Low-tension Gas Modeling in Surfactant Alternating Gas and Surfactant/Gas Coinjection Processes

SPE-174678-MS

Low-tension Gas Modeling in Surfactant Alternating Gas and Surfactant/Gas Coinjection Processes Mohammad R. Beygi, Abdoljalil Varavei, Mohammad Lotfollahi, Mojdeh Delshad, The University of Texas At Austin

Copyright 2015, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Enhanced Oil Recovery Conference held in Kuala Lumpur, Malaysia, 11–13 August 2015. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract In this paper, we present a framework to model low-tension gas flood process and implement the model into the UT in-house

compositional gas reservoir simulator (UT-DOECO2). A gas compositional model is coupled with microemulsion phase

behavior to capture important mechanisms in hybrid gas-chemical flood processes in porous media.

Two different surfactant molecules are simultaneously applied: one to lower interfacial tension to ultra-low values and

one to keep foam stable as gas mobility control agent. This process cannot currently be modeled using the commercial reservoir

simulators. We implemented the option for two surfactants into the existing gas compositional simulator with foam and

hysteresis options. A predictive simulator would make it possible to select the best candidates for field application and tailor

process design to particular characteristics of each field.

In the field-scale application of the Surfactant Alternating Gas (SAG) process, multiphase fluid behavior in porous media

is modeled using three-phase compositional relative permeability and three-phase hysteresis models to include both

compositional and saturation history effects. These models represent a more-accurate prediction of the cycle-dependent

properties of SAG. The gas entrapment in the foam flow is used to predict the hysteresis effect within each cycle using a

dynamic Land coefficient. The in-situ foaming behavior is estimated based on the mechanistic foam models. This study, further,

evaluates mobilization and displacement of residual oil in tight reservoirs using the low-tension gas flood and compares the

results with other EOR options.

Using a reliable multiphase simulator low-tension gas experiments can be scaled up to the field and to optimize chemical-

gas EOR process design. Numerical simulation of the SAG with and without hysteresis is used to assess the effect of the gas-

entrapment on oil recovery and gas utilization factor in a field-scale application.

Introduction Low-tension-gas Enhanced Oil Recovery (EOR) method is a gas-chemical hybrid technique to increase oil production

and/or oil recovery efficiency. Gas flooding using hydrocarbon or non-hydrocarbon components, i.e. carbon dioxide, nitrogen,

flue gas, and enriched natural gas, helps to improve oil production and/or recovery due to elevated mass transfer between oil

and injected solvent. Surfactant flooding can recover trapped oil by reducing the interfacial tension between oil and water

phases. To increase solvent injection sweep efficiency, a wide range of gas-mobility-control techniques is introduced: water-

alternate gas (WAG), simultaneous water and gas injection, polymer assisted WAG, gas viscosifying with polymer and foam.

The foaming surfactant agent could be dissolved in water or in gas. Recently, in-situ strong foam generation with surfactant

dissolved in CO2 were proposed. Gas can be injected along with an aqueous surfactant solution to create in-situ foam--low-

tension gas flooding [Kamal and Mardsen (1973); Lawson and Reisberg (1980); Wang (2006); Srivastava et al. (2009); Li et

al. (2010), Szlendak et al. (2013); Farajzadeh et al (2013)].

Most fundamentally, wide applications of low-tension-gas flooding is limited due to associated risks: uncertainties in

reservoir characterization and heterogeneity and lack of understanding of the process and consequently lack of a predictive

2 SPE-174678-MS

reservoir simulator to mechanistically model the process. Moncorgé et al. (2012) presented a framework aimed at integration

of new physics for improved recovery process with black-oil and equilibrium phase distribution ratio models. Trouillaud et al.

(2014) simulated the effect of pressure and oil composition on microemulsion phase behavior by coupling a gas/oil/water phase

behavior model with a microemulsion phase behavior model. Lotfollahi et al. (2015) developed a hybrid black-oil/surfactant

reservoir simulator to model chemical EOR processes with gas.

Foam can help to improve poor sweep efficiency due to reservoir heterogeneity, gravity override, and viscous instability.

The foam can be applied as a gas mobility and/or conformance control method. The gas mobility is controlled by foam texture

in the flowing part and the gas entrapment in porous medium. The increased gas trapping due to increased capillary-pressure

difference across the curved lamellae plays a crucial rule in gas mobility reduction. The experimental results show hysteretic

behavior in foam generation due to two general parameters: foam parameters and saturation direction. A coarse foam at

minimum required pressure-gradient jumps to a strong foam experiencing an irreversible process [Gauglitz et al. (2002); Shi

(1996)]. The mobility reduction factor exhibited a hysteresis behavior in a cycle of increasing/decreasing surfactant

concentration [Simjoo et al., (2013)]. The population balance models capture the abrupt jump in foam generation. The

saturation direction, also, affects the foam strength: the generated foam in increasing and decreasing gas saturation processes

are not identical. Gas trapping is a dynamic process even in microscopic scale in that the foam is trapped and remobilized

continuously in porous media. Nevertheless, the change of saturation direction impacts gas entrapment and must be explicitly

considered in the reservoir process modeling. An appropriate hysteresis model could assist in better modeling of foam behavior

in porous media. The foam applications involve alternative injection scheme in many places. The hysteresis model, thereby,

must capture cycle-dependent trapped saturation effect arising from the multicycle process.

