Introduction

Microbes are ubiquitous in almost all global oil reservoirs; normally, they are noted for biodegradation of alkane components of hydrocarbons, thereby changing its physical property (e.g. viscosity). The use of microbes to recover oil has been in existence for over a century, often referred to as microbial enhanced oil recovery (MEOR). MEOR is best suited for depleted and marginal reservoirs, thereby extending the life of oil wells (Lazar et al. 2007). The environmental and economic advantage of this method makes it the point of interest as per this research. MEOR could be achieved by the reduction in IFT through biosurfactant or bacteria cell, selective plugging by biopolymer, and oil viscosity reduction by biogas, acids and solvents.

The development of detailed MEOR model proves to be challenging not only by the complexity of microbiology but also because of the variety of physical and chemical variables that control the microbe’s behaviour in porous media. Table 1 highlights past researches conducted to bring light to MEOR simulation and the respective challenges outlined.

Table 1 Past studies related to microbial enhanced oil recovery (MEOR) modelling
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Considering related works regarding MEOR modelling, most neglect fluid viscosity changes by biodegradation and gas production, temperature variation and biogeochemistry (or redox chemistry) of the MEOR process (Table 1). More so, MEOR per gas production is simulated as conventional water-alternating gas flooding. Hence, the need to model and optimizing MEOR considering fluid viscosity and reservoir heterogeneity at field scale.

Since the early 1990s, there have been many reported MEOR projects involving oil viscosity reduction and its accompanying oil recovery increment. The San Andreas well in the USA discovered in 1945 started with the primary drive mechanism, water injection in 1967 and lastly MEOR in 1994. After 19 months of MEOR operations, there were decreased oil viscosity and 10% increase in average daily production (Segovia et al. 2009). In China, the Huaibei field (1995) and Xinjiang field (1996) were both treated to MEOR operation after water injection. After 12 and 24 months of evaluation, the Huaibei field recorded 52% incremental daily production and 36% increase for the Xinjiang field, respectively. Both recovered these oil increments because of reduction in oil viscosity (Segovia et al. 2009). Also, in 2004, two producer wells, part of the Peruvian Block X which were under water flooding, were treated by microbe flooding. After 2 months of evaluation, the oil viscosity reduced by 20% but with no significant oil decline rate improvement (Segovia et al. 2009).

The geological heterogeneity of most oil wells is important regarding the optimization of most EOR field applications and its optimization. Unfortunately, geological uncertainty is an inherent characteristic of reservoir models because of the noisy and sparse nature of seismic data, error-prone core measurements and well logs (Yang et al. 2011). Aside other crucial factors—such as rock–fluid properties, injected component and well-operating conditions—a change in reservoir model distribution per heterogeneity significantly influences EOR performance (Al-Mudhafar et al. 2018). Porosity and permeability heterogeneity might influence microbe growth, its transport and metabolism, which will in turn influence oil recovery.

Recently, artificial intelligence (AI), such as artificial neural networks (ANNs), has been adopted to tackle the issues of reservoir heterogeneity and many other applications in the oil industry. For instance, Ahmadi et al. (2014a) and Ahmadi and Chen (2018) demonstrated the accuracy of an ANN model in predicting reservoir heterogeneity comparing real petrophysical data (porosity and permeability data). Also, Ahmadi (2012) developed an ANN model to predict asphaltene precipitation—indicating a high accuracy between ANN model and the experimental precipitation data. Also, ANN was utilized to generate a predictive model to define condensate-to-gas ratio and dew point pressure in retrograded condensate gas reservoirs (Ahmadi et al. 2014b; Ahmadi and Ebadi 2014). Other diverse applications in production technology are: (1) machine learning-based ANN to predict the bottom hole pressure in multiphase flow in vertical oil production (Ahmadi and Chen 2019); (2) a robust intelligent model to monitor the performance of chemical flooding in oil reservoirs (Ahmadi 2015); (3) performance monitoring of CO2-foam flooding for EOR and CO2 storage (Moosavi et al. 2019); and (4) improving CO2 water-alternating-gas (WAG) combining sequential Gaussian simulation (SGS), co-kriging and ANN to optimize both CO2 storage and enhance oil recovery (Vo Thanh et al. 2020).

In this study, we show that a compositional model is necessary for MEOR full-field modelling through complicated geological heterogeneity and biogeochemical process. The basic objective was to maintain hydrocarbon component balance so that the recoverable hydrocarbon (both light/heavy) could be determined as a function of the injected microbe and their bioproduct effect. Hence, we modelled microbe-induced fluid viscosity variations by a thermophile, Petrotoga japonica sp. (Purwasena et al. 2014a, b). Objectively, we developed a model that incorporates: (1) reservoir simulation of microbe-induced oil viscosity reduction and (2) field-scale simulation and robust geological uncertainty workflow considering the influence of well placement. Adopting the same methodology as Vo Thanh et al. (2020), a robust workflow is presented herein to capture the critical effects of uncertain geological distribution on MEOR performance. In this light, this study is intended to expand the scope of MEOR simulation studies from 1D to field scale focussing on fluid viscosity variation and heterogeneity which lacks in most MEOR studies.

