and p represent the rock phase and liquid phases, respectively. Both, Kads and Neq depend on the temperature and surfactant concentration.

Finally, the constitutive equations for foam generation, coalescence, trapped fraction and apparent viscosity are (Kovscek and Bertin 2003; Kovscek and Radke 1993, 1994; Kovscek et al. 1995):

$$ r_{\text{g}} = K_{1} v_{\text{f}}^{a} v_{\text{w}}^{b} $$
(14)
$$ r_{\text{c}} = K_{ - 1}^{0} v_{\text{f}} n_{\text{f}} \left( {\frac{{P_{\text{c}} }}{{P_{\text{c}}^{*} - P_{\text{c}} }}} \right)^{2} $$
(15)
$$ P_{\text{c}}^{*} = P_{{{\text{c}},\hbox{max} }}^{*} \tanh \left( {\frac{{C_{\text{s}} }}{{C_{\text{s}}^{0} }}} \right) $$
(16)
$$ X_{\text{t}} = X_{{{\text{t}},\hbox{max} }} \left( {\frac{{\beta n_{\text{t}} }}{{1 - \beta n_{\text{t}} }}} \right) $$
(17)
$$ \mu_{v}^{f} = \mu_{v}^{0} + \frac{{\alpha n_{f} }}{{v_{v}^{c} }} $$
(18)

where K1 and K−1 are the foam kinetic generation and coalescence parameters, Cs is the foamer concentration in aqueous phase, Cs0 is the reference foamer concentration where the foam is generated and a, b, c, β and α are model parameters. Where the trapped foam Xt is used to modify the gas saturation in the relative permeability calculation.

Numerical Solution Strategy

The dispersed foaming model has a set of nine coupled and non-linear partial differential equations that must be numerically solved to simulate the process. The conservation equations are discretized based on finite volume method (Versteeg and Malalasekera 2007), using the upstream weighting method for implicit mobilities calculation (Ertekin et al. 2001). Primary variables are pressure, gas-phase saturation, water-phase saturation and chemical concentration in each phase. The bubble density is explicit and calculated sequentially after the main cycle iteration. Equations are linearized using Newton method and solved using GMRES with ILU preconditioning (Saad 2003). Two grid systems were used: 1D for core-flooding parameters estimation and a 2D for well-scale predictions and analysis.

Results and Analysis

In order to validate the mechanistic model, we simulated the co-injection test reported by Kovscek et al. (1995). The model coefficients reported by Kovscek et al. (1995) were used in our simulation and can be found in Tables 1 and 2. The simulated pressure and saturation distributions are presented in Fig. 2 as well as the experimental observations reported by Kovscek et al. (1995).

Table 1 Foam population balance model parameters (Kovscek et al. 1995)
Table 2 Flow parameters (Kovscek et al. 1995)
Fig. 2
figure2

Pressure (upper) and saturation (lower) distributions. Lines: simulation results (Dark), Kovscek results (Gray). Symbols: experimental data from Kovscek et al. (1995)

A good agreement between experimental observations and simulation results is observed in Fig. 2. The simulation results of foam texture form our model and from Kovscek et al. (1995) are shown in Fig. 3.

Fig. 3
figure3

Foam texture distribution. Lines: simulation results. Symbols: simulation results from Kovscek et al. (1995)

Although simulation results from both solvers have a similar behavior, our simulations predict an increase in the foam texture at the foam front. A similar behavior has been observed in other works (Kam 2008; Apaydin and Kovscek 2001; Ma et al. 2018). Once the foam model was successfully validated with experimental data and simulation results from Kovscek et al. (1995), the dispersed foaming model parameters will be adjusted based on experimental tests.

Parameter Fitting

Since multiple mass transfer dynamics are included in the model, their coefficients must be determined by a history matching procedure of laboratory or field data. Therefore, the parameters adjustment is based on the simulation of experimental conditions reported by Ocampo et al. (2018), following the respective protocols. The parameter fitting is done with the following workflow: (1) The adsorption and desorption kinetic coefficients are adjusted using dynamic adsorption tests at different concentrations of aqueous solution injection. (2) The disperse retention kinetic parameters are adjusted using disperse foamer retention core test in dry cores. (3) Finally, core-flooding tests with different foam blockage conditions are used to adjust the foam parameters and their effect on oil mobility.

The core used in laboratory test has the properties shown in Table 3 (Ocampo et al. (2018)).

Table 3 Core properties

Three different foamer solutions with 1000 ppm, 2000 ppm and 3000 ppm of foamer were injected liquid to the core at the first test, measuring the foamer concentration in effluent until the rock sample becomes saturated. Then, a batch of water is injected to evaluate desorption behavior. The experimental and simulated breakthrough curves for 1000 and 3000 ppm inlet foamer concentration presented in Fig. 4, indicates that the dynamic sorption model reproduced the experimental observations, the adjusted parameters can be found in Table 4. Table 4 shows the dynamic adsorption kinetic parameters.