Accurate multiphase relative permeability model is an indispensable part in numerical simulation of advance reservoir

processes: it must capture the fundamental phenomena of multiphase fluid flow in porous medium, e.g. saturation-path

dependency and compositional effects. Besides, it must be simple, and impose the minimum number of parameters to the

numerical simulation. Otherwise, it may not truly follow the multiphase process especially when saturation history changes or

mass transfer between the phases exists. On the other hand, it may cause numerical instability leading to convergence problem

in reservoir simulation. There are above thirty three-phase relative permeability models developed based on different

mathematical modeling while a few are industry approved models [Beygi et al. (2015) and references therein]. The existing

commercial reservoir simulators still lack a comprehensive three-phase flow model of coupled relative permeability and

capillary pressure including hysteresis and compositional effects. Predicting phase relative permeability at low saturation region

is another limitation of the commercially approved three-phase relative permeability models.

The objective of this paper is to present a new framework for the four-phase compositional/ chemical simulator to model

gas/chemical EOR processes including low-tension-gas flooding and foam. The four phases that may flow simultaneously are

(1) aqueous, (2) oil, (3) gas and (4) microemulsion phases. In this formulation, a hydrocarbon compositional model is coupled

with microemulsion phase behavior. Table 1 summarizes the component type and the phases in which each component is

allowed in this code. The following section describes the modeling of the hybrid chemical-gas process including robust three-

phase relative permeability and hysteresis models for better modeling of common situations faced in this cyclic process:

multiphase but low-saturation region, compositional effects due to mass transfer between the phases, phase appear/disappear,

and saturation-history dependency of relative permeability and capillary pressure.

Table 1: Component and phase allocation in UT-DOECO2

Phase

Aqueous Oleic Gaseous Microemulsion

Component

Water X X

Polymer X X

Hydrocarbon X X X

Non-condensable gases X X X X

Surfactant X

SPE-174678-MS 3

Modeling

UT-DOECO2 overview The in-house UT-DOECO2 reservoir simulator is an isothermal, three-dimensional, compositional gasflood simulator. The

solution scheme is IMPEC (implicit pressure/explicit concentration). It applies a three-phase hydrocarbon flash using Peng-

Robinson EOS. The gridding options are Cartesian and unstructured/corner point type. A geomechanical package was coupled

with reservoir simulator. Figure 1 shows an overall flowchart of UT-DOECO2 simulator. The following sections briefly

overviews the modeling of relevant parts of the low-tension gas flooding surfactant in the UT-DOECO2 code.

Surfactant phase behavior The microemulsion phase behavior is based on Winsor (1954) and Pope and Nelson (1978). The formulation of the binodal

curve using Hand’s rule (Hand, 1939) is assumed the same in all phase environments. Hand’s rule is based on the empirical

observation that equilibrium phase concentration ratios are straight lines on a log-log scale.

The binodal curve is computed from

𝐶3𝑙

𝐶2𝑙= 𝐴 (

𝐶3𝑙

𝐶1𝑙)

𝐵,…………………………………………………………… Eq. 1

where l denotes aqueous phase, the A and B are empirical parameters, volume of the ith component in the jth phase is divided by

volume of the jth phase. For a symmetric binodal curve where B = -1, which is the current formulation used in the code. Phase

concentrations are calculated explicitly in terms of oil concentration 𝐶2𝑙 (recalling ∑ 𝐶𝑘𝑙 = 13𝑘=1 ). The microemulsion phase

is designated as phase one, which is the aqueous phase.

While, the microemulsion/excess-oil IFT decreases drastically as brine salinity increases, the microemulsion/excess-brine

IFT increases drastically as brine salinity increases. The salinity at the crossover point of these two IFTs is called the optimum

salinity. At the optimum salinity, the same amount of water and oil are dissolved in the microemulsion phase (surfactant rich

phase - in this code aqueous phase). For intermediate salinities less than or equal to the optimum salinity, parameter A in

binodal curve formulation is calculated as follow:

𝐴 = (𝐴0 − 𝐴1) (1 −𝐶𝑆𝐸

𝐶𝑆𝐸𝑂𝑃) + 𝐴1 𝑓𝑜𝑟 𝐶𝑆𝐸 ≤ 𝐶𝑆𝐸𝑂𝑃 ,…………..……………………… Eq. 2

where CSE is the salt concentration in the aqueous phase and CSEOP is the optimum salinity. As=0,1 is the parameter related to the

height of the binodal curve (𝐶3𝑚𝑎𝑥,𝑠) and is defines as,

𝐴𝑠 = (2𝐶3𝑚𝑎𝑥,𝑠

1−2𝐶3𝑚𝑎𝑥,𝑠)

2

, …………………………………………………… Eq. 3

where s=0, 1 represents the zero and optimum salinities, respectively.