Microbial enhanced oil recovery simulation

We conducted reservoir simulations using both CMG STARS and CMOST. An 8-component model: water, microbe, reproduced microbe, yeast extract, CH4, CO2, dead/heavy oil fractions (C17–C20) and light oil fractions (C10–C15) were used to model the dynamic flood data (Table 2).

Table 2 Component composition and fluid properties for simulation
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Governing equations

The multiphase multidimensional flow through the porous media is represented by the following equations for oil, water, microbe, nutrient and bioproduct, respectively. \( R_{\rm{c}} \), \( R_{\rm{m}} \) and \( R_{\rm{p}} \) describe the various rates associated with microbe growth, nutrient consumption and bioproduct production (Sugai et al. 2007):

$$ \alpha \frac{\partial }{\partial t}\left( {\phi S_{\rm{o}} \rho_{\rm{o}} } \right) = \nabla \left( {\alpha \frac{{k_{\rm{o}} }}{{\mu_{\rm{o}} }}\rho_{\rm{o}} \nabla \varPhi_{\rm{o}} } \right) - \alpha q_{\rm{op}} $$
(1)
$$ \alpha \frac{\partial }{\partial t}\left( {\phi S_{\rm{w}} \rho_{\rm{w}} } \right) = \nabla \left( {\alpha \frac{{k_{\rm{w}} }}{{\mu_{\rm{w}} }}\rho_{\rm{w}} \nabla \varPhi_{\rm{w}} } \right) + \alpha (q_{\rm{wi}} - q_{\rm{wp}} ) $$
(2)
$$ \alpha \frac{\partial }{\partial t}\left( {\phi S_{\rm{w}} \rho_{\rm{w}} W_{\rm{c}} } \right) = \nabla \left( {\alpha \frac{{k_{\rm{w}} }}{{\mu_{\rm{w}} }}\rho_{\rm{w}} W_{\rm{c}} \nabla \varPhi_{\rm{w}} } \right) + \alpha \left\{ {\rho_{\rm{w}} R_{\rm{c}} - W_{\rm{c}} (q_{\rm{wi}} - q_{\rm{wp}} )} \right\} $$
(3)
$$ \alpha \frac{\partial }{\partial t}\left( {\phi S_{\rm{w}} \rho_{\rm{w}} W_{\rm{m}} } \right) = \nabla \left( {\alpha \frac{{k_{\rm{w}} }}{{\mu_{\rm{w}} }}\rho_{\rm{w}} W_{\rm{m}} \nabla \varPhi_{w} } \right) - \alpha \{ \rho_{\rm{w}} R_{\rm{m}} - W_{\rm{m}} (q_{\rm{wi}} - q_{\rm{wp}} )\} $$
(4)
$$ \alpha \frac{{\text{d}}}{{\text{d}t}}\left( {\phi S_{\rm{w}} \rho_{\rm{w}} W_{\rm{p}} } \right) = \nabla \left( {\alpha \frac{{k_{\rm{w}} }}{{u_{\rm{w}} }}\rho_{\rm{w}} W_{\rm{p}} \nabla \varPhi_{\rm{w}} } \right) + \alpha \left\{ {\rho_{\rm{w}} R_{\rm{p}} - W_{\rm{p}} (q_{\rm{wi}} - q_{\rm{wp}} )} \right\} $$
(5)

Reaction engineering

Normally, microbe cell grows as an attachmemt to the alkane, even though growth with n-alkanes is slower (Widdel and Grundmann 2010). All n-alkanes per literature are degraded anaerobically to oxidized CO2 or completely converted to CO2 and CH4 as per the following reactions (Eqs. 6–7), in the presence of sulphate or nitrate source (Widdel and Grundmann 2010).

$$ 5{{\rm{C}}_n}{{\rm{H}}_{2n + 2}} + \left( {6n + 2} \right){\rm{NO}}_3^- + \left( {6n + 2} \right){{\rm{H}}^+ }\mathop {\longrightarrow}\limits^{{\rm{yields}}} {\rm{ }}5n{\rm{C}}{{\rm{O}}_2} + \left( {3n + 1} \right){{\rm{N}}_2} + \left( {8n + 6} \right){{\rm{H}}_2} $$
(6)
$$ 4{{\rm{C}}_n}{{\rm{H}}_{2n + 2}} + \left( {2n - 2} \right){{\rm{H}}_2}{\rm{O}}\mathop {\longrightarrow}\limits^{{\rm{yields}}} {\rm{ }}\left( {n - 1} \right){\rm{C}}{{\rm{O}}_2} + \left( {3n + 1} \right){\rm{C}}{{\rm{H}}_4} $$
(7)

In CMG STARS, the related reaction of a process in a general form is defined as:

$$ n_{A} \cdot M_{A} + n_{B} \cdot M_{B} + \cdots = n_{C} \cdot M_{C} + n_{D} M_{D} + \cdots $$
(8)

To this effect, the validation of the reaction and the reaction stoichiometry is done by mass balance, so that moles of each component and energy will be conserved:

$$ \sum n_{\rm{reac}} i \cdot M_{\rm{reac}} i = \sum n_{\rm{prod}} i \cdot M_{\rm{prod}} i $$
(9)

According to Alkan et al. (2016); Bultemeier et al. (2014), Monod’s kinetics can be replaced by the following reaction rate for microbe growth as per the CMG STARS equation for chemical reactions:

$$ r = F_{\rm{Freq}} \cdot {\text{e}}^{{\left( { - E_{\rm{act}} |R \cdot T} \right)}} \mathop \prod \limits_{i = 1}^{{n_{\rm{c}} }} C_{i} $$
(10)

The exponential factor is responsible for the temperature dependency, and the model calculates a nonzero reaction rate at the initial reservoir temperature (60 °C).

