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\begin{document}

\title{Numerical Simulation of Enhanced Oil Recovery (EOR) studies for aqueous
Gemini Surfactant-Polymer-Nanoparticle systems}



\author[1]{Nilanjan Pal}%
\author[2]{Ajay Mandal}%
\affil[1]{Indian School of Mines}%
\affil[2]{Affiliation not available}%


\vspace{-1em}



  
  \date{May 04, 2024}


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\selectlanguage{english}
\begin{abstract}
The article investigates the efficacy of gemini
surfactant/polymer/nanoparticle flooding on chemical EOR. Initially,
physicochemical behavior of aqueous chemical fluids were investigated
via interfacial tension reduction, wettability alteration, adsorption,
viscosity moderation and oil displacement experiments. During
compositional analysis, Cartesian model with specified grid properties,
injection flow-rate, well pattern, and rock-fluid characteristics was
developed using CMG-STARS tool. Contour map analyses showed that oil
saturation decreased from \textasciitilde{}80\% (initial) to 31.96\%,
30.68\% and 29.30\% after \{14-6-14 GS + chase water\}, \{14-6-14 GS +
PHPA + chase water\} and \{14-6-14 GS + PHPA + SiO2 chase water\}
flooding respectively. Tertiary recoveries of 15-19\% were achieved,
depending on injected fluid composition. Experimental data were history
matched via CMOST tool to achieve good matching of simulated results.
The CMG flooding simulator provides a holistic approach to investigate
oil displacement profiles, assess flooding recovery capabilities with
near-accuracy and predict the feasibility of proposed chemical EOR
projects.%
\end{abstract}%



\sloppy


\textbf{}

\emph{}

\textbf{Introduction}

The importance of subterranean petroleum hydrocarbons as a dependable
energy resource has intensified on global scale owing to the
ever-increasing consumption of crude oil and/or associated products in
industrial, household, transportation and technological applications
{[}1,2{]}. This has led to the exploration and production of oil from
complicated reservoir formations, wherein problems such as low
permeability, heterogeneity and less accessibility persist during
extraction processes. The initial stage encompasses the application of
primary and secondary recovery techniques to produce one-thirds to
nearly one-half of the original oil in place (OOIP) by natural drive and
water/gas injection. Enhanced oil recovery (EOR) methods have attracted
widespread attention in the last few decades to attain optimized
production of residual oil trapped by alteration of reservoir fluid
properties after conventional recovery {[}3,4{]}. Surfactant flooding is
a promising EOR technique employed by the production sector since 1970s
decade {[}5,6{]}. This type of oil recovery functions by allowing
surfactants or ``surface-active agents'' to adsorb onto the interface of
oil/water, thereby decreasing interfacial free energy and increasing
dimensionless capillary number {[}5-7{]}. Polymer improves the viscosity
of displacing (injected) fluid to reduce the mobility ratio between
water and oil {[}8,9{]}. Furthermore, polymer addition increases the
viscous force perpendicular to oil-water interface and responsible for
pushing the residual oil towards the production well {[}8,9{]}. When
this force exceeds the capillary forces holding crude oil within
rock-pores, residual oil detaches from the rock surface and mobilizes
forward with increasing sweep efficiencies. Nanoparticles, in
conjunction with surfactant and polymer, adsorb onto interfaces to
enhance the mechanical barrier onto displaced crude oil surfaces and
produce impulsive emulsions with improved crude oil attracting ability
{[}10,11{]}. A pivotal aspect of chemical EOR lies in proper screening
and optimization of displacing fluid, keeping in mind the effectiveness
as well as cost-profitability of the method employed {[}12{]}. Hence,
surfactant, polymer and/or nanoparticle in chemical fluid must be
introduced to create a forward-moving oil bank within porous rock
formations, which can significantly improve the oil recovery and
maintain pressure gradient during chemical fluid +/ chase water
injection.