In brine/oil/surfactant, the phase behavior is a function of CSE among other factors such as co-solvent concentration,

temperature, pressure, and solution gas. The microemulsion phase behavior is characterized as Type I (oil solubilized in

aqueous phase) when CSE is equal or less than the lower effective salinity (CSEL) where two phases are in equilibrium: the oleic

phase which is essentially pure and the microemulsion phase containing water, salt, surfactant, and the solubilized oil. This

phase behavior environment is called Type I as well because the tie lines have the negative slop on a conventional ternary

diagram. In Type I or Type II(+) environment phase (water solubilized in oil) the tie lines have a positive slop and CSE is equal

or greater than the upper effective salinity (CSEU). In this case also there are two phases in equilibrium: microemulsion and

excess aqueous phase. The microemulsion phase contains surfactant, oil and solubilized water and the aqueous phase which is

essentially pure. For intermediate salinity CSEL ≤ CSE ≤ CSEU, there are three phases in equilibrium depending on the component

composition, oleic, microemulsion, and aqueous phase. This environment is called Type III (middle phase in equilibrium with

excess oil and water phases) and it has a Type I and a Type II(+) lobe on a ternary diagram. The implementation is currently

considered for Type I surfactant phase behavior in the UT-DOECO2 code. The following two parameters are evaluated to

obtain surfactant-rich microemulsion phase composition:

𝑅31 =𝐶3

𝐶1,…………………………………………………………… Eq. 4

𝑅32 =𝐴

𝑅31,…………………...……………………………………… Eq. 5

where 𝐶1 and 𝐶3 are total volume concentration of water and surfactant, respectively. The microemulsion-phase concentrations

are calculated as follows:

4 SPE-174678-MS

𝐶𝑖3 = {𝑅32 × (𝑅31 + 𝑅31 × 𝑅32 + 𝑅32)−1 𝑖 = 1

1 − (1 + 𝑅31)𝐶13 𝑖 = 21 − 𝐶13 − 𝐶23 𝑖 = 3

, ……………………………… Eq. 6

Surfactant Retention Surfactant loss due to adsorption and phase trapping is an important parameter in the chemical-EOR projects. A Langmuir-

type isotherm is used to describe the surfactant adsorption onto solid mineral surfaces and phase trapping in pore throats. The

model takes into account the salinity and surfactant concentration with reversibility Options. The salinity for surfactant

adsorption is defined as a linear summation of monovalent cation and effective divalent cations.

Interfacial tension Two models are implemented to calculate the interfacial tension between (IFT) microemulsion and oil phases: modified Healy

and Reed (1974) [Hirasaki, (1981)] and Huh (1979). The interfacial tension depends on solubilization parameter. In these

models, a constant oil-water interfacial tension is considered and in the absence of surfactant or in the case of low surfactant

concentration, i.e. below the Critical Micelle Concentration (CMC), the IFT reduces to water-oil IFT.

Microemulsion viscosity Microemulsion viscosity is modeled in terms of pure component viscosities and the concentrations of oil, water, and surfactant

in the microemulsion phase:

𝜇1 = 𝐶11𝜇𝑤𝑒𝛼𝑣1(𝐶21+𝐶31) + 𝐶21𝜇𝑜𝑒𝛼𝑣2(𝐶11+𝐶31) + 𝐶31𝛼𝑣3𝑒(𝛼𝑣4𝐶11+𝛼𝑣5𝐶21),…………………… Eq. 7

where Ci1 denotes the concentration of component i in the aqueous phase and the 𝛼𝑣parameters are determined by matching

laboratory microemulsion viscosities at several compositions. In the absence of surfactant and polymer, water and oil phase

viscosities reduce to pure water and oil viscosities (𝜇𝑤, 𝜇𝑜). When polymer is present, 𝜇𝑤 is replaced by 𝜇𝑃.

Hydrocarbon dissolution As surfactant concentrations higher than CMC the hydrocarbon solubility in the microemulsion phases. The mass transfer of

hydrocarbon components to the microemulsion phase is a function of the salinity, surfactant molecule, temperature etc.. Oil

dissolved in the aqueous phase can be either in equilibrium with the oil concentration in the oleic phase or with the limited

mass transfer. The equilibrium K-values, defined as the ratio of each component concentration in the aqueous phase to that in

the oleic phase are specified and sorted as a function of surfactant concentration. The kinetic mass-transfer rate can be further

added for the limited mass transfer option.

Surfactant mixing rule Typically, a mixture of surfactants is used during the low-tension-gas flood: a low interfacial tension surfactant and a foaming

surfactant. The former reduces the IFT to ultra-low values and, thereby, the residual oil saturation is decreased. The latter

provides the essential gas mobility/conformance control. In reality, all the surfactants have both IFT and foaming to different

degrees and are rarely independent. Antón et al. (2008) discuss mixing rules to estimate microemulsion phase behavior when

more than one surfactant is present. The impact of mixing two surfactants also needs to be evaluated on foaming properties

[Andrianov et al. (2012)].

For the “ideal” mixture of two surfactants, a nonlinear mixing rule is applied to model the changes in optimal salinity as a

function of surfactants concentration [Salager et al., (1979a)].

𝑙𝑛𝐶𝑆𝐸𝑂𝑃∗ = 𝑥1𝑙𝑛𝐶𝑆𝐸𝑂𝑃1

+𝑥2𝑙𝑛𝐶𝑆𝐸𝑂𝑃2,……………………………………… Eq. 8

where 𝐶𝑆𝐸𝑂𝑃∗ , 𝐶𝑆𝐸𝑂𝑃1

and 𝐶𝑆𝐸𝑂𝑃2 are the optimum salinities for the mixture of surfactants, surfactant 1 and surfactant 2,

respectively. 𝑥1 and 𝑥2 are mole fractions for surfactants 1 and 2. The optimum solubilization ratio follows a linear mixing

rule as [Mohammadi et al., (2009)]

𝑙𝑛𝜎𝑠∗ = 𝑥1𝑙𝑛𝜎𝑠1

+𝑥2𝑙𝑛𝜎𝑠2, ,……………………………………… Eq. 9

where 𝜎𝑠∗, 𝜎𝑠1

, and 𝜎𝑠2 are the optimum solubilization ratio of the mixture, surfactant 1, and surfactant 2, respectively.