Then, the rate of increase in biomass concentration, \( x \) (cells/ml) of AR80 at a time, \( t \) (h), and a specific maximum growth rate, \( r_{ \max} \) (1/h), are given as:

$$ \frac{{{\text{d}}x}}{{{\text{d}}t}} = r_{ \max } \cdot x $$
(11)

Integrating Eq. (11) solves the bacteria cell number at a time (Sugai et al. 2014):

$$ x_{t} = X_{{t -\Delta t}} .{\text{e}}^{{r_{\max } .\Delta t}} $$
(12)

In this study, a simplistic model in which the effect of temperature on microbe growth rates was ascertained using the Arrhenius expression. However, the decay rate was not considered primarily because the growth of microbe was assumed to proceed at a maximal rate, which is influenced positively by temperature until impairment (Goldman and Carpenter 1974). With the knowledge that the change of growth with temperature is expressed as activation energy, the maximum growth as a single rate-limiting step was computed as:

$$ r_{ \max } = A{\text{e}}^{{ - \left[ {\frac{{E_{\rm{a}} }}{RT}} \right]}} $$
(13)

where \( r_{ \max } \) is the maximum microbe growth rate (day−1), \( A \) is the frequency factor (−), \( E_{\rm{a}} \) is the activation energy (kJ mol−1), \( R \) is a molar gas constant (kJ mol−1K−1) and \( T \) is the reaction temperature (K).

Then, the concentration factors are calculated based on their concentration in the respective reference phases as (wherein j is the phase in which component i is reacting, and \( X_{i,j} \) represents water, oil or gas mole fractions):

$$ C_{i} = \left( {\emptyset_{f} S_{j} \rho_{j} X_{i,j} } \right)^{\text{Expi}} $$
(14)

Also, per CMG STARS, component (say nutrient) consumption is correlated to bacteria growth by a division factor, \( F_{\rm{div}} \):

$$ r_{\rm{div}} = \frac{r}{{F_{\rm{div}} }};\;F_{\rm{div}} = (1 + A_{x i,j} )^{\text{B}} $$
(15)

Heretofore, \( F_{\rm{div}} \) is defined per the bacteria mole fraction to model a plateau to which the bacteria amount does not exceed.

The phase viscosity (\( \mu \)) depends on its respective component viscosity and a weighting factor, f:

$$ \ln \left( {\mu_{i,j} } \right) = \mathop \sum \limits_{j} \left[ {f_{i,j} \cdot \ln \left( {\mu_{i,j} } \right)} \right] $$
(16)

where \( f_{i,j} = X_{j} \) (specific phase mole fraction) for linear mixing; i = water or oil phase; j = specific component in either water or oil.

Also, the liquid viscosity (\( \mu_{{{\text{L}}_{\rm{i}} }} \)) in relation to absolute temperature (\( T_{\rm{abs}} \)) follows the equation:

$$ \mu_{{{\text{L}}_{\rm{i}} }} = {\text{avisc}}_{\rm{i}} * {\text{e}}^{{\left[ {\frac{{{\text{bvisc}}_{\rm{i}} }}{{T_{\rm{abs}} }}} \right]}} $$
(17)

wherein \( {\text{avisc}}_{\rm{i}} \)—viscosity (cP) and \( {\text{bvisc}}_{\rm{i}} \)—temperature difference. Specifying the brine concentration (% NaCl) accounts for the water viscosity (\( \mu_{{{\text{p}},{\text{T}}}} \)) at specific temperatures and pressures as:

$$ \mu_{{{\text{p}}, {\text{T}}}} = \mu \cdot T*f_{{{\text{p}}, {\text{T}}}} $$
(18)

Assuming the incompressible fluid condition, the liquid component (oil or water) viscosity, \( \mu_{{{\text{L}}_{\rm{i}} }} \), in the reservoir can be said to be a function of the microbe growth rate, \( r_{\max } \) (n-alkane biodegradation rate) and mobility, \( \lambda \).

$$ \mu_{{{\text{L}}_{\rm{i}} }} = r_{\max } \cdot \lambda $$
(19)

where mobility defines the relative permeability with respect to a phase (\( k_{\rm{r}} \)) over its viscosity (\( \mu \)):

$$ \lambda = k_{\rm{r}} /\mu $$
(20)