Simulation studies are important to assess the flooding performance of
injected chemical fluids, and predict how oil displacement will occur
under specified reservoir/fluid conditions {[}13,14{]}. Prior to
simulation, the technological feasibility of different EOR routes are
tested by experimental investigations {[}14,15{]}. Such studies provide
useful input information to allow the simulator to identify reservoir
parameters, predict recovery and testing the effectiveness of different
EOR projects with similar components {[}13-16{]}. The current industry
is involved in the application of realistic chemical flood simulators
like STARS by Computer Modelling Group (CMG), UTCHEM by the University
of Texas at Austin (UT Austin), REVEAL by Petroleum Experts (Petex), and
ECLIPSE by Schlumberger (SLB). The physics associated with fluid
properties' evaluation differ in each type of reservoir simulator
{[}17-19{]}. UTCHEM is a compositional simulator capable of simulating
different types of EOR processes owing to the provision of four
different phases (gas, aqueous, oil, microemulsion) and incorporation of
advanced numerical concepts {[}20{]}. REVEAL, a full field reservoir
expert, is similar to UTCHEM with surfactant phase behavior and mobility
control options, permeability reduction and polymer degradation
parameters {[}21{]}. However, this tool is not well known among
professionals and engineers in production areas and the existence of a
fourth phase i.e. microemulsion may cause problems in field studies
{[}17,20,21{]}. As per UTCHEM and REVEAL, the presence of a
microemulsion phase is a key parameter to model displacement efficiency,
in spite of the fact that microemulsion properties are not generally
measured in pilot tests and field operations {[}18-21{]}. Both ECLIPSE
and STARS do not consider microemulsion phase as contributor to flooding
simulation and represent oil displacement behavior via analyses of
relative permeability curves for experimental results {[}17,22,23{]}.
However, ECLIPSE software, though common in the industry, does not
encompass the technical functionalities such as salinity effects,
adsorption, polymer concentration mixing, multi-component EOR, shear
thickening and degradation regimes required for accurate modelling
{[}22{]}. Another powerful flooding simulator is CMG, which is capable
of modeling flooding results and manage complex behavior of
oil-chemical-water systems in laboratory-scale and field-scale porous
media {[}24,25{]}. Goudarzi and other researchers {[}17,19{]} assessed
the performance of different reservoir simulators and developed an EOR
benchmark to improve chemical design for field-scale as well as
lab-scale operations. Pandey et al. {[}26{]} employed CMG-STARS for
coreflood modelling experiments and investigated flow parameters that
could be subsequently used in pilot field tests. Kazempour and others
{[}18{]} investigated the validity of multi-phase component EOR systems
in detail, and identified the dynamic behavior of fluid components
existing within core-flood model. Tunnish et al. {[}27{]} successfully
matched experimental flooding results using CMG to effectively tune
relative permeability curves and predict the chemical fluid's ability to
produce in-situ crude oil. Dahbag et al. {[}28{]} reported the
performance of ionic liquid/surfactant flooding during chemical oil
recovery processes, and found the results can be used to predict future
scenarios. CMG tool is reliable and instrumental in evaluating the
potential of conventional and modern EOR methods {[}17-19,24-28{]}.

In this article, a series of flooding experiments were performed to
investigate the secondary and tertiary oil recoveries using surfactant,
surfactant-polymer and surfactant-polymer-nanoparticle slugs. Initially,
physicochemical behavior of designed fluids were evaluated by a series
of experimental studies. A Cartesian grid model was developed using
CMG-STARS software, and parameters such as rock-fluid properties,
interfacial tension, viscosity, adsorption and injector/producer
geometry were entered in the simulation model. Thereafter, the
experimental results obtained in the laboratory were history-matched for
specified builder and injection pattern/time was set with CMOST tool.
Emphasis is put on the injected fluid composition, flow rate and
flooding period. Using detailed methodical approach to identify and
predict well-matched recovery data, produced recovery data were
optimized with minimal error as compared to laboratory results. This
model is useful to simulate surfactant/polymer/particle behavior on
core-scale, and optimize brine/chemical flooding from functional
viewpoint.

\textbf{Experimental and Simulation}

\textbf{Materials}

The surfactant employed in this study is
N,N'-bis(dimethyltetradecyl)-1,6-hexanediammonium bromide (abbreviated
as 14-6-14 GS) with molecular weight of 726 g/mol. This gemini
surfactant was synthesized and characterized in our earlier papers
{[}29,30{]}. Partially hydrolysed polyacrylamide (PHPA), a water-soluble
polymer was purchased from SNF Floerger, SNF SAS, ZAC de Millieux,
Andr\selectlanguage{ngerman}ézieux, France. It has molecular weight of 2.1 ×
10\textsuperscript{7} g/mol with 26.4\% hydrolysis. Aqueous polymer
solutions were prepared in accordance with the American Petroleum
Institute: Recommended practices for evaluation of polymers used in EOR
operations (API RP 63). Silica (SiO\textsubscript{2}) nanopowder (5-15
nm) was obtained from Merck Industries. Sandstone core employed in
flooding experiments was procured from Kalol field in Gujarat, India.
Crude oil sample has total acid number (TAN) of 0.044 mg KOH/g,
kinematic viscosity of
6.147×10\textsuperscript{-5}m\textsuperscript{2}/s and 23.55° API
gravity at 303 K. It was procured from Ahmedabad oil field, ONGC Asset,
India. Double distilled water was extracted from distillation apparatus
in our laboratory.

\textbf{Physicochemical evaluation tests}

Wettability behavior of 14-6-14 GS was investigated by contact angle
studies with the help of Kruss DSA25 Drop Shape Analyzer. Adsorption
behavior of gemini surfactant molecules onto sand surface was conducted
by UV spectrometric analyses to determine the amount of 14-6-14 GS
adsorbed per weight sand (in mg/g). Interfacial tension experiments were
performed by analyzing rotating crude oil drop profile in continuous
surfactant/polymer/nanoparticle containing aqueous solution with the
help of spinning drop SVT20 tensiometer (Dataphysics). Viscosity values
of aqueous chemical fluids were measured using cup and bob geometry in
Bohlin Gemini 2 Rheometer instrument at 303 K. The obtained experimental
results serve as input-data during simulation studies.