We plan to implement the mixing rule for foaming surfactant and ultra-low IFT surfactant in the simulator in the near

future.

SPE-174678-MS 5

START

Constant phase-independent parameters in EOS, transmissibility,

well factor and component low-pressure viscosity

Reservoir initialization: hydrocarbon phase composition,

phase density, phase saturation, in-place water and hydrocarbons

Read time and well data

Phase equilibrium calculation: phase stability analysis +

hydrocarbon flash calculation (excluding surfactant components)

(Compute overall composition and hydrocarbon phase composition)

Compute/read time-step size

Fluid volume partial derivatives, potential difference, upstream

weighting, relative mobility and transmissibility

Physical dispersion

Solve pressure equation

Well flow rate and flowing BHP

Poroelasticity model (Update porosity)

Potential difference between grid blocks,

phase velocity, and overall composition

Phase density (update aqueous phase density if surfactant exist), phase

saturation, fluid volume, and material balance (in-place, produced, injected)

END t<tfinal

GO TO 1

Read hydrocarbon and reservoir properties,

initial condition, and tracer concentration data

1

Modify gas phase relative permeability

and back-calculate gas phase viscosity Foam exists?

((𝐶𝑠𝑟𝑢𝑓2 > 𝐶𝑠𝑙𝑖𝑚& 𝑆𝑜 < 𝑆𝑜

𝑙𝑖𝑚)

Material balance error

Trapping number, hysteretic relative permeability and capillary pressure

ME exists? (𝐶𝑠𝑟𝑢𝑓1 > 𝐶𝑀𝐶 )

Molar volume and phase viscosity

Y

N

N

Y

Y N

Select hydrocarbon

partition coefficient

Update aqueous and oil

phase compositions

Update aqueous phase

density and viscosity

Update IFT

Simplified chemical flash

Figure 1: Summary flowchart of UT-DOECO2 code

6 SPE-174678-MS

Oil composition effect on microemulsion phase behavior Key surfactant properties depend on crude oil composition [Salager et al. (1979a); Salager et al. (1979b); Baran et al. (1994)].

The crude oil composition effect is introduced by the equivalent alkane carbon number (EACN) concept. The surfactant phase-

behavior parameters, e.g. optimum salinity, solubilization parameter, and width of Winsor Type III salinity, are estimated using

the following linear formulations,

𝐿𝑛 𝐶𝑆𝐸𝑂𝑃 = 𝑆𝑠𝑒(𝐸𝐴𝐶𝑁 − 𝐸𝑚𝑖𝑛), ………………………..…………….. Eq. 10

𝜎𝑠 = 𝑆𝑅,𝑆𝐸𝐴𝐶𝑁 + 𝑏𝜎,𝑆, ……………..……………………………. Eq. 11

𝐶𝑆𝐸𝑈−𝐶𝑆𝐸𝐿

𝐶𝑆𝐸𝑂𝑃= 𝑆𝑑𝑠𝐸𝐴𝐶𝑁 + 𝑏𝑑𝑠,.…………..……………………………. Eq. 12

where 𝑆𝑠𝑒 , 𝐸𝑚𝑖𝑛 , 𝑆𝜎,𝑆, 𝑏𝜎,𝑆, 𝑆𝑑𝑠, and 𝑏𝑑𝑠 are constants and dynamically calculated based upon a linear EACN-interpolation

scheme between the two experimentally matched sets of surfactant phase behavior parameters for the same surfactant but

having different EACNs. When the effect of EACN on the surfactant phase behavior is considered, 𝐴𝑆 in the Hand’s rule

formulation is evaluated as follows:

𝐴𝑠 = 𝜎𝑆−2,……..………………….………………….……… Eq. 13

In this study, the EACN of a given crude oil corresponds to the lipophilicity of the crude oil, i.e. the salinity at the transition

from Winsor Type I to II environment: the number of carbon atoms of an alkane exhibiting a hydrophobicity equivalent to the

crude oil. EACN for an oil mixture with provided components and composition is estimated using Cash et al. (1977) linear

mixture formulation,

𝐸𝐴𝐶𝑁 = ∑ 𝑥𝑖𝐴𝐶𝑁𝑖𝑁𝑐𝑖=1 ,……..…………..………………….……… Eq. 14

where 𝑁𝑐 is the number of components in the mixture, 𝑥𝑖 is the mole fraction of component i and 𝐴𝐶𝑁𝑖 is the alkane carbon

number of the hydrocarbon component i.

Three-phase relative permeability We use a general, robust, simple, compositionally consistent, three-phase relative permeability model [UTKR3P model, Beygi

et al. (2015)]. To calculate dynamically changing three-phase relative permeability model parameters, this model applies a

linear saturation-weighted interpolation scheme between measured two-phase relative parameters. Three-phase residual

saturation is a saturation-path-dependent parameter and is calculated using the saturation of the other phases and one parameter

per phase (b). The b parameter is the only parameter to adjust and depends on rock and fluid properties: rock wettability, phase

composition, pressure, and temperature. It is an input parameter calculated either based upon multiphase residual-saturation

lab measurement or gained from the history matching process. The UTKR3P model results in continuous and smooth relative

permeability and relative permeability derivative with respect to primary variables, i.e. phases saturation. The relative

permeability is inherently saturation-path dependent. Besides, it is applicable to mixed-wet rocks and captures the

compositional effects due to phase composition and/or capillary-desaturation at high trapping number region, i.e. low capillary,

high viscous, and high gravitational forces. This feature helps to better estimate the phase relative permeability in more complex

processes such as hybrid chemical-gas EOR where there is a considerable amount of mixing/mass transfer between the phases.