Generation of produced biogas (say CO2) to reduce oil viscosity is modelled as the partitioning of gas between two phases (oil and water) at different pressures and temperatures via K-value as:

$$ K_{{{\text{CO}}_{2} }}^{\text{g}} = \frac{{x{\text{CO}}_{{2\left( {\text{f}} \right)}} }}{{x{\text{CO}}_{{2\left( {\text{l}} \right)}} }} = \frac{{x{\text{CO}}_{{2\left( {\text{l}} \right) + x{\text{CO}}_{{2\left( {\text{g}} \right)}} }} }}{{x{\text{CO}}_{{2\left( {\text{l}} \right)}} }} = 1 + \frac{{x{\text{CO}}_{{2\left( {\text{g}} \right)}} }}{{x{\text{CO}}_{{2\left( {\text{l}} \right)}} }} $$
(21)

The influence of pressure was considered during the simulation even though it was not observed experimentally. At high biodegradation rate, low oil viscosity and high oil velocity flow, the influence of pressure diffuses.

Various models were considered based on the microbe and substrate reaction and its accompanying metabolite(s) responsible for enhanced oil recovery:

  • Model 1 Microbe growth for biomass increase and possible selective plugging

    No geochemical effect and gas production were considered

    $$ 49{\text{H}}_{2} {\text{O}} + 1.001{\text{microbe}} + 1.1{\text{yeast extract}} + 1{\text{CO}}_{2} \to 3.299{\text{microbe}}_{1} $$
    (22)

  • Model 2 Microbe growth for biomass increase and oil degradation by the microbe

    No geochemical effect and gas production were considered

    $$ 49{\text{H}}_{2} {\text{O}} + 1.001{\text{microbe}} + 1.1{\text{yeast extract}} + 1{\text{CO}}_{2} \to 3.299{\text{microbe}}_{1} $$
    (23)
    $$ 2.15{\text{microbe}}_{1} + 1{\text{dead oil}} \to 2.34{\text{light oil}} $$
    (24)

  • Model 3 Microbe growth for biomass increase and oil degradation by microbe and biogas production. Geochemical knowledge was incorporated.

    $$ 49{\text{H}}_{2} {\text{O}} + 1.001{\text{microbe}} + 1.1{\text{yeast extract}} + 1{\text{CO}}_{2} \to 4.299{\text{microbe}}_{1} + 4{\text{CH}}_{4} $$
    (25)
    $$ 2.15{\text{microbe}}_{1} + 1{\text{dead oil}} + 1{\text{CO}}_{2} + 1.45{\text{CH}}_{4} \to 3.34{\text{light oil}} $$
    (26)

Furthermore, these assumptions regarding the injected microbe and nutrient into the oil reservoir contended: (1) the reservoir is not unfriendly to the injected microbe; (2) there is no indigenous microbe presence in the reservoir competing for the injected nutrient; (3) limiting the nutrient, yeast extract mostly influences growth and is influenced by temperature, salinity and its quantity injected; (4) both microbe and nutrient adsorption were negligible; (5) all nutrients, metabolites and microbe components are microscopic; hence, transportation is only in the aqueous phase; (6) the only time the system is in equilibrium is when all the nutrients have been consumed. So long as there is nutrient availability, bacteria growth is bound to happen infinitely.

Implementation of reservoir wettability

Considering special conditions (as microbe and nutrient concentration changes, large increases in applied flow velocities, etc.), the assumption is that rock–fluid properties are functioned only of fluid saturation and saturation histories were not enough to accurately describe the observed flow behaviour. In these cases, the relative permeability and capillary pressure were interpolated as functions of phase saturation and/or capillary number. To this effect, two base sets of real permeability and a log of capillary number interpolant were used to history match water flooding and MEOR flooding laboratory experimental data (Fig. 1). Corey’s expression was used to attain the endpoints for the relative permeability.

Fig. 1
figure 1

Oil and water relative permeability curves a during waterflooding and b during microbe flooding

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Interfacial tension can change the relative permeability curve. Reduction in the IFT caused the relative permeability curves to approach linearity (Fig. 1), thereby causing more oil to be displaced during the microbe flooding due to the less frictional force between the oil/water phases. As shown in Fig. 1, the straightening of the curves can also be due to an increase in viscosity of the hydrophilic phase and the decrease in viscosity of the oil phase as bacteria metabolism proceeds. As observed, the intersection points of the two curves (the water saturation equilibrium point between the oil and water relative permeability) decreased from about 63% at the water flooding stage to below 45% during the microbe flooding. Also, the relative permeability to water at maximum water saturation was less than 30% during the water flooding stage but increased sharply beyond 80% for the microbe flooding. Lastly, a gradual decrease in the irreducible water saturation from beyond 56% to less than 20% strongly indicates a shift from an initial water-wet state to a mixed wet state.

The shift in wettability to a mixed wettability state as represented in Fig. 2 can be attributed to the adhesion of the microbe to the oil/rock interface phase, formation of a stable emulsion by the biomass/biofilm of the microbe and the presence of heavier chain n-alkanes residual after the biodegradation. Figure 2 highlights three stages responsible for the possible wettability variations. Initially, at point (1) the microbes are in a suspension of biofilm (having the injected nutrient and hydrocarbon substrate) with little adherence to the rock mineral. Assuming the presence of fewer organics (solutes, solvents and acids) in contact with the rock surface, the rock is in a water-wet state, putatively. At point (2), the microbes start settling at the rock–fluid interphase with possible consolidation and reversible adhesion. Finally, at point (3), the microbes colonize the rock surface, forming a patch of microcolonies and confluent of biofilm on it. Hence, the presence of higher organics amount changes the wettability to a mixed wet state.

