Microbial Enhanced Oil Recovery - A Modeling Study ...

xxxx manuscript No. (will be inserted by the editor)

Microbial Enhanced Oil Recovery - A Modeling Study of the Potential of Spore-forming Bacteria S. M. Nielsen · I. Nesterov · A. A. Shapiro

Received: date / Accepted: date

Abstract Microbial enhanced oil recovery (MEOR) utilizes microbes for enhancing the recovery by several mechanisms, among which the most studied are: 1) reduction of oil-water interfacial tension (IFT) by the produced biosurfactant, and 2) selective plugging by microbes and metabolic products. One of the ways of bacterial survival and propagation under harsh reservoir conditions is formation of spores. A model has been developed that accounts for bacterial growth, substrate consumption, surfactant production, attachment/filtering out, sporulation and reactivation. Application of sporeforming bacteria is an advantageous novelty of the present approach. The mathematical setup is a set of 1D transport equations involving reactions and attachment. Characteristic sigmoidal curves are used to describe sporulation and reactivation in response to substrate concentrations. The role of surfactant is modification of the relative permeabilities by decreasing the interfacial tension. Attachment of bacteria reduces the pore space available for flow, i.e. the effective porosity and permeability. Clogging of specific areas may occur. An extensive study of the MEOR on the basis of the developed model has resulted in the following conclusions. In order to obtain sufficient local concentrations of surfactant, substantial amounts of substrate should be supplied; however, massive growth of bacteria increases the risk for clogging at the well inlet areas, causing injectivity loss. In such areas starvation may cause sporulation, reducing the risk of clogging. Substrate released during sporulation can be utilized by attached vegetative S. M. Nielsen CERE, DTU Chemical Engineering, Technical University of Denmark Lyngby, Denmark Tel.: +45 45252983 E-mail: [email protected]

bacteria and they will continue growing and producing surfactant, which prolongs the effect of the injected substrate. The simulation scenarios show that application of the spore-forming bacteria gives a higher total production of surfactant and the reduced risk of clogging, leading to an increased period of production and a higher oil recovery. Keywords microbial enhanced oil recovery · bacteria · spores · surfactant · modeling 1 Introduction Microbial enhanced oil recovery (MEOR) is a tertiary recovery method, which has received an increasing interest due to its potential and the low cost investment. The MEOR strategy should be tailored specifically for each reservoir, since variations of the reservoir conditions and characteristics including the microbial community would influence the outcome to a large extent [3, 22, 48, 49]. Different MEOR flooding strategies exist; 1) indigenous bacteria are activated in the reservoir by injecting nutrients, or 2) bacteria compatible with reservoir microbiology and nutrients are injected into the reservoir [7]. A typical nutrient is molasses: a cheap waste product from sugar cane processing [7]. Examples where reservoir oil serves as the sole carbon source also exist [10]. The metabolic products are biomass, surfactants, polymers, solvents, acids and gases, which all to some extent contribute to mobilization of oil. The applied strains should be able to survive the harsh conditions found in the reservoirs. A range of strains has already been investigated and to some extent applied for MEOR (see Table 1) [12, 57]. A part of the MEOR studies is based on Bacillus and Pseudomonas strains [17, 42, 64]. Several MEOR field applications with both

2

S. M. Nielsen et al.

Table 1 Bacteria and their products relevant for MEOR [12]. Family

Products

Clostridium

Gases, acids, alcohols and surfactants Acids and surfactants Surfactants and polymers, can degrade hydrocarbons Polymers Polymers Gases and acids, sulfatereducing Surfactants and alcohols Surfactants Gases and acids

Bacillus Pseudomonas Xanthomonas Leuconostoc Desulfovibrio Arthrobacter Corynebacterium Enterobacter

the activation and injection strategy has been carried out with different degrees of success [6, 7, 11, 27, 41, 65], but to validate the MEOR process, the field applications should in general take place for a longer period of time, and monitoring and analyses should be more systematic and comprehensive [41]. Overall, there is a large future potential in the MEOR processes. The main mechanisms accounting for MEOR are [3, 5, 12, 17, 22, 23, 38, 41]: – Reduction of interfacial tension (IFT) between oil and water due to in situ surfactant production – Fluid diversion due to microbial growth and attachment (selective plugging) – Reduction of oil viscosity by oil degradation and/or gas and other metabolites production The two first mechanisms are regarded the most important ones [57]. The MEOR has primarily been investigated for sandstone reservoirs. Bacteria in the reservoirs are exposed to different kinds of stresses such as starvation, high salinity, high temperatures, and high pH. Bacteria cope with the stress to ensure a better chance of survival. For spore-forming bacteria the last option for survival is sporulation [4, 15, 43, 52]. Spores are smaller, dormant (non-growing) versions of vegetative bacteria, which can survive in very harsh environments [40]. The surface properties of spores make them less likely to attach to the rock surface. They can rather be found in the water phase where they are transported to better conditions for survival [15, 21]. The spores can stay as such for a long time and become reactivated only when the conditions are favorable [15, 43, 52]. In tight reservoirs, such as chalk reservoirs of the Danish part of North Sea, there is an additional stress related to the fact that the pore throat sizes in chalk rock (0.1 − 1 µm [25]) are comparable to the sizes of