Three-phase hysteresis A hysteresis model taking into consideration the phase trapping is an equally important feature of the gas-mobility-control

modeling. In foam applications, implementing the hysteresis model directly to the foam texture model is an accurate approach.

In this complicated approach, the foam behavior would be directly a function of saturation history and foam parameters, e.g.

foam quality and gas velocity. In a simpler approach, one can add the hysteresis model to a reliable multiphase-relative-

permeability model to capture the impact of trapped saturation on the gas mobility reduction. We select the latter method

incorporating the saturation-history effect on hysteretic behavior of foam rheology.

Irreversibility in relative permeability plays a key role in multiphase flow modeling and in multicycle processes. Although

two-phase or reversible hysteresis models, e.g. Carlson model (1981), could distinguish between the primary increasing and

decreasing saturation processes, they cannot capture the change in relative permeability within the following cycles. The

physical phenomenon is important in more accurate reservoir modeling because could decrease the non-wetting phase (i.e. gas)

relative permeability up to five folds. It is especially important at low-saturation region that occurs in multicycle processes.

SPE-174678-MS 7

We implemented the irreversible UTHYST hysteresis model to the UT-DOECO2 code. This model is a general, simple,

fast, robust, three-phase hysteresis model. There are three main observations from the lab experimental results and field data

that incorporated into the UTHYST model: 1) monotonic increase in trapped-saturation in multicycle processes; 2) dynamic

Land coefficient behavior as cycle number increases; and 3) impact of a conjugate-phase saturation on phase entrapment within

each cycle [Beygi et al. (2015) and references therein]. The amount of phase trapping decreasing due to mass transfer between

phases is then added to the model for high trapping number conditions. The model adds one additional parameter for each

phase to include the level of relative permeability reduction due to the presence of a conjugate phase. We implemented the

UTHYST three-phase hysteresis model to the UTKR3P multiphase relative-permeability model and added to the simulator.

Foam The implicit texture UT-foam model [Rossen et al., (1999)] and local-equilibrium population-balance foam model [Chen et al.,

(2010)] are incorporated in the simulator. The UT-foam model gives a steep increase in gas mobility as water saturation

decreases in the immediate vicinity of the limiting water saturation (Sw*) and a constant reduction in gas mobility for larger

value of water saturation. The model allows for non-Newtonian behavior in the low-quality regime: the mobility-reduction

factor is a power-law function of gas superficial velocity.

In Chen et al. (2010) foam model, lamella-generation rate is taken as a power-law expression, proportional to the

magnitude of the interstitial velocity of surfactant solution and 1/3 power of the interstitial gas velocity. The model employs a

capillary-pressure-dependent kinetic expression for lamella coalescence (to reflect the limiting capillary pressure) and a term

to represent the trapped fraction of foam. This model uses the shear-thinning expression of Hirasaki and Lawson (1985) for the

effective gas viscosity.

In presence of microemulsion phase, most of the surfactant remains in this phase. The results of pipette foaming test by

Srivastava (2010) showed Type I and Type III microemulsion phases form significant foam but foam does not form in Type II.

Foam in Type I is more stable compared to Type III due to lower salinity and lower amount of solubilized oil in the

microemulsion phase. Foam does not generate in excess aqueous phases from Type III and Type II due to surfactant partitioning

into microemulsion phase. As a result, when microemulsion phase is present the aqueous phase properties in each foam model,

i.e. aqueous phase saturation in the UT model and aqueous velocity and aqueous/gas capillary pressure in the Chen et al. model,

will be replaced with their corresponding values for the microemulsion phase [Naderi et al. (2013); Delshad et al. (2014)]

Simulation results and discussion In this section, we discuss the simulation results for a synthetic, 2D reservoir to validate the low-tension gas flood model.

The reservoir is 300×10×100 ft discretized in 300 gird cells (30× 1 × 10) and is a homogenous with one high-permeability

streak in the fourth top layer replicating the low-perm, intermediate-wet sample of Oak (1991). One quarter of a five-spot well

pattern is modeled: two wells, an injector and a producer, which are located at the opposite corners of the reservoir model.

Four-component oil composition is modeled with Peng-Robinson Equation-of-State. Table 2 and Table 3 list a summary of

reservoir and fluid properties. Phase numbering 1, 2, and 3 represents aqueous/microemulsion, oil, and gas phases. The model

represents a mature waterflooded reservoir with large resource of stranded oil: no initial mobile oil saturation. Two mechanisms

for oil recovery are lowering capillary trapping and increasing sweep efficiency. Two surfactants are used where one is

primarily reducing interfacial tension and another to mainly generate foam. Table 4 represents UT-foam model parameters,

surfactant properties, and oil composition effect based on two sets of experimental results versus EACN.