Fig. 2
figure 2

Schematic diagram for relative permeability changes highlighting three stages of adsorption: suspension of microbes right after injection, reversible adsorption stage at the onset of microbe growth and irreversible adsorption and microbe colonization stage

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The uptake of alkane, liquid plus solid alkanes (above C5), is poorly soluble in water, forming droplets (Eastcott et al. 1988; Wilhelm et al. 1977). In anaerobic alkane degradation, accessing alkanes—the attachment of microbe by hydrophobic cell surface to the alkane phase is concurrent with the production of amphiphilic emulsifying compounds that form micelles (Widdel and Grundmann 2010). Furthermore, attachment of the microbes to the oil surface prevents retrapping, hence increasing mobility and enhanced oil recovery. With this said, MEOR can be more effective in the mixed wet core than on the water wet core, because the residual oil is mostly in interconnected films in mixed wet cores against dislodged drops, which might be in the water-wet cores (Kaster et al. 2012).

Homogeneous 1D simulation

A representative model, as well as input data used in this study, is elaborated in Table 3. The model had one injection well and production well, which were in the first and last blocks, respectively. The injector fluid rate was 2.00746 × 10−06 m3/day for the water flooding stage and then switched to 2.0597 × 10−06 m3/day for both the MEOR stage and post-flush stage. The porosity, permeability, injection scenario and other reservoir and production properties used in this model were as from dynamic flooding experiments (Purwasena et al. 2009, 2014b).

Table 3 Simulation input data
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Experimental data for model validation

A thermophilic (Petrotoga Japonica sp.) type of microbe, hereby coded as AR80, was isolated using brine-based and substrate-poor solid culture medium supplemented by CO2 (Purwasena et al. 2014a). Table 4 highlights the composition of the culture medium and brine used in this study. From experimental studies, AR80 degraded n-alkanes under anaerobic conditions at 60 °C as highlighted. They observed the original oil viscosity reduces by almost 70% after 14 days of bacteria incubation with the crude oil (Purwasena et al. 2014b).

Table 4 Ionic composition of brine used for enrichment (of AR80) culture medium a [6]
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A detailed description for optimum controllable conditions (salinity/temperature/pressure/type of crude oil and CO2 analysis) is reported elsewhere (Purwasena et al. 2014b). AR80 could grow under 3% salinity, 60 °C and 6 MPa. Furthermore, both abiotic and biotic core flooding experiments were carried using AR80 to estimate its injectivity, AR80 growability in a porous medium, and EOR potential of AR80. Crude oil with API of 33°, a viscosity of 7 cP (measured at 60 °C) and a density of 0.958 (measured at 15 °C) were used. Detailed core flooding methodology and results are elaborated elsewhere (Purwasena et al. 2009, 2014b). Experimentally, main oil recovery mechanism was due to oil viscosity reduction, resulting from alkane biodegradation (Purwasena et al. 2009, 2014b). Also, they assumed a decrease in mobility ratio from 10 to 6 and increase in sweep efficiency from 0.830 to 0.90 in the core (Purwasena et al. 2009, 2014b).

Microbial growth rate modelling

Figure 3 highlights the bacteria growth rate and its relation to oil viscosity reduction. As per the Arrhenius expression elaborated in Fig. 3a, the exponential microbe growth phase was modelled—a satisfactory agreement between the model and data set is reported. Figure 3b shows the microbe growth against viscosity reduction. The experimental data are as per static bottle test (contacting the microbe with the hydrocarbon—oil), whereas dynamic simulations were conducted to model the experimental data under the same conditions. As the microbe growth proceeds, oil viscosity reduces radically from initial 26.6 to 17.6 cP (for the model) and 16.6 cP (per experiment). The model was run for only 15 days to ascertain this effect at a higher fraction of light oil, CO2 and CH4 by increasing their stoichiometry coefficients (Fig. 3b).

Fig. 3
figure 3

History matching for a oil viscosity reduction and microbe growth rate and b microbe growth rate per temperature variation

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Reservoir simulation: assessment of model types

Figure 4a shows the oil recovery (%) investigated for each model scenario. The increase in oil recovery for all the investigated cases can be related to oil displacement as a function of oil viscosity. As indicated, the oil viscosity decreases from the upstream (injector) to the downstream (producer), accompanied by a mobility increase for heightened oil recovery (Fig. 4b). Fluid acceleration is transferred from one fluid layer to another. It is inferred that the total oil recovered after brine and microbe flood for model type 3 was the highest comparing the two other cases. In the first (1st) case, the biomass cells of the microbe can be said to have played the main role of oil viscosity reduction (Fig. 4b).