bacteria. In spite of that, bacteria are able to penetrate through the rock, and the spore-forming bacteria penetrate chalk better compared to non-spore-forming bacteria [24]. The potential that MEOR brings may be improved by the application of spore-forming bacteria, as was realized already in 1962 [26]. For the modeling study of the potential of sporeforming bacteria in MEOR, the previously developed MEOR simulator has been extended to include sporeforming bacteria, i.e. also covering the processes as sporulation and spore reactivation. Besides them, the 1D generic MEOR simulator includes growth, consumption, and surfactant production. Bacterial surfactant reduces oil-water interfacial tension (IFT) affecting the relative permeability curves. Bacteria and spores attach due to filtration [47–50]. The different injection schemes (alterations of bacteria, spores and nutrient in the injection stream) have been studied. Control over the conversion to or from spores, by selection of the proper injection regime, makes it possible to place the bacteria at specific locations, to control their growth, and to avoid reservoir clogging, resulting in better utilization of the bacteria for the enhanced oil recovery.

2 Background MEOR models have been developed with different selections of mechanisms of bacterial actions [9, 13, 36, 39, 50]. However, as mentioned earlier, the main contribution to the additional oil recovery originates from in situ surfactant production and the selective plugging effect. In this context, the most important mechanisms are that bacteria are able to produce surfactant in sufficient amounts and that bacteria are able to attach at right locations and subsequently plug selected areas.

2.1 Bacteria The applied bacteria must be able to survive under the reservoir conditions and carry out the desired bacterial actions. Typical bacteria are Bacillus and Pseudomonas [29, 32, 38]. An advantage for Bacillus is that it is a facultative anaerobe adapted to reservoir conditions with higher temperature and salinity, and that it can produce surfactant both under aerobic and anaerobic conditions [5, 63]. Several Bacillus strains have been investigated due to their production of surfactants and that they can survive under the harsh reservoir conditions [5, 23, 42, 57, 63]. Bacillus has been emphasized to be a proper bacterium for MEOR when surfactant

MEOR - A Modeling Study of the Potential of Spore-forming Bacteria

production and selective plugging are to be the main mechanisms [57].

2.2 Attachment The transport of bacteria and spores through porous medium depends on different factors. The biological factors include bacterial sizes and shapes [30, 61], surface hydrophobicity [1, 61], tendency to form agglomerates [30], electrostatic or surface charge [34, 44, 61]. Characteristics of the porous medium contributing to the attachment are also the surface charge, as well as the pore throat sizes [34, 44]. Different models have been proposed to describe bacterial attachment during transport in porous media also for the purpose of investigating the selective plugging mechanism. Reversible equilibrium adsorption and filtration are the two main ways for bacterial attachment. Filtration may cover both reversibly and irreversibly attached bacteria [9, 19, 20, 34, 39, 50, 55]. In tight rocks such as chalk bacteria may be filtered out, as described in the deep bed filtration theory, where it is generally believed that the 1/3 − 1/7 rule can be applied [51]. Hence, in this work we assume that the main process of attachment is filtering out [50]. This is contrary to many studies carried out under conditions where pore throat sizes are much larger than the bacteria and with only one phase [33, 59], where other attachment mechanisms become important. Due to smaller sizes and different shapes and surface properties of the spores, it may be assumed that they attach less (or filter out less) compared to vegetative cells. The transport of cells is strongly influenced by their shapes and surface properties [30, 61]. We assume that this is also valid for spores. The spores penetrate easier, since interaction of a spore with a mineral surface is more repulsive in comparison to a vegetative cell. The total free energy of interaction of B. subtilis with the silica sand is estimated as 1.38 · 10−17 J [14], while the total free energy of interaction of B. subtilis spores of different kinds with the same porous medium varies from 2.88 · 10−15 to 6.85 · 10−15 J [15]. Thus, spores tend to remain in the water phase [15] or stick to the water-oil interface due to higher hydrophobicity of their surface [45]. Additionally, they are smaller than cells, which also decrease the probability of their capturing.

2.3 Surfactant production Surfactants are surface-active compounds lowering IFT between oil and water that may help mobilizing additional oil [57]. Different kinds of surfactants are produced by microorganisms [5, 57, 64]. Examples of sur-

3

factants are surfactin and the surfactant group of lichenysins produced by Bacillus [46, 62]. It was found that lichenysin B can lower IFT to 0.006 mN/m and has a critical micelle concentration of 10 mg/L. The effect of surfactant on recovery may be enforced when bacteria are present [31, 35]. The surfactant considered in our model will be of this type. In the appendix, more details on the implementation of the surfactant effect can be found. 2.4 Sporulation Bacteria are turned into spores when substrate is scarce. Reactivation is the reverse process that takes place when substrate is plentiful. The signal transduction network the phosphoelay in the Bacillus bacteria determines whether the bacteria should commit to sporulation as the best strategy of survival or not. The phosphoelay controls initiation of sporulation by phosphorylating specific transcription factors [18, 43]. In comparison with vegetative bacteria, spores are half the size or smaller. The remains of the cell after the sporulation will go into the substrate pool and can be used for growth and production by the other bacteria [4, 43]. Triggering of the sporulation due to starvation depends on the substrate concentration. The triggering function, or rate function, is a sigmoidal curve [52] (also called the logistic function). The sigmoidal nature of the response comes from the allosteric behavior of enzymes and transcription factors involved in the phosphoelay [18, 28]. In addition, the sigmoidal response can amplify the signal, only above a certain threshold [53]. Different approaches to the sporulation process have been presented, but they mainly resulted in the sigmoidal curves to describe the triggering [52, 53]. Reactivation has been modeled in a manner similar to sporulation, where the triggering of reactivation also depends on the substrate concentration [52].