\textbf{Flooding procedure}

The experimental flooding apparatus (Porous Material Inc.) consists of
core-holder, positive displacement pump, chemical slug injectors and
measuring cylinder for collecting effluent samples. Sandstone core with
8.74 cm length and 3.66 cm diameter was initially saturated with 1.0\%
NaCl brine for 72 h to saturate the cores; and obtain porosity values in
the range 17-18\%. The core sample showed permeabilities in the range
350-400 milliDarcies (mD). When placed within core-holder apparatus, a
confining pressure of \textasciitilde{}1000-1200 psi was employed to
hold the core in vertical position. Crude oil was injected into the
pores to displace aqueous phase, until irreducible saturation state was
achieved. This was followed by an ageing period of 6 days to obtain an
oil-saturated reservoir model in the laboratory. Secondary flooding was
investigated by brine flooding at the rate of 10 ml/h to recover a
fraction of crude oil. When water cut percentage exceeds \selectlanguage{english}[?] 95\%,
chemical aqueous fluid containing surfactant +/ polymer +/ nanoparticle
was flooded at 5-10 ml/h rate to sweep residual oil during EOR. Finally,
chase water was injected at the same flow-rate to maintain pressure drop
for favorable oil displacement. Effluent liquid produced during
secondary and tertiary recovery studies were collected in graduated
cylinders.

\textbf{Simulation methodology}

The STARS simulator package in CMG is widely employed compositional tool
in the petroleum industry, with the capacity to develop reservoir models
{[}24-27{]}. A Cartesian grid system with specified divisions along
X-axis, and the developed model was simulated to match flooding history
data using CMOST analysis tool. Prior to running the STARS simulation
for aqueous flooding model and subsequent history-matching of
experimental recovery data, the following assumptions were made to
obtain accurate findings {[}31,32{]}:

\begin{enumerate}
\tightlist
\item
  The reservoir initially consists of two phases, namely, crude oil and
  water.
\item
  The amount of free gas/solvent gas in the core model is assumed as
  zero.
\item
  A grid-based core model is considered, with uniform properties and no
  geological complexities/heterogeneities.
\item
  Fluid flow in radial direction is negligible as compared to that in
  axial direction.
\item
  Salinity effect on phase behavior is ignored.
\item
  Chemical reactions do not occur.
\item
  Oil and water flowing through porous media obeys the Darcy's Law.
\end{enumerate}

Porosity, permeability and crude oil properties were introduced as input
data for reservoir characterization. In recent years, the need to
develop appropriate flooding model has paved the way to make informed
decisions during chemical fluid selection/optimization and field
implementation {[}33-35{]}. Druetta and co-workers {[}35{]} developed a
flooding simulator to investigate EOR properties of different chemical
fluid compositions. Arhuoma et al. {[}36{]} found that CMG simulation
model is useful to determine displacement phenomena governing flooding
behavior, depending on injection fluid type. The effectiveness of
numerical simulation studies on chemical flooding showed far-reaching
consequences during oilfield applications, as evident from the findings
of earlier papers {[}34,37{]}. This kind of grid-based model helps in
understanding fluid flow behavior prior to injection; as well as achieve
a sufficiently robust numerical model {[}33,35,36{]}. Table 1 presents
the core and fluid properties employed in STARS model.

\textbf{Table 1.} Core model and fluid parameters for flooding
simulations.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\textbf{Core ID} & \textbf{Sandstone}\tabularnewline
\midrule
\endhead
Core type & Berea sandstone\tabularnewline
Core diameter & 3.66 cm\tabularnewline
Core length & 8.74 cm\tabularnewline
Bulk volume & 91.95 cm\textsuperscript{3}\tabularnewline
Porosity & 17-18\%\tabularnewline
Permeability & 350-400 mD\tabularnewline
Crude oil Gravity & 23.55\selectlanguage{ngerman}° API\tabularnewline
Crude oil viscosity & 10.94 cP\tabularnewline
Crude oil API & 23.55\selectlanguage{ngerman}° API\tabularnewline
Formation Water viscosity & 0.8177 cP\tabularnewline
Initial reservoir pressure & 101 kPa\tabularnewline
Temperature & 303 K\tabularnewline
\bottomrule
\end{longtable}

\textbf{Governing equations for Multi-phasic reservoir modeling}

CMG-STARS is a finite difference numerical tool that describes
mathematical equations for fluid flow in a petroleum reservoir. In
multiphase flow equations, the simulation model is governed by the
conservation of mass, energy and momentum. These functions relate
conservation equations with an elementary volume or specified region of
interest; wherein each component of volumetric change is related to the
fluids entering or leaving the system {[}38,39{]}. This includes the
material balance equations, Darcy's law, relative permeability
correlations, capillary pressure equations, and phase equilibrium
equations in two- and three-phase porous media {[}39-41{]}. The
conservation law states that the conserved quantity within a volume or
at a point depends on the net rate of fluids that flow in and out of the
volume (or region). With the depiction of an appropriate set of
initial/boundary conditions, the governing models are applied to develop
an understanding of simultaneous flow of two or more fluid phases. The
conservation equation for mass is presented for a flowing and/or
adsorbed component `\emph{i} ' within the system as Eq. (1):