Fig. 4
figure 4

a Oil viscosity variation per the different models and b oil recovery (%) per the different models considered

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However, in models 2 and 3, contributions by the biomass cells plus biogenic CO2 and CH4 induced the oil viscosity reduction. As per this, it can be concluded that incorporating the idea of nutrient speciation and rock–fluid/fluid–fluid interaction to produce CH4 and CO2 leads to heightened oil recovery for both the brine and microbe flood stages. Of the three model types, model type 1 had more viscous oil left behind after 90 days (end of the microbe flooding process) (Fig. 4b). An increase in oil viscosity reduction ensured more oil recovery resulting from increased mobility to the production well. Therefore, model type 3 was adopted for history matching of the experimental data.

Figure 5 highlights the history match results for the laboratory experimental data. Due to the intuitive and qualitative nature of manual history match, automatic history match with a quantitative approach was conducted (Fig. 5). Automatic history match (HM) was performed to have a range of plausible HM solution other than one precise HM results. The automatic history match shows improvement in the matching quality and an average history match error of less than 3%.

Fig. 5
figure 5

Oil recovery—history match against experimental data (blue dot)

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Component concentration effect on oil viscosity reduction

Throughout this whole study, it has been established that oil viscosity reduces per alkane biodegradation to improve oil recovery. In this section, elucidation on the phenomenon behind component concentration effect on fluid viscosity variation depicted by the sensitivity assessment is discussed.

We investigated the effect of the various component compositions and reaction frequencies on the oil viscosity and possibly oil recovery (Fig. 6a, b). For instance, the fraction of the initial CO2 in the oil phase (originally in the reservoir) was varied from 0.000148 to 0.005 to promote the reactions in case study 3, and more light components were produced (Fig. 6b). We realized this could also be achieved by changing the stoichiometric coefficient of the components. It can be observed that the viscosity of oil reduced considerably after 90 days of MEOR operation from an initial 7.1–7.07 cP and 6.40 cP, respectively (Fig. 6b).

Fig. 6
figure 6

Oil viscosity variation per component content: a light oil fraction and b CO2 fraction. Start of simulation (left); End of simulation (right)

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Also, the higher amount of lower weight n-alkane originally present in the reservoirs (C10–15) ensured high biodegradation rate and less residual viscous oil. This is so because microbes are known to be able to degrade easily aliphatic chains compared to aromatic or heavier n-alkane chains.

Biomass influence on water viscosity variation

The water viscosity increased from 0.5 to 1.72 cP after the microbe growth and increased biomass/biofilm. It was observed that as the biomass population increased with increasing biomass viscosity (from 5 to 10 cP), there was a correlated increase in the water viscosity (Fig. 7). Increments in the water viscosity can be said to have improved sweep efficiency of the reservoir to recover residual oil. Figure 7 shows the frontal advancement of the reproduced microbe (mass fraction of aqueous phase) in the homogeneous core model. Increasing the biomass population and subsequent biomass viscosity led to selective plugging of preferential areas of the reservoir, ensuring fewer thief zones in the reservoir, because microbes are known to exist in water droplets in the oil phase or even in water film surrounding rock mineral grains (Meckenstock et al. 2014).

Fig. 7
figure 7

Water viscosity variation per biomass increase. Start of simulation (left); End of simulation (right)

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Artificial Neural Network for geological modelling

First, a realistic geological model was created by considering all the crucial factors, including facies, distribution porosity and permeability. The model is a fluvial sandstone reservoir that has two different facies: fluvial channel sand and floodplain shale. The facies model was distributed using a geological package based on object-based modelling using the parameters as shown in Table 5. The distribution of the two facies modelled is presented in Fig. 8. The reaction engineering of the 1D simulation as presented above was upscaled assuming an isothermal condition by fixing the enthalpy of reaction at zero. All other conditions unless otherwise mentioned were kept unchanged.

Table 5 Input parameters used in lithofacies modelling
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Fig. 8
figure 8

Facies model in this study

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Sequential Gaussian simulation (SGS), co-kriging and artificial neural network (ANN) were used for the petrophysical modelling. The ANN was employed to train the seismic attributes and well log to predict porosity and permeability models. SGS and co-kriging were adapted to combine the facies model and ANN prediction cube into one single model. Next, the drill stem test matching was performed to validate the accuracy of the model for further investigation (Vo Thanh et al. 2019a, b). Figure 9 depicts the reasonable porosity and horizontal permeability models for this work.

Fig. 9
figure 9

The reasonable porosity and horizontal permeability models for this study

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Performance of the ANN model

This section highlights the performance of the ANN model. The seismic data and well-log data were represented as input layers in the ANN model, whilst porosity and permeability were the output layers in the training framework. The seismic data were created using four different seismic attributes: signal-processed attributes, complex trace attributes, structural attributes and stratigraphic attributes. Then, the ranking of the seismic attributes was performed using ANN MATLAB toolbox. The performance of the developed ANN model was based on training, validation and blind testing data set. The correlation factor and mean square error (MSE) were then utilized to evaluate the quality and accuracy of the developed ANN model.

After repeated trails training, it was indicated that the neural network model with eight hidden neurons in the hidden layer obtained the excellent performance for the porosity and permeability with a validation MSE value of 3.96 × 10−5 and 2.78 × 10−4, respectively.