3 Model setup The reservoir is made of porous rock, which a part is rock (1−φ) and the pore volume is φ. The initial porosity is φ0 . In the pore volume, three phases may exist: oil (o), water (w), and the attached phase (a) formed by the attached bacteria and spores. The saturation of a phase is defined as the phase volume over the pore volume; water, oil and attached phase saturations are denoted by sw , so and σ. The phase saturation constraint becomes: sw + so + σ = 1

(1)

4


Oil Water Substrate

Surfactant

Bacteria

Surfactant

Surfactant

Substrate

Bacteria Substrate

Spores Bacteria

Spores

Bacteria

Substrate

γ

Bacteria (attached)

Spores Spores (attached)

Fig. 1 Diagram of flow, components and reactions.

The generic model proposed in this work includes the description of bacteria growing and producing metabolites by consumption of substrates. The reactive transport model describes convection, bacterial growth, bacterial attachment, substrate consumption, and metabolite production. The metabolite is surfactant, which decreases IFT influencing the relative permeability curves. It is assumed that surfactant can be distributed between both phases as described in Nielsen et al [49] and Nielsen [47]. The model presumes that the bacteria can be attached irreversibly due to filtering out. The bacteria can be converted to spores, differing physically and chemically from the vegetative bacteria. The components are shown in table 2, where components are water (w), oil (o), substrate (s), surfactant (m), bacteria (b) and spores (d). The mass concentrations of the components are denoted by ωij , where indices refer to component i in phase j.

Table 2 The mass concentration ωij [kg/m3 ] is displayed for each component i and phase j. Component Oil Water Oil Substrate Surfactant Bacteria Spores

ωoo ωmo -

Phases Water ωww ωsw ωmw ωbw ωdw

Attached ωba ωda

The amounts of other products such as acids, solvents and gases are considered to be negligible, so that only the important components are included [22, 56]. For instance, a limited amount of dioxide will be produced under anaerobic conditions [40]. Diffusion is not included, since it becomes negligible on reservoir scale [8].

A general transport equation is used to describe the transport of each component:     np np ∑ ∂ ∂  ∑ v φ ωij sj  + ωij fj  = qi , ∂t ∂x j=1 j=1 i = {o, w, s, m, b, d}, j = {o, w} (2) The source terms comprise reactions, such as bacterial growth, substrate consumption and surfactant production. Bacterial growth is described by the Monod kinetics depending on concentrations on substrate and bacteria. Reduction of IFT is a function of surfactant concentration. IFT influences residual oil saturation used for calculation of the relative permeabilities that determine the fractional flow function (eq. (2)). Bacteria attach due to the filtering out according to the deep bed filtration theory through a dimensionless rate expression dependent on the filtration coefficient and the bacteria concentration [49, 50]. The overview of flow, components and reactions is shown in figure 1. Sporulation takes place in both water and attached phases, so that both flowing and attached bacteria can be turned into spores. Due to the different surface properties and smaller sizes of the spores, a fraction of the spores formed from the attached bacteria will be released from the attached phase to the water phase. This is determined by the fraction γ of the spores that go into the water phase from the converted attached bacteria. The fraction of spores staying attached is, correspondingly, (1 − γ). The attached bacteria will therefore only be released due to sporulation. The transport equations are thus formulated for flowing bacteria, attached bacteria, flowing spores and attached spores. This system is strongly coupled.

3.1 Sporulation setup It is assumed in the model that sporulation occurs solely due to starvation. The sporulation is described as a first

order reaction for the bacteria, where the rate constant depends on the substrate concentration. The bacteria commit to sporulation when the substrate is below a certain low threshold, and the sporulation becomes very low at high substrate concentrations. Similarly, reactivation takes place when the spores encounter an environment with plentiful of substrate at a high rate. We also assume that spores are half the size of the bacteria, so that during sporulation half of the bacteria will become spores and the other half will be turned into substrate: 1 bacteria 0.5 spore + 0.5 substrate

5

Conversion rate (d-1)


All sporulation rates are dependent on substrate concentration, e.g. Kbd = Kbd (ωsw ). The sporulation rate expressions are as follows, where production is positive. Flowing bacteria rspor,bw = −Kbd (ωsw ) · ωbw

(3)

Attached bacteria rspor,ba = −Kbd (ωsw )γ ωba

3.2 System of dimensionless equations (4)

Spores in water phase and attached phase rspor,dw = −0.5 (rspor,bw + γ rspor,ba )

(5)

rspor,da = −0.5 (1 − γ) rspor,ba

(6)

Substrate production rspor,s = −0.5 rspor,bw

(kg/m3)

Fig. 2 Illustration of conversion rates Ksb from spores to bacteria and Kbs from bacteria to spores as a function of substrate concentration ωsw .

(7)

Similar are the rate expressions for reactivation for flowing bacteria, attached bacteria, water phase spores, attached spores, and substrate, respectively.