\(\frac{\partial}{\partial t}\left[V_{f}\left(\rho_{w}S_{w}w_{i}+\rho_{o}S_{o}x_{i}+\rho_{g}S_{g}y_{i}\right)+V_{v}\text{Ad}_{i}\right]=\sum_{k=1}^{n_{f}}\left[T_{w}\rho_{w}w_{i}\selectlanguage{greek}\text{ΔΦ}\selectlanguage{english}_{w}+T_{o}\rho_{o}x_{i}\selectlanguage{greek}\text{ΔΦ}\selectlanguage{english}_{o}+T_{g}\rho_{g}y_{i}\selectlanguage{greek}\text{ΔΦ}\selectlanguage{english}_{g}\right]+V\sum_{k=1}^{n_{r}}{\left(s_{\text{ki}}^{{}^{\prime}}-s_{\text{ki}}\right)r_{k}}+\sum_{k=1}^{n_{f}}\left[\phi D_{\text{wi}}\rho_{w}{\Delta w}_{i}+\phi D_{\text{oi}}\rho_{o}\selectlanguage{greek}\text{Δx}\selectlanguage{english}_{i}+\phi D_{\text{gi}}\rho_{g}{\Delta y}_{i}\right]+\rho_{w}q_{\text{wk}}w_{i}+\rho_{o}q_{\text{ok}}x_{i}+\rho_{g}q_{\text{gk}}y_{i}+\delta_{\text{iw}}\sum_{k=1}^{n_{f}}\rho_{w}\text{qaq}_{\text{wk}}\)(1)

where,\(\frac{\partial}{\partial t}\left[V_{f}\left(\rho_{w}S_{w}w_{i}+\rho_{o}S_{o}x_{i}+\rho_{g}S_{g}y_{i}\right)+V_{v}\text{Ad}_{i}\right]\)is the time-derivative for material
accumulation. The total fluid volume and void volume are represented by
terms, \emph{V\textsubscript{f}} and\emph{V\textsubscript{v}}
respectively. In above relation,\emph{w\textsubscript{i}} ,
\emph{x\textsubscript{i}} , and\emph{y\textsubscript{i}} refer to mole
fraction of component `\emph{i'}in water, oil and gas respectively,
whereas \selectlanguage{greek}\emph{ρ} \selectlanguage{english}and \emph{S} stand for density and saturation of
different phases.\([T_{w}\rho_{w}w_{i}\selectlanguage{greek}\text{ΔΦ}\selectlanguage{english}_{w}+T_{o}\rho_{o}x_{i}\selectlanguage{greek}\text{ΔΦ}\selectlanguage{english}_{o}+T_{g}\rho_{g}y_{i}\selectlanguage{greek}\text{ΔΦ}\selectlanguage{english}_{g}+\phi D_{\text{wi}}\rho_{w}{\Delta w}_{i}+\phi D_{\text{oi}}\rho_{o}\selectlanguage{greek}\text{Δx}\selectlanguage{english}_{i}+\phi D_{\text{gi}}\rho_{g}{\Delta y}_{i}]\)is the flow term for component
`\emph{i'} . {[}\(\rho_{w}q_{\text{wk}}w_{i}+\rho_{o}q_{\text{ok}}x_{i}+\rho_{g}q_{\text{gk}}y_{i}]\)is well source/sink term,
and\(V\sum_{k=1}^{n_{r}}{\left(s_{\text{ki}}^{{}^{\prime}}-s_{\text{ki}}\right)r_{k}}\)stands for the reaction source/sink term for
component `\emph{i'} . For water component, \(\sum_{k=1}^{n_{f}}\rho_{w}\text{qaq}_{\text{wk}}\)is aquifer
source/sink term wherein \emph{qaq\textsubscript{wk}}represents the
volumetric flow rate through the block face \emph{k}to/from adjacent
aquifer.

\emph{T} is the component transmissibility between two regions/points,
which accounts for cross-sectional area, distance between the elementary
volumes, and fluid permeability. Eq. (2) depicts the relation between
volumetric flow rate, \emph{v} and transmissibility, \emph{T} , as:

\(v_{j}=T\left(\frac{k_{\text{rj}}}{\mu_{j}r_{j}}\right){\Phi}_{j}\)(2)

In this equation, the term `\emph{j} ' can be applied to different
phases, i.e. water (\emph{w} ), oil (\emph{o} ) and gas (\emph{g}
).\selectlanguage{greek}\emph{ΔΦ\textsubscript{j}}\selectlanguage{english} represents potential difference for
phase\emph{`j',} and it may be either positive or negative, depending on
the inflow/outflow of fluid component. \emph{r\textsubscript{j}} is
phase resistance factor, \emph{k\textsubscript{rj}} is relative
permeability and \selectlanguage{greek}µ\selectlanguage{english}\textsubscript{j} is viscosity of phase \emph{j} .
Component dispersibility in water, oil, and gas phases are shown
by\emph{D\textsubscript{wi}} , \emph{D\textsubscript{oi}} ,
and\emph{D\textsubscript{gi}} . The well rate
(\emph{q\textsubscript{jk}} ) of any phase `\emph{j} ' in the layer
`\emph{k} ' is shown in Eq. (3):