The illustration of the ANN network is depicted in Fig. 10. For porosity-type ANN model, the training process was achieved at 35 epochs with a validation MSE of 3.96 × 10−5 (Fig. 11a). Figure 11b depicts the best validation performance and the regression plots of ANN porosity model for training, validation and blind testing groups, respectively. The predictive porosity model matches so well to the well-log porosity values for all training, validation and blind testing groups as can be observed in their correlation factor (R) of 0.946, 0.988 and 0.994 for training, validation and blind testing, respectively.

Fig. 10
figure 10

The architecture of neural network for this work

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Fig. 11
figure 11

Performance and regression plot of porosity ANN model

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Similarly, the performance and regression plot of ANN permeability model are highlighted in Fig. 12. For permeability ANN model, the training process was successfully truncated at 86 epochs with a validation MSE of 2.78 × 10−4. Also, the ANN permeability model fits so well to the well-log permeability values for all training, validation and blind testing groups as can be investigated in their correlation factor (R) of 0.989, 0.983 and 0.978 for training, validation and blind testing, respectively.

Fig. 12
figure 12

Performance and regression plot of permeability ANN model

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Comparison between the developed ANN model and existing artificial intelligence studies

There are many previous studies focussing on the prediction of porosity and permeability using artificial intelligence (AI). Table 6 points out some of these related studies, and the comparison between those AI models and this study. According to Table 6, it can be observed that the prediction accuracy of this study significantly differs from several existing works. In that, the developed ANN model of this study outperforms other AI models. The main reason is because the current ANN model uses less number of neurons in the hidden layer as compared to the previous AI model. Regarding the results in terms of error and efficiency, the ANN models in this study are demonstrated to be more suitable for prediction of porosity and permeability due to higher R2 and low MSE compared to previous AI models.

Table 6 Comparison between the developed ANN model and previous AI models
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Field-scale simulation and optimization

In this section, full-field simulation and optimization are conducted to give insight into recovery efficiency under various drive mechanisms (comparing MEOR and water flooding) and also to show variations through complex reservoir heterogeneity and better tracking of injected microbe (Fig. 13). For field-scale implementation, we set the activation energy to zero to assume isothermal reactions and quicken the MEOR growth and metabolism reaction. When the reaction front sweeps through the reservoir, a certain amount of oil serves as a carbon source for microbe growth. The rest of the mobile oil gets pushed further downstream through viscosity reduction.

Fig. 13
figure 13

Schematic of full-field model simulation and optimization

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Afterwards, multiple geological realizations were generated and ranked to select nine representative realizations to capture geological uncertainties. The geological uncertainty assessment was performed by including the nine quantiles of ranked geostatistical realizations (P10, P20, P30… and P90) for porosity, permeability and anisotropy ratio. To capture the geological uncertainties, 200 porosity and permeability realizations were generated honouring geological constraints using sequential Gaussian simulation. Since it was difficult to simulate all these geological realizations in the optimization process due to limited computational resources, ranking, based on the oil recovery factor, was considered for permeability and pore volume for porosity to select the P10, P20, P30, …, and P90 that represent the overall geological uncertainties. All these permeability models were evaluated in the MEOR reservoir model for the ranking process within 25 years of production.

Figure 14a shows the histogram of the generated 200 porosity realizations based on the pore volume. Also, this figure illustrates the selected nine quantiles (P10, P20, P30, …, and P90) that were obtained based on the cumulative probability curve. Moreover, the 3D model’s distribution of porosity ranking is shown in Fig. 14b. In this illustration, the porosity models show significant difference distribution that covers over all the geological uncertainties. The plot of ranked nine representative permeability models is highlighted in Fig. 14c.

Fig. 14
figure 14

a Histogram of the 200 porosity realization. b 3D models’ distribution of the porosity realizations. c The nine ranked permeability models selected for optimization studies. d Oil recovery factor for the different geological realizations

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Furthermore, Fig. 14d shows the oil recovery factor for the nine different realizations simulated over a 25-year period. This highlights the geological uncertainty effect on oil recovery.

Afterwards, the nine quantiles (P10, P20, P30, …, and P90) were adapted in the robust design for the MEOR process optimization. This high-resolution model consists of 2 million grid blocks. Therefore, it was upscaled to a simulation model with 15,000 grid cells to satisfy the CPU demand in the reservoir simulation. These geological models were later coupled with dynamic flow and physics mechanism of the microbe and substrate reaction in the reservoir simulator as described in the 1D simulation case. Figure 15 depicts the reservoir model with a five-spot line for well placement optimization purpose. The well pattern is the following specification conditions (Table 7).

Fig. 15
figure 15

Five-spot quarter model designed for well optimization

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Table 7 Well conditions for the simulation
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The goal was to optimize the average oil recovery of the total 25 years of MEOR operation by determining the best well location and operating conditions for the four producers from 2018 to 2043. The well placement was considered to evaluate the effectiveness of the most suitable well location to enhance the microbial enhanced oil recovery under geological uncertainties.