The system of dimensionless equations is used as developed and presented in Nielsen et al [50]. Modifications are performed in order to include sporulation and reactivation. An important parameter for the system is α, describing duration of injection of one pore volume. The linear injection velocity is vinj , L is the reservoir length, and φ0 is the initial porosity of the reservoir. α =

φ0 L vinj

rreac,dw =

−Kdb (ωsw ) · ωdw

(8)

The injection velocity is expressed as:

rreac,da =

−Kdb (ωsw ) · ωda

(9)

vinj =

rreac,bw =

−2 rreac,dw

(10)

rreac,ba =

−2 rreac,da

(11)

rreac,s = − (rreac,dw + rreac,da )

(12)

It should be noted that reactivation moves components from one phase to another, similar to sporulation. The sigmoidal response curves come into play through the conversion rate. More details are given in the appendix. Figure 2 shows the resulting sporulation and reactivation response curves as functions of the substrate concentration. The curves are located between a lower and an upper concentration with corresponding maximum and minimum conversion rates.

Qinj H B φ0

(13)

(14)

where Qinj is the volumetric injection rate, H is reservoir height, and B is reservoir width. The dimensionless reservoir length is defined as follows. x (15) ξ = L The dimensionless reservoir length may also be interpreted as the volumetric fraction of the total pore volume. The dimensionless time variable τ is expressed in pore volumes injected (PVI) and is defined as: t α The dimensionless injection velocity is ud : v ud = vinj τ =

(16)

(17)

6


The full system of equations expressed in terms of dimensionless time, velocity and distance is presented below. The fractional flow functions for water fw and oil fo depend on water saturation and IFT, and further details can be found in the appendix. Water ∂ ∂ ( ωww sw ) + (ud ωww fw ) = 0 ∂τ ∂ξ

(18)

The transport equations are fully coupled through saturation constraint, fractional flow functions, reactions, attachment/detachment processes, sporulation, and reactivation. The fractional flow function is a function of saturations through relative permeabilities and indirectly a function of the surfactant concentration, determining the modification of the residual oil saturation. Reactions are depending on bacteria and substrate concentrations.

Oil ∂ ∂ ( ωoo so ) + (ud ωoo fo ) = 0 ∂τ ∂ξ

(19)

Substrate ∂ ∂ ( ωsw sw ) + (ud ωsw fw ) ∂τ ∂ξ ( = α − (sw ωbw + σρb ) · µmax

ωsw Ks + ωsw

)

+ α (rspor,s + rreac,s ) (20) Surfactant ∂ ∂ ( ωmw sw + ωmo so ) + (ud ωmw fw ) ∂τ ∂ξ = α Ysm (sw ωbw + σρb ) µmax

ωsw Ks + ωsw

(21)

Surfactant is distributed between oil and water phases according masses of oil and water through a distribution constant [50, 54]. The equations for the flowing and attached bacteria have the form, respectively: ∂ ∂ ( ωbw sw ) + (ud ωbw fw ) ∂τ ∂ξ ωsw − φ0 λ sw ωbw = α Ysb sw ωbw µmax Ks + ωsw + α (rspor,bw + rreac,bw ) (22)

ωsw ∂ (ωba σ) = α Ysb (ωba σ) µmax ∂τ Ks + ωsw + φ0 λ sw ωbw + α (rspor,ba + rreac,ba ) (23) Spores in water phase ∂ ∂ (ωdw sw ) + (vωdw fw ) = −φ0 λd sw ωbw ∂t ∂x + α (rspor,dw + rreac,dw ) (24) Spores in attached phase ∂ (ωda σ) = φ0 λd sw ωbw ∂t + α (rspor,da + rreac,da ) (25)

4 Parameters and initial conditions The parameters used in the simulations are listed in table 3. The reservoir is considered to be homogenous with respect to initial water and oil saturations. The initial amount of bacteria in the reservoir is assumed to be negligible, since we assume that the bacteria injected are favored under these specific conditions. Bacteria and substrate are continuously injected into the reservoir with the same rate. In the literature related to both enhanced oil recovery and wastewater treatment, many different injection concentrations are used ranging from 10−5 to 10 kg of substrate per m3 [9, 13, 55, 58, 60]. We have chosen a substrate mass fraction from the higher concentration range. This is the standard concentration, serving the basis for further comparison. Either spores or bacteria are injected with the concentrations listed in the table. The bacteria produce surfactant in the reservoir. The particular surfactant involved in the model has a low critical micelle concentration at 10 mg/L and can lower IFT almost three orders of magnitude from 29 mN/m to 0.06 mN/m in order to mobilize the residual oil. The attachment of bacteria may lead to clogging. We assume that clogging takes place when the volumetric fraction of attached bacteria and attached spores, σ, reaches 0.60 anywhere in the reservoir.