\(q_{\text{jk}}=I_{\text{jk}}\left(p_{\text{wfk}}-p_{k}\right)\)(3)

where, \emph{p\textsubscript{wfk}} is wellbore
pressure,\emph{p\textsubscript{k}} is pressure existing within volume
and\emph{I\textsubscript{jk}} refers to phase index. The phase index
property of the system depends on various factors such as geometry,
permeability, layer thickness, and skin factor. Therefore, individual
changes in each component contribute toward conservation studies for
mass. Total energy of the material volume is an important field of
research analysis, which has significant repercussion in defining fluid
flow behavior. During CMG simulation, the rock volume does not change,
and the internal energy of the rock remains constant. The energy
conservation equation is shown in Eq. (4) as:

\(\frac{\partial}{\partial t}\left[V_{f}\left(\rho_{w}S_{w}U_{w}+\rho_{o}S_{o}U_{o}+\rho_{g}S_{g}U_{g}\right)+V_{v}{c_{s}U}_{s}+V_{r}U_{r}\right]=\sum_{k=1}^{n_{f}}\left[T_{w}\rho_{w}H_{w}\selectlanguage{greek}\text{ΔΦ}\selectlanguage{english}_{w}+T_{o}\rho_{o}H_{o}\selectlanguage{greek}\text{ΔΦ}\selectlanguage{english}_{o}+T_{g}\rho_{g}H_{g}\selectlanguage{greek}\text{ΔΦ}\selectlanguage{english}_{g}\right]+\sum_{k=1}^{n_{f}}{KT}+\rho_{w}q_{\text{wk}}H_{w}+\rho_{o}q_{\text{ok}}H_{o}+\rho_{g}q_{\text{gk}}H_{g}+V\sum_{k=1}^{n_{r}}{H_{\text{rk}}r_{k}}+HL_{o}+HL_{v}+HL_{c}+\sum_{k=1}^{n_{f}}\left(HA_{\text{CV}}+HA_{\text{CD}}\right)_{k}\)(4)

In the above equation,\(\frac{\partial}{\partial t}\left[V_{f}\left(\rho_{w}S_{w}U_{w}+\rho_{o}S_{o}U_{o}+\rho_{g}S_{g}U_{g}\right)+V_{v}{c_{s}U}_{s}+V_{r}U_{r}\right]\)is the time-derivative for
energy accumulation, and\emph{U\textsubscript{j}} is the internal energy
of the rock system. It is primarily influenced by two factors, namely,
temperature and phase composition. \emph{H\textsubscript{j}} denotes the
enthalpy of the respective phases. Reaction source/sink term for energy
is represented by \(V\sum_{k=1}^{n_{r}}{H_{\text{rk}}r_{k}}\), wherein\emph{H\textsubscript{rk}}
and \emph{r\textsubscript{k}} stand for enthalpy and volumetric rate of
reaction in layer `\emph{k'}respectively. \emph{HL\textsubscript{o}} ,
\emph{HL\textsubscript{v}} and\emph{HL\textsubscript{c}} represents the
total heat transfer rate, heat transfer rate for convection model and
constant heat transfer model respectively.\(\sum_{k=1}^{n_{f}}\left(HA_{\text{CV}}+HA_{\text{CD}}\right)_{k}\)describes
the aquifer source/sink term for energy,
wherein\emph{HA\textsubscript{CV}} and \emph{HA\textsubscript{CD}}
represent respective rates of heat transfer via convection; and
conduction to/from adjacent aquifer. {[}\(T_{w}\rho_{w}H_{w}\selectlanguage{greek}\text{ΔΦ}\selectlanguage{english}_{w}+T_{o}\rho_{o}H_{o}\selectlanguage{greek}\text{ΔΦ}\selectlanguage{english}_{o}+T_{g}\rho_{g}H_{g}\selectlanguage{greek}\text{ΔΦ}\selectlanguage{english}_{g}+KT]\)represents
the energy term for flow between two regions, and
{[}\(\rho_{w}q_{\text{wk}}H_{w}+\rho_{o}q_{\text{ok}}H_{o}+\rho_{g}q_{\text{gk}}H_{g}]\)is the well source/sink term for energy.