Base case simulation results

This study focuses on EOR based upon the promotion of microbial activity that in turn generates appropriate chemicals within the reservoir. Our analysis treats only reservoir inoculation with function-specific microbes, thereby incorporating reaction engineering into reservoir engineering.

Our base case is an exogenous microbe injected and making use of in situ carbon source. As indicated by well bottom hole pressure (Fig. 16), there was improved flow conformance and increased sweep efficiency by preferential plugging of high permeable zones, thereby forcing water to produce oil from previously unswept part of the reservoir. This is highlighted by the increase in pressure at the start of the microbe injection after the pressure flattens at the end of the water flooding regime. Also, assessing the pre- and post-MEOR oil production rate (Fig. 16), we witness two main typical MEOR field responses (Segovia et al. 2009):

Fig. 16
figure 16

Oil rate and well bottom hole pressure for MEOR flooding

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  1. 1.

    Sweeping effect This happens within a relatively short period of time and is characterized by a peak oil rate just after injecting microbes. This further resulted in an increase in oil production due to starting production in originally by-passed oil zones.

  2. 2.

    Radial colonization This happened at the tail end of the microbe treatment at a low oil flow rate. This prolonged MEOR effect causes a continuous oil decline rate due to metabolism (CH4 and CO2) as well as biodegradation of oil n-alkanes specifically at zones further away from colonization radius.

Figures 17 and 18 show the oil saturation map, CO2 and CH4 from the injection wells to the production wells, respectively. This is indicative that the microbe at the onset of injection can grow and be transported from the injection point to the production well whilst producing the needed metabolites for oil recovery. As the microbe grows, the oil saturation decreases from about 0.7 to 0.2 with time (Fig. 17), while the production of biogas increases (Fig. 18).

Fig. 17
figure 17

Oil saturation map

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Fig. 18
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CO2 (top) and CH4 (bottom) saturation maps

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Role of geology in the MEOR process

Using the already generated 200 porosity and permeability realizations, we ranked these to emphasize the critical influence of geology on the MEOR process. As indicated in Fig. 19, the porosity and permeability model variations had a strong influence on the performance of the MEOR process. This plot depicts a wide range of MEOR oil recovery factors, from 28.2 to 44.9% OOIP for the various 200 realizations.

Fig. 19
figure 19

Oil recovery in relation to different geological realizations

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Figure 20 highlights three representative geological realizations with significant dissimilarity in the oil recovery factor. Since the well placement is the same for all realizations, the difference in the permeability distribution amongst the realizations affected the microbes’ transport and subsequent interaction with nutrient during injection and transport. Also, the difference in permeability led to a change in sweep efficiency which influenced the oil recovery factor. These three realizations represent three different classes of MEOR performance, judging from their different geological makeup. The ultimate oil recovery significantly changed from realization 195 (41.6% OOIP) to realization 70 (35.1% OOIP) and to realization 32 (29.2% OOIP), respectively.

Fig. 20
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Three different geological realizations selected for further analysis

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The realization number 32 had the lowest the final oil recovery factor compared with the other realizations, as per its oil saturation map (Fig. 21). The main reason is that the five-spot injection pattern was in a region of floodplain shale facies. Hence, resulting inflow severe associated with the injected aqueous phase through this low-porosity and low-permeability regions. This resulted in less oil displacement compared with realizations 70 and 195, as illustrated in Fig. 21. This case demonstrates that considering only the influence of injected nutrient-brine composition on MEOR without geological uncertainties is not adequate. Basically, salinity brine contact with mineral compositions should influence the microbe growth, transportation and its subsequent production of metabolites to enhance oil recovery. However, placing an injection well in an extreme environment such as a high shale, low-porosity and low-permeability area can be detrimental to oil production and the overall success of MEOR. Therefore, well placement optimization is noted to be very necessary for any MEOR approach and should be considered during the initial field development plan for MEOR implementation.

Fig. 21
figure 21

Residual oil saturation maps for three selected realizations (32, 70 and 195)

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Conclusion

This study has demonstrated that through systematic simulation considering both physical and biochemical parameters, the uncertainties in predicting MEOR can be enlightened. Simultaneous consideration for both geochemical and reservoir simulation reveals these key findings:

  • This study predicted the possibility of modelling fluid viscosity variation that is induced by microbes incorporating the influence of reservoir heterogeneity.

  • Per the core scale model: (1) MEOR can be more effective in the mixed wet core than on the water wet core; (2) water viscosity increased from 0.5 to 1.72 cP after the microbe growth and increased biomass/biofilm; and (3) by changing the stoichiometric coefficient of the components (e.g. CO2), the viscosity of oil reduced considerably after 90 days of MEOR operation from an initial 7.1–7.07 cP and 6.40 cP, respectively.

  • The challenge of upscale from laboratory- to field-scale arises from upscaling the reaction and adjusting well placement to ensure efficient transportation of the microbe from the injection to the targeted zone of recovery.

  • The innovative field-scale workflow by considering multiple plausible geological models simultaneously showed that placing an injection well in an extreme environment such as a high shale, low-porosity and low-permeability area can be detrimental to oil production and the overall success of MEOR.