5 Numerical solution procedure The total reservoir volume along the one-dimensional grid and is divided into blocks with a defined volume. Injection takes place to the first block and production from the last block. A tanks-in-series approach is used, where the each volume block is considered to be a well-mixed tank. The system of equations (18)-(25) is discretized and solved in a sequential manner using the multivariable Newton-Raphson method (Aziz et al. 2003; Nielsen 2014). The numerical solution is a semiimplicit finite difference technique, where component


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Table 3 Parameters. Value

Dimension

Ks

20

kg/m3

µmax

0.4

day−1

Ki

1

-

ϕ0

0.4

-

Reservoir length L

400

m

Reservoir width B

100

m

Reservoir height H

100

m

Volumetric injection velocity, Qinj

800

m3 /day

µw

1

cP

µo

3

cP

ρi , i = {w, s, b, m, d}

1000

kg/m3

800

kg/m3

σow

29

mN/m

Ysm

0.18

kg/kg

ρo

0.82

kg/kg

ωbw,inj

Ysb

10−3

kg/m3

ωdw,inj

0.5·10−3

kg/m3

ωsw,inj

1

kg/m3

ωmw,inj

0

kg/m3

min Ωbd

10−8

kg/m3

max Ωbd

10−4

kg/m3

0.2

day−1

min Kbd

10−10

day−1

min Ωdb

10−4

day−1

max Ωdb

10−2

day−1

0.5

day−1

10−10

day−1

Kbd0

Kdb0 min Kdb

n

6

-

krwor

0.5

-

krowi

0.8

-

a

2

-

b

2

-

swi

0.3

-

sor

0.4

-

β

500

-

λb

5

-

λd

0.5

-

γ

0.8

-

∆τ

0.05

PVI

Number of cells

2000

-

Bacteria attached Bacteria aq. Surfactant aq.

1.2x10-2

Volume fraction

Parameter

8.0x10-3

4.0x10-3

0.0 0.0

0.1

0.2

0.3

0.4

ξ

Fig. 3 Profile for attached bacteria, flowing bacteria and for surfactant, where ξ is the dimensionless reservoir length.

mass balances and the total volume balance are satisfied. The default number of cells is 2000 and the time step is 0.05 PVI.

6 Results and discussion The bacteria in aqueous phase grow and produce surfactant as they are transported through the reservoir. Bacteria filter out during the transport and accumulate close to the inlet site (fig. 3). Both attached and flowing bacteria produce surfactant, which results in a surfactant peak near the inlet and around the highest concentration of flowing bacteria; however, this is strongly dependent on the relation between flow rate, growth rate and filtration coefficient [50]. The effect of the produced surfactant often appears at a certain distance from the injection point, due to the flowing bacteria peak. Then, due to the bacteria accumulated at the inlet site, surfactant is produced in sufficient amounts and residual oil is mobilized in the space between the area reached from the inlet and the initial mobilization point. Figure 3 shows the profiles of flowing bacteria, attached bacteria and surfactant. When spores or vegetative bacteria are injected, they may filter out. The spores are activated and transformed into vegetative bacteria when the substrate concentration is high enough. The bacteria grow while the substrate is available, producing surfactant and reproducing themselves. In one dimension, the main mechanism for oil mobilization is in situ production of the surfactant. Consequently, the filtration process results in that most attached bacteria and spores are found close to the inlet. A peak of bacteria in the water phase flows

8

through the reservoir. Its growth and reduction depends on, whether the dominating mechanism is that of growth or of the filtering out. Both bacteria in flowing and attached phase grow. When substrate is injected, the bacteria at the inlet area will consume substrate. The remaining substrate is transported to the bacteria found deeper in the reservoir. When the concentration of bacteria at the inlet is high, the inlet bacteria consume all the substrate, grow and may finally clog the reservoir. Prevention of the inlet clogging is thus necessary for the MEOR. One strategy is to limit the substrate injection. However, this may prevent that the full potential for the MEOR process is reached. Application of the spore-forming bacteria for the MEOR process is an advantage since they can reduce the risk of clogging. Continuous injection of substrate and bacteria or spores may still be dangerous. A better idea may be to alter such injection with a water slug of certain size or duration. Then the lack of substrate will imply a state of starvation for the bacteria. Consequently, bacteria will start to sporulate.


consequence, the already produced surfactant is transported with the flow through the reservoir. As a result the residual oil saturation used for the relative permeability calculations increases to initial value. Hereafter, only the water flows and no additional oil is produced. The attached bacteria are mainly accumulated close to the inlet, but the attached spore-forming bacteria will start sporulating during water injection. Sporulation creates spores and substrate, and the latter can be used by remaining attached bacteria for further growth and surfactant production. If the bacteria concentration is high enough, the amount of substrate produced from sporulation will slow down the sporulation rate. Therefore, we see that surfactant is still produced after stopping the substrate injection, reducing the residual oil saturation. In fact, surfactant is produced at suffi-

sw NSP slug 0.20 sw SP slug 0.20 sor NSP slug 0.20 sor SP slug 0.20

0.9 0.8 0.7

second water front

Application of a 5 × standard substrate concentration for injection leads to faster growth and thus the surfactant effect appears faster as well. If the substrate injection concentration is high, then for the spore-forming bacteria there is no difference in injecting spores or vegetative spore-forming bacteria (not shown). Under continuous injection with this substrate concentration and non-spore-forming bacteria, the reservoir clogs already at 0.25 PVI. We compare the spore-forming and non-spore-forming case by applying an injection scheme with a slug with bacteria and substrate from 0 PVI to 0.20 PVI followed by waterflooding. With this bacteria slug size, clogging does not occur and it is possible to focus on the other important effects. Figure 4 shows the comparison of saturation profile at 0.43 PVI and the corresponding recovery curve for injection of spore-forming and non-spore-forming bacteria. The non-spore-forming bacteria have an initial advantage, since a small fraction of spore-forming bacteria will be converted to spores, losing a small fraction of the bacteria, but producing surfactant and more bacteria. The surfactant effect occurs a little earlier for the non-spore-forming bacteria. The second water front for both cases moves almost synchronous during injection of substrate and bacteria slug. When pure water injection starts, the non-spore-forming bacteria stop producing and growing due to the lack of substrate. As a