CMG-STARS employs various equations to generate relative permeability
curves, which convey rock-fluid interactions in porous media flow
studies. Corey's correlation is an important alternative to calculate
relative permeability curves, particularly in situations wherein
displacing/displaced fluid properties are not available in detail
{[}42-44{]}. This behavior is described in Eqs. (5), (6), (7), and (8)
as:

\(K_{\text{rw}}=K_{\text{rwiro}}\left(\frac{S_{w}-S_{\text{wcrit}}}{1.0-S_{\text{wcrit}}-S_{\text{oirw}}}\right)^{N_{w}}\)(5)

\(K_{\text{row}}=K_{\text{rocw}}\left(\frac{S_{o}-S_{\text{orw}}}{1.0-S_{\text{wcon}}-S_{\text{orw}}}\right)^{N_{\text{ow}}}\)(6)

\(K_{\text{rog}}=K_{\text{rogcg}}\left(\frac{S_{l}-S_{\text{org}}-S_{\text{wcon}}}{1.0-S_{\text{gcon}}-S_{\text{org}}-S_{\text{wcon}}}\right)^{N_{\text{og}}}\)(7)

\(K_{\text{rg}}=K_{\text{rgcl}}\left(\frac{S_{g}-S_{\text{gcrit}}}{1.0-S_{\text{gcrit}}-S_{\text{oirg}}-S_{\text{wcon}}}\right)^{N_{g}}\)(8)

\emph{K\textsubscript{rw}} , \emph{K\textsubscript{row}}
,\emph{K\textsubscript{rog}} and \emph{K\textsubscript{rg}} refer to
respective values of water phase relative permeability for water-oil
table, oil phase relative permeability for water-oil table, liquid phase
relative permeability for liquid-gas table, and gas phase relative
permeability for liquid-gas table. Different saturation terms were
employed to characterize wetting characteristics of reservoir rock
{[}43,44{]}. It is to be noted that \emph{K\textsubscript{rocw}}
is\emph{K\textsubscript{ro}} at connate water
saturation,\emph{K\textsubscript{rgcl}} is \emph{K\textsubscript{rg}} at
connate liquid saturation, \emph{K\textsubscript{rwiro}}
is\emph{K\textsubscript{rw}} at irreducible oil
saturation,and\emph{K\textsubscript{rogcg}} is
\emph{K\textsubscript{rog}} at connate gas saturation. Connate water
saturation, critical water saturation, irreducible oil saturation for
water-oil table, and residual oil saturation for water-oil table are
represented by\emph{S\textsubscript{wcon}} ,
\emph{S\textsubscript{wcrit}} ,\emph{S\textsubscript{oirw}} and
\emph{S\textsubscript{orw}}respectively. Irreducible oil saturation,
residual oil saturation, connate gas saturation and critical gas
saturation are depicted by respective terms \emph{S\textsubscript{oirg}}
,\emph{S\textsubscript{org}} , \emph{S\textsubscript{gcon}}
and\emph{S\textsubscript{gcrit}} for liquid-gas
table.\emph{N\textsubscript{w}} , \emph{N\textsubscript{ow}}
,\emph{N\textsubscript{og}} and \emph{N\textsubscript{g}} are exponent
terms determined from relative permeability curves. Equations (5) and
(6) describe the water-oil permeability table, whereas equations (7),
(8) are used to generate liquid-gas relative permeability data.
Alterations occurring within physicochemical properties of reservoir
fluids due to presence of chemicals i.e. surfactant, polymer and/or
nanoparticle lead to varying fluid flow profiles during EOR.
Interpolation of relative permeability curve is performed by
corresponding to relative permeability datasets in-between high and
ultralow IFT conditions {[}45,46{]}. The interpolated relative
permeability data is described as function of dimensionless parameters,
as shown in Eqs. (9), (10) and 11):

\(k_{\text{rw}}=k_{\text{rwA}}.\left(1-\text{ratn}^{\text{WCRV}}\right)+k_{\text{rwB}}.\text{ratn}^{\text{WCRV}}\)(9)

\(k_{\text{ro}}=k_{\text{roA}}.\left(1-\text{ratn}^{\text{OCRV}}\right)+k_{\text{roB}}.\text{ratn}^{\text{OCRV}}\)(10)

\(k_{\text{rg}}=k_{\text{rgA}}.\left(1-\text{ratn}^{\text{GVRV}}\right)+k_{\text{rgB}}.\text{ratn}^{\text{GCRV}}\)(11)

In the above equations, \emph{ratw} and \emph{ratn} refer to
interpolation parameters with values ranging between zero and unity. The
curvature interpolation parameters are represented by \emph{WRCV}
,\emph{OCRV} , and \emph{GCRV} , with the default value of one.
Furthermore, the interpolation parameters are related to the capillary
number as shown in Eq. (12) and Eq. (13) as follows:

\(ratw=\frac{\operatorname{}{\left(N_{c}\right)-DTRAPWA}}{DTRAPWB-DTRAPWA}\)(12)

\(ratn=\frac{\operatorname{}{\left(N_{c}\right)-DTRAPNA}}{DTRAPNB-DTRAPNA}\)(13)

where, N\textsubscript{c} is the capillary number, whereas\emph{DTRAPWA}
and \emph{DTRAPNA} describe interpolation parameters for high IFT value
(low N\textsubscript{c} condition) and ultralow IFT value (favorably
high N\textsubscript{c} condition) respectively, for wetting phase. On
the contrary, \emph{DTRAPNA} and \emph{DTRAPNB} are similar
interpolation terms for the non-wetting phase. Relative permeability
plot analysis is important during CMG-STARS modelling studies for
accurate investigation of fluid-rock interactions and flooding
performance of injection fluids.