Fig. 4
figure4

Foamer concentration in the core exit for different inlet concentrations: 1000 ppm (upper), 5000 ppm (lower); lines: Simulation results; symbols: Experimental data from Ocampo et al. (2018)

Table 4 Dynamic adsorption kinetic parameters from aqueous phase

In the disperse dynamic adsorption–retention tests, a foamer solution dispersed in the gas stream is injected in a dry core. Surfactant solution volume and concentration are measured in the effluent stream. Based on experimental measurements, the interception coefficient is estimated through a history matching procedure. A good matching was obtained using 0.028 s−1 as Kint, as shown in Fig. 5.

Fig. 5
figure5

Dispersed foamer retention test for an inlet foamer solution concentration in gas of 103 ppm carried by 1000 cc/min (standard conditions) of gas rate. Saturation adjustment (upper), Foamer adsorption validation (lower); Symbols: Experimental data form Ocampo (2018), Line: Simulation

Once the dynamic sorption and retention coefficients are estimated, the foam generation and destruction coefficients are adjusted based on blocking foam generation and oil recovery tests. These tests start with oil-saturated cores with connate water saturation, which are initially flooded with a gas injection at different gas rates. Oil recovery is registered during the gas flooding test until no significant volumes are further produced. Then, a batch of foamer solution is dispersed in the gas stream and injected to the core. The test finishes with a gas postflush. Incremental oil production is permanently recorded. One case reported by Ocampo et al. (2018) was simulated.

We selected an experimental case showing a good blocking performance and a high recovery factor. Dry gas was injected initially into the core at a rate of 11.8 cc/min (at test conditions) and an interstitial velocity of 10.8 m/day, achieving a recovery factor of 52% OOIP after 160 min (45 PV at test conditions). Then, the foaming solution was dispersed on the injection gas stream at a concentration of 140 ppm, creating a blocking foam after 560 min (369 PV at test conditions). At the end of the test, the blocking foam reduced the gas conductivity to 94%. During the history matching of the foaming stage, we found that water saturation must be corrected because of the injected dry gas makes water to evaporate. If no correction is made, the model predicts that foam generates earlier than the experimental observations. The chemical concentration and water saturation distribution predicted by the model without saturation correction are presented in Figs. 6 and 7. It is noted in Fig. 6 that the critical micelle concentration (300 ppm) is reached after 140 min (114 PV at test conditions) at the foamer injection stage, much earlier than the experimental observation (300 and 400 min, or 200–260 PV at test conditions). In Fig. 7 water saturations increases above the residual condition, allowing the foam to be created. Therefore, we corrected the initial water saturation of the core at the beginning of the foamer injection stage using the correlation from Khaled (2007). The evaporated water volume was approx. 1 cc, accounting for a reduction in water saturation from 0.2380 to 0.1993 (16.4%). Once the corrected residual water was used, the experimental data was properly reproduced by the simulation. The simulated water saturation distribution, after correcting the initial saturation at the beginning of the foamer injection stage, is presented also in Fig. 7.

Fig. 6
figure6

Active foamer concentration in water at different times from the beginning of the foamer injection stage. Continuous line: 160 min or 125 PV at test conditions. Dashed-dotted line: 560 min or 358.7 PV at test conditions

Fig. 7
figure7

Water saturation distribution after 320 min (211 PV at test conditions) of the foamer injection stage Dashed-dotted line: without evaporation correction. Continuous line: with evaporation correction

Figure 8 shows that the foam is generated and destroyed uniformly in the core. The foam begins to generate and to stabilize at 520 min after the disperse injection starts (continuous line), reaching a maximum texture 40 min later (580 min since the beginning of the disperse injection as shown by the dashed line). Then, the foam texture decreases as shown by the texture distribution at the end of the test (604 PV) indicated in the dotted line in Fig. 8. This could be the reason why the foams generated in the core test by foamer dispersions are more stable than the foams generated by SAG, as concluded by Ocampo et al. (2018).

Fig. 8
figure8

Foam texture at different times from the beginning of the foamer injection stage. Continuous line: 520 min (340 PV at test conditions). Dashed line: 580 min (360 PV at test conditions). Dotted line: at the end of the test (604 PV at test conditions)

The comparison of the core conductivity, gas flow rate and recovery factor predicted by the model and experimental measurements are presented in Figs. 9, 10 and 11. A good agreement between the experimental results from Ocampo (2018) and the simulated results was found. The oil recovery factor prediction reaches a close value to the experimental data, where the recovery factor changes from 52.0% OOIP after the gas base injection to a recovery of 70.5% after the generation of the blocking foam. It is important to remark that the simulation results have a different behavior for oil recovery factor, since it shows two phases of incremental oil production: the first, when the blocking foam is formed, and the second, when the foam begins to coalesce. The adjusted parameters can be found in Table 5.