0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.2

0.4

0.6

0.8

1.0

ξ Cumulative recovery (fraction of OOIP)

6.1 Spore-forming versus non-spore-forming bacteria

Saturation

0.6

1 x slug 0.20 NSP 1 x slug 0.20 SP

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.5

1.0

1.5

2.0

τ (PVI)

Fig. 4 Profile and recovery for spore-forming (SP) and non-spore-forming (NSP) bacteria slug injection. Injection of 0.20 PVI slug with bacteria and substrate followed by water injection. (Top) Residual oil saturation sor used for the relative permeability curves and water saturation sw against the dimensionless reservoir length ξ. (Bottom) Cumulative recovery measured as the fraction of OOIP against the dimensionless time τ .


cient amounts from the substrate released from sporulation until 0.90 PVI, compared to 0.20 PVI where the substrate injection was ended. When the substrate injection stops, the second water front appears and travels with different speeds for the non-spore forming and for the spore-forming bacteria (fig. 4, ξ ≈ 0.55). For the non-spore-forming bacteria, less oil is mobilized behind the second water front and more water moves forward creating a higher water phase saturation, i.e. a lower oil saturation in the oil bank and the second water front advances slower due to this effect. The low oil saturation in the oil bank gives a lower production rate as appearing on the recovery curve. Later breakthrough results in a higher oil recovery for non-spore-forming bacteria, 1.15 PVI vs 0.75 PVI. To this moment, the spore-forming bacteria have produced more oil due to the longer-lasting reduced residual oil saturation. The spore-forming bacteria show a better performance, since reservoir clogging is avoided and the period of oil mobilization is extended, due to the prolonged period of surfactant production and improved utilization of the substrate. The removal of the inlet bacteria by the injected water slug, due to sporulation, is an effect making the slug injection schemes more advantageous in MEOR.

6.2 Effect from water slug injection In order to investigate the effect of water slug injection on the system containing spore-forming bacteria, the water slug of size 0.10 PVI was injected under the different starting times; 0.40 PVI, 0.50 PVI and 0.60 PVI. First, an initial slug with spores only is injected during 0.05 PVI. It is followed by substrate injection before and after the water slug (fig. 5). Fig. 6 shows

9

the profiles for the attached bacteria and the substrate for the case where the water slug is injected from 0.60 PVI to 0.70 PVI. At the front of each water slug, small ’shelves’ of substrate emerge, where the concentration of bacteria is so high that sporulation produces sufficient amount of substrate and thus slows down the conversion rate (see circled area in fig. 6). Sporulation in the water slug results in this substrate ’shelf’, while the main part of the attached bacteria stays attached. Besides reducing the sporulation rate, substrate is used for growth and surfactant production. When the second substrate slug reaches the attached bacteria, the bacteria receive plenty of substrate again for growth and surfactant production leading to accumulation of the attached bacteria and occurrence of the surfactant effect at the location where they are attached, deeper into the reservoir. After some lag time, reactivation of spores takes place. Again, bacteria will grow and accumulate at the inlet. Additional oil can be recovered in a shorter time, if the water slug is injected later. In this case the maximum attachment of bacteria is achieved closer to the inlet. The additional oil is recovered from a larger area, starting at the peak of attached bacteria. The reason is that the concentration of attached bacteria sufficient for reducing sporulation rate is reached faster. However, the bacteria should able to become mobilized within the duration of the water slug in order to get removed and accumulated at a certain distance from the inlet. As an example, the case for the water slug starting at 0.7 PVI produces a higher recovery than the other two cases (0.4 and 0.5 PVI). Application of the spore-forming bacteria can be used to prevent clogging, but also to make bacteria accumulating in specific zones within the reservoir, which can be useful in connection with selective plugging.

Substrate

Water

Substrate

Spores

6.3 Substrate concentration

τ Fig. 5 Illustration of current slug injection scheme.

Selection of a proper substrate concentration is important for growth, production, sporulation and reactivation. Injection substrate concentrations from 1 × to 5 × of the standard concentration have been investigated. Five injection cycles have been performed followed by water flooding. One cycle comprises a 0.07 PVI slug with substrate and bacteria followed by a 0.13 PVI water slug. Fig. 7 shows the recovery curves for this slug injection scheme with the five different substrate injection concentrations. A higher substrate concentration gives an earlier response to the MEOR treatment and also determines the amount of additional oil that is recovered during production of the MEOR oil bank.

10


1.25x10-4

r te wa g slu

Volume fraction

1.00x10-4

Bacteria attached Substrate

7.50x10-5

5.00x10-5

2.50x10-5

0.00 0.0

0.2

0.4

0.6

0.8

ξ

Fig. 6 Effect of the water slug. Initial injection of bacteria and substrate until injection of 0.1 PVI water slug at 0.6 PVI. The circle emphasizes the substrate in the water slug, which originates from the sporulation reaction of attached bacteria. ξ is the dimensionless reservoir length.