Simulation cases start with a low-tension surfactant slug of 1% (vol. frac.) to reduce water-oil interfacial tension and

mobilize the residual oil followed by four different injection schemes with or without hysteresis option as summarized in Table

5. Injection schemes include chase water, water-alternate-gas (WAG), foam surfactant-alternate-gas injection (SAG), and in-

situ foam generation with aqueous surfactant-gas co-injection (CoInj) plans. The injection salinity is 0.13 meq/mL. The WAG

scenarios are in multi cycles of 60 days of water injection followed by 60 days of N2 injection with WAG ratio 1:1. The

cumulative injection after 990 days is 5.0 PV. The injection well is rate controlled with switching option to bottomehole

pressure control of 3000 psi. The production well is pressure constrained with producing bottomehole pressure of 1500 psia.

For cases 2, 3, and 4, the cumulative water and gas injection are close to 36,500 STB and 14.5 MMSCF, respectively (5 PV

injection).

Table 2: 2D Base case fluid and reservoir properties

Initial pore volume= 8495.05 m3 (53.42 MSTB) and porosity=0.2

Horizontal permeability=0.0493 𝜇𝑚2 (50 md) and kv/kh=1.0 (except for high permeable streak)

𝑇𝑖𝑛𝑖𝑡𝑖𝑎𝑙=32.5 °C (90°F) and 𝑃𝑖𝑛𝑖𝑡𝑖𝑎𝑙=10.34 MPa (1500 psia)

𝑆𝑤𝑖𝑛𝑖𝑡𝑖𝑎𝑙 =0.65, 𝑆𝑜

𝑖𝑛𝑖𝑡𝑖𝑎𝑙 =0.35, Initial salinity (meq/mL)=0.10

Initial oil composition: N2=0.0%; C10 =30%; C15=40%; C20=30%;

oil composition EACN: N2=0; C10 =10; C15=15; C20=20;

Formation compressibility =48.32 1/Pa (3× 10−6 1/psi )

8 SPE-174678-MS

Table 3: 2D Base case relative permeability model parameters

𝑆1𝑟2𝐿 = 𝑆1𝑟3

𝐿 0.20 𝑆3𝑟1𝐿 = 𝑆3𝑟2

𝐿 0.35

𝑆2𝑟1𝐿 0.35 𝑆2𝑟3

𝐿 0.25

𝑘𝑟120𝐿 = 𝑘𝑟13

0𝐿 0.12 𝑘𝑟310𝐿 = 𝑘𝑟32

0𝐿 0.90

𝑘𝑟210𝐿 0.70 𝑘𝑟23

0𝐿 0.70

𝐶112𝐿 = 𝐶112

𝐿 2.00 𝐶131𝐿 = 𝐶132

𝐿 2.50

𝐶121𝐿 2.16 𝐶123

𝐿 2.70

𝐶1𝑗𝑖𝐻 , j,i=1,2,3 1.0 𝐶2𝑗𝑖

𝐿 = 𝐶2𝑗𝑖𝐻 , j,i=1,2,3 0.0

𝑆𝑗𝑟𝑖𝐻 , j,i=1,2,3 0.0 𝑘𝑟𝑗𝑖

𝐻 , j,i=1,2,3 1.0

𝑏𝑗, j=1,2,3 0.0 Gas hysteresis parameter (𝛼ℎ3) 6.0

* 1, 2, and 3 represent water/microemulsion, oil, and gas phases, respectively

Table 4: Surfactants, microemulsion, and foam model parameters

UT-Foam model parameters

𝑅𝑟𝑒𝑓=200; 𝑆𝑤∗ =0.3; 𝑆𝑜

∗=0.25; 𝐶𝑠∗=0.001; 𝜀=0.01; 𝜎=1; 𝑢𝑔,𝑟𝑒𝑓 = 1(𝑓𝑡/𝑑𝑎𝑦)

Surfactant parameters

Surfactant compressibility (at P=14.65 psi) = 0.; CMC=0.001; Huh’s IFT model parameter: 0.3

Compositional aqueous phase viscosity parameters: 𝛼𝑣1 = 1.5; 𝛼𝑣2 = 1.3; 𝛼𝑣3 = 3.0; 𝛼𝑣4 = 𝛼𝑣5 = 1.0

Oil composition effect on ME phase behavior (two set of parameters vs. EACN)

1st solubility experiment parameters: 2nd solubility experiment parameters:

No. of hydrocarbon components in the experiment=1 No. of hydrocarbon components in the experiment=1

EACN1=10 EACN2=20

𝐶𝑆𝐸𝑂𝑃,1 = 0.26, 𝜎0 =25, 𝜎1 =40, (𝐶𝑆𝐸𝑈 − 𝐶𝑆𝐸𝐿)1 = 0.2 𝐶𝑆𝐸𝑂𝑃,2 = 0.30, 𝜎0 =8, 𝜎1 =18,(𝐶𝑆𝐸𝑈 − 𝐶𝑆𝐸𝐿)2 = 0.30

Hydrocarbon dissolution vs. surfactant concentration

Component partition coefficient

N2 C10 C15 C20

0.1 0.0 0.0008 0.0008 0.0008

0.2 0.0 0.002 0.002 0.008

0.7 0.0 0.008 0.01148 0.01148

0.99 0.0 0.01148 0.01148 0.01148

Table 5: summary of simulation cases and oil recovery factor after 5 PV injection

Case

Injection scheme Gas

hysteresis option

Oil RF

(%) Surfactant

slug Drive

1 1% SI Water No 13.62

2-A

1% SI Water-Alternate-Gas

(WAG)

No 25.85

2-B Carlson Model 27.28

2-C UTHYST Model 28.93

3-A

1% SI 0.1% SF-Alternate-Gas

(SAG)