\begin{enumerate}
\tightlist
\item
  \textbf{Results and Discussion}
\item
  \textbf{Experimental investigations}
\item
  \textbf{Rock-wetting characteristics of 14-6-14 GS}
\end{enumerate}

Wettability alteration characteristics was investigated by sessile drop
analyses of aqueous surfactant fluid onto crude oil-saturated sandstone
rock. Figs. 1(a) and 1(b) show the variation of contact angle with time.
At initial time (t = 0), contact angle was measured as 102.8\selectlanguage{ngerman}°,
confirming the intermediate wet nature of rock surface. For sandstone
rock, contact angle progressively reduced to 72.6°, 61.9°, 50.9°, 32.1°
and 14.2°; at the end of 30 s, 60 s, 120 s, 240 s and 480 s
respectively. This trend is indicative of ``spreading'' of aqueous
chemical fluid and ``detachment'' of crude oil molecules from rock
surface {[}47{]}. Rock-wetting process is mainly dependent on rock
morphology, inter-ionic electrostatic interactions and attractive and
attractive/hydrophobic interactions among 14-6-14 GS molecules and crude
oil components. As time elapses, surfactant molecules gradually
destabilize the ordered arrangement of previously adsorbed oil molecules
and spread onto the rock substrate. Hence, 14-6-14 GS possess the
capability to favorably ``wet'' oil-saturated rock and mobilize
entrapped crude oil within reservoir formations effectively.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Fig. 1(a).} Dynamic contact angle values expressed a function of
time for 0.10\% 14-6-14 GS system; \textbf{(b)} Sessile drop profiles of
surfactant fluid at different time intervals for sandstone rock at 303
K.

\textbf{Surfactant adsorption behavior}

Surfactant adsorption is a major problem encountered during chemical EOR
owing to material losses observed within reservoir pore-throats.
Adsorption profile, obtained from UV spectroscopic analysis as a
function of 14-6-14 GS concentration for sandstone, is presented in Fig.
2. At low 14-6-14 GS concentrations (\textgreater{} CMC), surfactant
molecules begin to form aggregates/micelles and are subsequently
attracted to dispersed rock particle charge as electrical double layer
{[}48,49{]}. This ultimately leads to a sharp increase in adsorbed
surfactant. With further addition, 14-6-14 GS dimer molecules start to
occupy active ``adsorption'' sites; and repel previously adsorbed
micelles or aggregates {[}48{]}. Consequently, rock adsorption for
14-6-14 GS increased gradually with increasing concentration. At this
stage, solid surface shows a very slow increasing trend for 14-6-14 GS
adsorption density profiles owing to nearly complete saturation of
rock-liquid interfaces with surfactant dimer molecules. The main
influencing factor responsible for 14-6-14 GS adsorption is the
formation of an ionic or electrostatic pairing bond between cationic
head-groups of surfactant molecules and negatively charged rock surface
{[}49{]}. However, attractive forces such as electrostatic pairing
between surfactant head and charged rock surface, dispersive forces,
hydrophobic forces among adsorbed and free surfactant molecules,
hydrogen bonding and covalent interactions also aid in enhancing the
adsorption behavior of surfactant species {[}48,49{]}.

\textbf{Fig. 2.} Adsorption density onto sand surface for 14-6-14 GS at
303 K.

Experimental data for rock adsorption was investigated by Langmuir and
Freundlich isotherms. The model parameters obtained by fitting
experimental data with adsorption theories are depicted in Table 2.
Though both isotherms have their respective behavioural traits and
applications, a careful evaluation of adsorption density versus
surfactant concentration plots with these theories may help in
understanding the molecular arrangement of adsorbed 14-6-14 GSs onto
sandstone rock. Langmuir model assumes that surfactant molecules form a
single layer onto adsorbent rock surfaces, wherein Freundlich model
suggests a multiple layer stacking arrangement of adsorbed surfactant
species {[}50{]}. Langmuir model exhibited better results as compared to
Freundlich adsorption model, which was evident from larger values of
coefficient of determination (R\textsuperscript{2}). Furthermore,
smaller values of chi-square statistic (\selectlanguage{greek}χ\selectlanguage{english}\textsuperscript{2}) were
obtained during Langmuir isotherm fitting, which further corroborated
our inclination to the Langmuir isotherm model to predict surfactant
adsorption data. Therefore, monomolecular layer of adsorbed 14-6-14 GS
molecules is proposed with no stacking behavior during rock adsorption
studies.