1x 2x 3x 4x 5x

Cumulative recovery (fraction of OOIP)

0.8

0.6

0.4

0.2

0.0 0.0

0.5

1.0

1.5

τ (PVI) Fig. 7 Cumulative recovery for different substrate concentrations against dimensionless time τ . A cycle consisting of 0.07 PVI of substrate and bacteria followed by 0.13 PVI of water has been injected. This cycle is injected five times. Hereafter, only flooding with water occurs. Application of the highest substrate concentration results in reservoir clogging. The lowest substrate concentration results in no additional oil mobilization due to insufficient amounts of surfactant produced. Therefore, this recovery curve for (1×) corresponds to the water flooding recovery curve

Again, this is dependent on the zones in the reservoir where the surfactant effect occurs. Injection of the standard concentration with the current scheme is regarded to be unsuccessful, since no additional oil is recovered, compared to waterflooding only. Injection of 4 × substrate concentration is successful, since it results in production of the two MEOR oil banks and gives a high recovery. The second MEOR oil bank appears because the surfactant effect occurs ear-

lier and closer to the inlet. With this injection scheme, 5 × substrate concentration leads to clogging already at 0.7 PVI, so that a different slug injection scheme is required for this concentration. Therefore, a high substrate concentration is desirable for the faster MEOR response as long as clogging can be prevented. Injection of vegetative spore-forming bacteria and spores gives similar results for the 3 × standard substrate concentration and higher. Injection of spores in-


11

a b c d e f g h

Fig. 8 Zoom of recoveries for different slug injection scenarios. (a) One 0.15 PVI slug with bacteria and substrate followed by water flooding. (b) One 0.20 PVI slug with bacteria and substrate followed by water flooding. (c) Two cycles with 0.12 PVI slug with bacteria and substrate followed by water flooding 0.30 PVI. Hereafter, flooding with water. (d) Five cycles with 0.07 PVI slug with bacteria and substrate followed by water flooding 0.30 PVI. Hereafter, flooding with water. (e) Five cycles with 0.07 PVI slug with bacteria and substrate followed by water flooding 0.20 PVI. Hereafter, flooding with water. (f) One 0.20 PVI slug with non-spore-forming bacteria and substrate followed by water flooding. (g) 0.20 PVI slug with bacteria and substrate, and then water flooding for 0.95 PVI. Hereafter, 0.06 PVI substrate followed by water flooding. (h) 0.20 PVI slug with bacteria and substrate, and then water flooding for 0.85 PVI. Hereafter, 0.06 PVI substrate followed by water flooding.

stead of spore-forming bacteria gives a deeper penetration into the reservoir. However, surfactant cannot be produced as long as bacteria exist in the form of spores.

6.4 Slug injection design A slug injection scheme may be composed of different slug sizes, compositions and concentrations for optimizing the MEOR process. The main task for slug injection design is to mobilize as much oil as possible. A number of sequences of slugs of substrate and spores interrupted by water slugs have been investigated. Especially, the influence of the slug sizes and interchanges, under constant total injected amount, has been studied. A high injection concentration (5× standard) has been the basis for the slug design, since application of the high substrate concentration leads to the fastest response to MEOR. An important factor is to allow the buildup of attached bacteria near the inlet, before it will clog or, in

real life, before it will reduce the injectivity more than allowed. Recoveries for different slug injection designs are shown in figure 8. They range from 0.69 OOIP to 0.73 OOIP for successful designs. The only case with reservoir clogging is shown. Production with a 0.2 PVI slug with substrate and non-spore-forming bacteria is also studied (scenario f , red line), resulting in the lowest recovery. The scenarios with one large slug initially mobilize more oil (scenario b, blue line), but the scenarios with several and smaller slugs also result in significant production and in some cases end up with a higher recovery (light green and dark green lines, scenarios dand c). The highest recovery is achieved by a combination of the two injection schemes, where, importantly, the active slugs should be separated with water slugs that are large enough to prevent clogging during the subsequent substrate injection. The best injection design is as follows: 0.20 PVI slug with bacteria and substrate,

12

0.85 PVI water slug, 0.06 PVI slug with bacteria and substrate, and finally water slug post flush (scenario h, black dotted line). This design results in the recovery of 0.73 OOIP.


8 Acknowledgments We acknowledge the Danish National Advanced Technology Foundation, Maersk Oil and DONG E&P for financial support. As a part of the BioRec project, we also would like to acknowledge all other project partners for relevant scientific input: Maersk Oil, DONG E&P, Danish Technological Institute, Novozymes and Roskilde University.