No 30.29

3-B Carlson Model 30.63

3-C UTHYST Model 36.12

4-A

1% SI 0.1% SF-Gas Coinjection

(CoInj)

No 38.36

4-B Carlson Model 38.55

4-C UTHYST Model 38.69

* SI: Low-tension surfactant , SF: Foaming surfactant

𝐶𝑠 (lbmsurfactant

lbmwater − hydrocarbon solution)

SPE-174678-MS 9

Figure 2 compares the oil recovery factor for the simulation cases. The foam mobility control methods results in higher oil

recovery factor-- incremental oil recovery by SAG and CoInj schemes over WAG strategy are 7.2% and 9.8%, respectively,

for the UTHYST three-phase hysteresis option. The generated foam mitigates the gas override to the high permeable zone/top

layers. It results both in improved gas vertical conformance at the injector well and in areal sweep efficiency. Although

coinjection plan is effective to increase oil recovery due to continuous in-situ foam generation, however it elevates the injection

flowing BHP and brings injectivity and consequently operational issues. Figure 2 reveals that impact of hysteresis option is not

unique and is process dependent. Figure 3 compares the injection well flowing BHP for water flood and three cases including

the UTHYST model. While flowing BHP fluctuates due to alternate fluid injection in WAG and SAG cases, it constantly boosts

for the coinjection scheme due to constant in-situ foam generation close to the wellbore area. Figure 4 compares oil distribution

for three aforementioned cases (including phase-3 UTHYST hysteresis option) at the end of injection plans. Figure 4 highlights

the high permeable area in red box. It reveals the foaming strategies potential to boost the areal sweep efficiency of the

mobilized oil through the low-tension process.

Figure 2: Oil recovery vs. time for different processes listed in Table 5

Figure 3: Injection well BHP vs. time for different multicycle processes compared to waterflood

0 100 200 300 400 500 600 700 800 900 1K

Time (day)

0

0.1

0.2

0.3

0.4

Oil R

ec

ov

ery

(fr

ac

tio

n)

1 2-A 2-B 2-C 3-A 3-B 3-C 4-A 4-B 4-C

0 100 200 300 400 500 600 700 800 900 1K

Time (day)

1500

2000

2500

3000

3500

BH

P (

ps

i)

1 2-C 3-C 4-C

WAG

Water

SAG

CoInj

(Water) (WAG, 𝛼3ℎ=6) (SAG, 𝛼3ℎ=6) (CoInj, 𝛼3ℎ=6)

10 SPE-174678-MS

Figure 4: Phase-2 (oil) saturation distribution for three cases at 5 PV injection (high permeable streak highlighted in red box)

As Figure 5 and Figure 6 imply, an important parameter for higher oil recovery for SAG and CoInj plans compared to that

of WAG scheme is the increased gas entrapment (compare cases 2-C and 3-C). These figures show the UTHYST model

potential to monitor the monotonically increasing gas trapping. The increased gas trapping is reflected by increased in-situ gas

saturation in the reservoir. As the only free parameter (𝛼ℎ3) of the UTHYST model increases (from 6 to 9), the gas trapping

within the current cycle decreases and approaches to the predicted values of the Carlson model. 𝛼ℎ3 denotes the impact of the

conjugate phase (water) saturation at the start of the current cycle on phase entrapment.

Figure 7 and Figure 8 depict the phase-3 (gas) relative permeability and phase trapping for a selected grid block (grib block

5,1,1 highlighted in purple box in Figure 4b) within 8-cycle WAG process. It shows the cycle-dependency of gas relative

permeability due to gas trapping. Note that the saturation path dependency incorporated in the UTKR3P three-phase relative

permeability model is not modeled since bj parameter value is set to zero. As a result, the cycle dependency is only because of

the saturation history effect imposed by the UTHYST model. The phase-3 relative permeability substantially decreases (40%)

as the cycle number increases. This simple concept can be applied to different relative permeability models by appropriate

definition of free and trapped saturation.

4b) Case

3-C

4c) Case

4-C

WAG

SAG

CoInj

4a) Case

2-C

SPE-174678-MS 11

Figure 5: Average phase-3 (gas) saturation in reservoir for different multicycle processes including UTHYST hysteresis model

Figure 6: Impact of 2-phase Carlson and 3-phase UTHYST hysteresis model parameter (𝛼3ℎ) on oil recovery of multicycle SAG processes

0 100 200 300 400 500 600 700 800 900 1K

Time (days)

0

0.1

0.2

0.3

0.4

0.5

Av

era

ge

ga

s s

atu

rati

on

3-A (SAG, No Hyst) 3-B (SAG, Carlson) 3-C (SAG, alpha,g=6

3-C (SAG, alpha,g=7 3-C (SAG, alpha,g=9 2-C (WAG, alpha,g=6

(𝛼3ℎ=6)

(𝛼3ℎ=7) (𝛼3ℎ=9) (𝛼3ℎ=12)

(No Hyst) (Carlson)

(SAG, 𝛼3ℎ=7)

(SAG, No Hyst) (SAG, 𝛼3ℎ=6)

(WAG, 𝛼3ℎ=6)

(SAG, Carlson)

(SAG, 𝛼3ℎ=9)

Ave

rage

ph

ase

-3 (

gas)

sat

ura

tio

n

12 SPE-174678-MS

Figure 7: Phase-3 (gas) relative permeability (solid line) and normalized trapped saturation (dash line)

in 8-cycle WAG process (case 2-C), grid-block (5,1,1)