Fig. 9
figure9

Gas conductivity along the core. Symbols: Experimental data from Ocampo (2018). Line: Simulation results

Fig. 10
figure10

Gas flow rate injected to the core. Symbols: Experimental data from Ocampo (2018). Line: Simulation results

Fig. 11
figure11

Oil recovery factor. Symbols: Experimental data from Ocampo (2018). Line: Simulation results

Table 5 Foam population balance model parameters

Finally, a sensitivity test was carried out to evaluate the impact of the main model parameters on the core conductivity. The conductivity value was taken when the blocking foam is generated after 160 min of test; the results of the sensitivity test can be found in Fig. 12. It can be seen that the parameters with greatest change in the blocking effect over the core are β and the lamellae generation kinetic parameter K1. These parameters affect the foamrelative permeability and the lamellae generation rate.

Fig. 12
figure12

Core conductivity tornado chart at time 160 min, after blocking foam generation

Table 6 presents the different scenarios for each variable to be evaluated. A total of 20 simulations were carried out varying parameter by parameter. This methodology allows to identify which parameter has a greater impact on the gas conductivity of the core. The conductivity value was taken when the blocking foam is generated after 160 min of test. The results of the sensitivity test can be found in Fig. 12.

Table 6 Sensitivity to foam population balance model parameters

Conclusions

  • A mechanistic model that reproduces successfully the foam process by the injection of dispersed droplets in the gas stream at core scale was developed. The implemented model is multiphasic and multicomponent, and represents both the mass transfer between phases and the foam kinetics.

  • After the model is calibrated using some experimental data sets, it can predict the behaviour of a much broader set of experimental conditions for the dispersed foam process. The ability of the model to predict different sets of laboratory tests after the adjustment validates the developed model.

  • One of the most critical factors for the generation of dispersed foams is the monitoring of the mobility of the aqueous phase, for that reason the volumetric contribution of the foaming solution was integrated into the model using the interception mechanism.

  • The model must be adapted to include the effects of water evaporation by dry gas injection, as observed in the development of the work the water evaporation is a determining factor to design a dispersed foams operation.

  • The foam is generated and destroyed uniformly through the core, which may indicate why the dispersed foam is more stable than the foam generated by SAG in the experimental cases of Ocampo et al. (2018).

Abbreviations

a, b, c :

Velocity exponents in Eqs. (14)–(18)

b :

Inverse of the formation volume factor (Shrinkage)

C s :

Foamer concentration

C sg :

Foamer droplets dispersion ratio

J :

Diffusion flux

K :

Kinetic mass transfer term

K − 1, K1 :

Generation and coalescence parameters

:

Mass transfer

N :

Adsorbed mass fraction

n :

Foam texture, bubble density

Pc :

Capillary pressure

Pct :

Threshold capillary pressure

q :

Flow

rg, rc :

Generation and coalescence foams kinetics

Rs, Rv :

Dissolved gas in the oleic phase, volatilized gas–oil ratio

S :

Phase saturation

t :

Time

u :

Darcy velocity

v :

Interstitial velocity

X :

Component concentration, Foam quality

α :

Foam model parameters

β :

Foam model parameters

ρ :

Phase density

ϕ :

Porosity

0:

Reference condition

f:

Flowing foam

g:

Gas phase

j:

Flow direction

o:

Oil

p:

Phase

r:

Rock

s:

Surfactant (foamer)

Sc:

Standard conditions

T:

Trapped foam

W:

Water phase

:

Pc ∞

0:

Reference

* :

Limit value

ads:

Adsorption

des:

Desorption

int:

Interception

dis:

Dissolution

Eq:

Equilibria

f:

Foam

Np:

Phase number

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Acknowledgements

Authors thank Equion, COLCIENCIAS and the Agencia Nacional de Hidorcarburos for financial support under Contract No. 273-2017. Authors also thank the Universidad Nacional de Colombia for logistic and financial support.

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Correspondence to Juan D. Valencia.

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Valencia, J.D., Ocampo, A. & Mejía, J.M. Development and Validation of a New Model for In Situ Foam Generation Using Foamer Droplets Injection. Transp Porous Med 131, 251–268 (2020) doi:10.1007/s11242-018-1156-5

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Keywords

  • Foam EOR
  • Foam modeling
  • Disperse foamer
  • Foam generation
  • Coalescence