7 Conclusions We have developed a model for MEOR involving the spore-forming bacteria. The bacteria produce surfactant that reduces the residual saturation and may clog the different zones of the reservoir. Sporulation has shown to be a useful property. It makes it possible to develop flexible injection schemes with alternating slugs of bacteria/spores/substrate followed by water buffers. Such schemes allow more uniform distribution of bacteria inside the reservoir, their attachment in the preferred zones, a possibility to avoid bacterial clogging at the inlet and, finally, a higher recovery than for application of the non-spore-forming bacteria. Sporulation results in the fact that a part of the spores converted from attached bacteria will penetrate deeply into the reservoir with the injected water, due to their smaller sizes and different surface properties. Substrate is also produced during the sporulation process. It helps the residing bacteria to grow and produce surfactant. The application of spore-forming bacteria leads to an improved utilization of substrate, higher total surfactant concentration and prolonged period of oil mobilization. The substrate released during sporulation results in reduction of the sporulation rate. Based on this mechanism, it becomes possible to organize bacterial attachment in the desired zones of the reservoir. This may be used to place bacteria for selective plugging. Different schemes of water, bacteria and substrate injection have been tested. For the conditions of the numerical experiment, the optimal slug injection design is composed of a 0.20 PVI slug with bacteria and substrate, followed by a 0.85 PVI water slug, a 0.06 PVI slug with bacteria and substrate and, finally, flooding with water. A large initial slug has a positive impact on the final recovery. A high substrate injection concentration gives a faster MEOR response, however, a too high concentration may result in clogging that should be avoided. The presented model study indicates that the sporeforming bacteria have a high production potential and thus they should be considered a candidate for MEOR.

9 Appendix 9.1 Basis for sigmoidal curves for sporulation and reactivation The logistic function has been used as the basis for the sigmoidal curve: y =

1 1 + e−x

(26)

9.2 Sigmoidal curves for sporulation The sigmoidal curve for sporulation has been fitted bemin tween a lower and a higher concentration, Ωbd and max Ωbd . The end points for low and high conversion rate min are Kbd and Kbd0 , respectively. Kbd0

Kbd = 1+

(27)

av ωs −Ωbd e Ebd

The average concentration is: av max min + Ωbd ) = 0.5 (Ωbd Ωbd

(28)

The constant for having the curves within the given interval is: Ebd =

max av (Ωbd − Ωbd )

log

(29)

min Kbd0 −Kbd min Kbd

9.3 Sigmoidal curves for reactivation The curve for reactivation is set up in a similar manner. 

 Kdb0

Kdb = Kdb0 −  1+

av ωs −Ωdb E db e



(30)

σow


with av max min Ωdb = 0.5 (Ωdb + Ωdb )

Edb =

max av (Ωdb − Ωdb )

log

min Kdb0 −Kdb min Kdb

.

(31)

(32)

13

The surfactant of interest is assumed to display the behavior shown in figure 9, which is given as the following logistic function showing the correlation between surfactant concentration in the water phase ωmw and ∗ ∗ interfacial tension between oil and water σow . σow means the IFT that is used in the relative permeabilities, eqns. (36)-(37).

∗ σow = σow ·

1 − tanh(180 ωmw − 2) + 41 · 10−4 1 − tanh(−2) + 41 · 10−4

(33)

The efficiency of a surfactant depends on how much the IFT can be lowered and the concentration where the IFT drops dramatically. As displayed in figure 9, the surfactant has a critical micelle concentration at 35 mg/L and minimum IFT is 0.06 mN/m. 9.4 Surfactant effect 9.4.2 Interpolation of residual oil saturation Different methods are used to correlate relative permeability curves to variations in IFT [35]. We use a correlation between surfactant concentration in the water phase and IFT. Typically, a reduction of interfacial tension decreases residual oil saturation affecting relative permeability curve endpoints, but it also straightens the relative permeability curves approaching full miscibility [2, 16]. This method interpolates the residual oil saturation used in the Corey type relative permeability curves. Nielsen [47] showed that this method performs similar to capillary number method [37] and the method by Coats [16] applying interpolation between two sets of relative permeability curves. 9.4.1 Interfacial tension

The residual oil saturation is correlated with the reduction of with the change in IFT through an interpolation function g [47]. The interpolation function is: ( ∗ ) n1 σow g(σow ) = (34) σow The residual oil saturation is interpolated and afterwards is used in the relative permeability curves, Eqs. (8) and (9). The index n is an adjustable exponent normally in the range of 4-10, which is used to fit to experimental relative permeability curves. Comparison between the methods can be found in Nielsen [47]. The residual oil saturation used for relative permeability calculations is: ∗ s∗or = g(σow ) · sor

(35)

where σow is current IFT, g(σow ) is the interpolation function with values from unity at the highest IFT toward zero at lower IFT. Index ∗ means modified/calculated values. The residual oil saturation used for calculations is used in the relative permeability equations (36) and (37). 9.4.3 Relative permeability curves For the relative permeability curves for oil kro and water krw , the Corey correlations are used [37]. ( )b 1 − sw − s∗or kro = krowi · (36) 1 − swc − s∗or

2

10

1

10

0

10

−1

10

Fig. 9 Relationship between surfactant concentration ωmw ∗ and IFT ωow . The surfactant has a critical micelle concentration of 35 mg/L and minimum IFT at 0.06 mN/m.

( krw = krwor ·

sw − swc 1 − swc − s∗or

)a (37)

14


where sw is water saturation, krowi is the endpoint relative permeability for oil (at swi ), krwor is the endpoint relative permeability for water (at 1 − sor ), swi is the initial water saturation, s∗or is the residual oil saturation, and the exponents for water and oil are a and b, respectively. The fractional flow function of phase j is fj and is dependent on the water saturation and IFT as it is based on the relative permeabilities for water and oil.

fj =

krj µj

∑

q=o,w

krq µq

(38)

10.

11. 12.

13.

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