Figure 8: Phase-3 (gas) relative permeability in 8-cycle WAG process (case 2-C), grid-block (5,1,1)

0

0.2

0.4

0.6

0.8

1

0

0.06

0.12

0.18

0.24

0.3

0 120 240 360 480 600 720 840 960

No

rmal

ize

d p

has

e-3

(ga

s)tr

app

ed

sat

ura

tio

n

Ph

ase-

3 (

gas)

rel

ativ

e p

erm

eab

ility

Time (day)

1st 2nd 3rd 4th 5th 6th 7th 8th

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35 0.4 0.45 0.5

Ph

ase

-3 (

gas)

rel

ativ

e p

erm

eab

ility

Phase-3 (gas) saturation

1st 2nd 3rd 4th 5th 6th 7th 8th

SPE-174678-MS 13

Conclusions A framework to model hybrid gas-chemical processes is proposed and implemented in the in-house gas flooding

compositional reservoir simulator. The framework captures the main mechanisms in low-tension gas flood and cyclic

injection schemes. This feature is not currently available in the commercial compositional reservoir simulators.

We conceptually validated the framework using a synthetic reservoir with experimental results for model parameters,

e.g. PVT, surfactant parameters, oil composition effect on surfactant phase behavior, foam model parameters,

multiphase relative permeability at low and high trapping numbers, and hysteresis.

The proper modeling of relative permeability and hysteresis in multicycle processes plays an indispensable role in

approaching toward more accurate reservoir simulation results. We, further, investigated the impact of hysteresis on

foam application where the effective phase trapping constantly changes.

Modeling multicycle processes in mixed-wet rocks requires the hysteresis option for more than one phase.

Nevertheless, we only applied hysteresis for the gas phase, where the phase trapping changes both with the saturation

history and foam generation. The increased number of fluid injection cycles results in more pronounced effect of

hysteresis on oil recovery, fluid injectivity, and field pressure response.

The multiphase UTHYST hysteresis model is a simple approach applicable to available relative permeability models

should the free phase saturation concept is correctly defined and implemented. The model parameter 𝛼ℎ plays a crucial

role in modeling cyclic processes and must be evaluated based on experimental results or through the history matching

of experiments/field application.

Acknowledgements The authors gratefully acknowledge the financial support provided by the DOE-NETL under contract number DE-FE0005952.

Nomenclature 𝐴 = Empirical parameters in Hand’s rule bimodal curve formulation

𝐴𝐶𝑁 = Alkane carbon number

𝐴𝑠=0,1 = Parameter related to the height of the binodal curve

𝑏𝑗=1,2,3 = Parameter for relating three-phase to two-phase relative permeability

𝑏𝑑𝑠 = Surfactant-EACN phase behavior model parameter

𝑏𝜎,𝑠 = Surfactant-EACN phase behavior model parameter

𝐵 = Empirical parameters in Hand’s rule bimodal curve formulation

C1ji and C2ji

= Two-phase relative permeability curvature parameters for phase j flowing with phase i (UTKR3P model)

𝐶3𝑚𝑎𝑥,𝑠=0,1 = Height of binodal curve at zero (𝑠=0) and optimum salinity (𝑠=1)

𝐶𝑖 = Volume concentration of component i

𝐶𝑖𝑙 = Volume concentration of component i in phase l

𝐶𝑆𝐸 = Salt concentration in the aqueous phase

𝐶𝑆𝐸𝐿 = Lower effective salinity limit for Type III environment

𝐶𝑆𝐸𝑂𝑃 = Surfactant optimum salinity

𝐶𝑆𝐸𝑈 = Upper effective salinity limit for Type III environment

𝐶𝑠∗ = Threshold surfactant concentration (UT-foam model)

𝐸𝐴𝐶𝑁 = Equivalent alkane carbon number

𝐸𝑚𝑖𝑛 = Surfactant-EACN phase behavior model parameter

krji0 = Two-phase end-point relative permeability for phase j flowing with phase i (UTKR3P model)

𝑅31, 𝑅32 = Surfactant phase behavior model parameter

𝑅𝑟𝑒𝑓 = Reference foam resistance factor at reference gas velocity (UT-foam model)

𝑆𝑑𝑠 = Surfactant-EACN phase behavior model parameter

𝑆𝜎,𝑆 = Surfactant-EACN phase behavior model parameter

𝑆𝑆𝑒 = Surfactant-EACN phase behavior model parameter

Sjri = Two-phase residual saturation for phase j with respect to phase i (UTKR3P model)

𝑆𝑜∗ = Maximum oil saturation for foam stability (UT-foam model)

𝑆𝑤∗ = Limiting water saturation (UT-foam model)

𝑢𝑔,𝑟𝑒𝑓 = Reference gas Darcy velocity (UT-foam model)

𝛼ℎ𝑗 = Permeability reduction factor of phase-j due to the conjugate phase (UTHYST model)

𝛼𝑣𝑖 = Microemulsion viscosity parameters, i=1-5

14 SPE-174678-MS

𝜇𝑜 = Oil viscosity

𝜇𝑤 = Water viscosity

𝜎𝑠 = Solubilization ratio, s=0 (at zero salinity ),1 (at optimum salinity)

𝜎 = Shear-thinning exponent (UT-foam model)

𝜀 = Dimensionless parameter (UT-foam model)

Subscripts and superscripts: * = Surfactant mixture property

𝐻 = High trapping number

L = Low trapping number

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