\textbf{Table 2.} Langmuir and Freundlich model parameters obtained by
fitting experimental adsorption data\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
\textbf{Gemini surfactant} & \textbf{14-6-14 GS} & \textbf{14-6-14 GS} &
\textbf{14-6-14 GS} & \textbf{14-6-14 GS}\tabularnewline
\midrule
\endhead
& \textbf{Adsorption parameters} & \textbf{Adsorption parameters} &
\textbf{Adsorption parameters} & \textbf{Adsorption
parameters}\tabularnewline
\textbf{Langmuir} & \textbf{K\textsubscript{L}} &
\textbf{Q\textsubscript{sat} (mg/g)} & \selectlanguage{greek}\textbf{χ\textsuperscript{2}}\selectlanguage{english} &
\textbf{R\textsuperscript{2}}\tabularnewline
& 4.0619 & 3.2988 & 0.0217 & 0.9128\tabularnewline
\textbf{Freundlich} & \textbf{Qsat*K\textsubscript{F} (mg/g)} &
\textbf{1/n} & \selectlanguage{greek}\textbf{χ\textsuperscript{2}}\selectlanguage{english} &
\textbf{R\textsuperscript{2}}\tabularnewline
& 3.7556 & 0.5995 & 0.0349 & 0.8601\tabularnewline
\bottomrule
\end{longtable}

\textbf{Interfacial tension experiments}

Evaluation of IFT is a pivotal parameter to evaluate the performance of
chemical fluid to recover tertiary crude oil. Aqueous surfactant
solutions were prepared at concentrations ranging between 0.05\% and
0.35\%, wherein silica particle dosages were varied at 0.01-0.10\% in
aqueous nanoparticle dispersions. Fig. 3(a) and 3(b) depicts the
variation of IFT with surfactant concentration at 303 K. It was observed
that IFT decreased with increasing surfactant/nanoparticle
concentrations up to a critical limit. In the absence of any
surface-active species, IFT value was found to be 18.2 mN/m. GS
exhibited ultralow IFT owing to their unique molecular structure and
capability to self-aggregate at low concentrations. IFT decreased
significantly with values of 0.1127 mN/m and 0.0594 mN/m at 0.05\% and
0.10\% 14-6-14 GS respectively. 14-6-14 GS molecules form micelles; and
arrange as mixed micellar phase existing at oil-aqueous interfaces
{[}51,52{]}. At 0.10\% concentration, the interface was completely
saturated with 14-6-14 GS molecules, which is evident from minima value
of IFT. Beyond this concentration, a slight increase in IFT was observed
due to variation of distribution of adsorbed molecules/micelles,
resulting in slightly higher rate of desorption as compared to
surfactant adsorption process. Once at the interface, 14-6-14 GS
molecules readjust and orient themselves such that the two tail groups
point towards crude oil phase in order to achieve equilibrium conditions
with minimum interfacial energy and favorable oil-attracting capacity
{[}47,52{]}. Like surfactant, nanoparticles adsorbed along interface of
oil and aqueous phases; and favorably improved interfacial activity. The
IFT decreased from 18.2 mN/m to \textasciitilde{}6.0 mN/m during
SiO\textsubscript{2} addition. It is evident that nanoparticles do not
achieve ultralow IFT values due to less efficient adsorption activity.
However, nanoparticle strengthen the mechanical barrier effect, which
ensure improved oil mobilization ability {[}53{]}.

\textbf{Fig. 3.} Oil-aqueous IFT profiles presented as a function of:
(a) 14-6-14 GS concentration, and (b) SiO\textsubscript{2} nanoparticle
concentration.

In this section, surfactant/polymer/nanoparticle fluids were placed in
contact with oil to identify synergistic associations among interacting
mixed species. Fig. 4 shows the IFT behavior of 14-6-14 GS +/ PHPA
aqueous fluids in the presence and absence of silica
(SiO\textsubscript{2}). Surfactant-polymer fluids exhibited greater
values of IFT in comparison to pure surfactant solutions. PHPA addition
favors inter-polymer and intra-polymer interactions, thereby reducing
their exposure to water {[}54{]}. This reduces the number of adsorbed
14-6-14 GS molecules in mixed micelles/aggregates in solution and lower
surfactant adsorption at liquid-liquid interfaces. The electrostatic
repulsive forces between surfactant dimer head-groups increases
significantly during polymer addition. Polymer chains diffuse to
adsorption sites and cause significant variation in inter-molecular
arrangement, resulting in IFT increase {[}54,55{]}. However, polymer
addition enhances oil mobility to improve the sweep efficiency of
displaced crude oil.

Nanoparticle addition showed better activity in terms of reduced IFT,
which is attributed to their favorable adsorption at oil-aqueous
interfaces and reduction in interfacial energy barrier {[}53,56{]}.
However, this behavior was observed until a favorable
SiO\textsubscript{2} concentration, referred to as critical
concentration. For surfactant solutions, IFT was reduced from 0.0594
mN/m to 0.0194 mN/m at 0.030\% SiO\textsubscript{2}. In case of
surfactant-polymer solutions, critical NP dosage of 0.025\% was obtained
with IFT minima of 0.0318 mN/m. The critical NP concentration obtained
in case of surfactant-polymer-nanoparticle (SPN) fluids is lower (0.025
wt. \%) as compared to that obtained for surfactant fluids (0.030 wt.
\%). Beyond this limit, IFT was observed to increase gradually owing to
improved steric effect in the presence of higher concentration species
{[}56,57{]}. This indicated desorption of interacting
molecules/particles from the interface to the bulk solution phase and
consequent transition of mixed micelles to super micelles or vesicles
{[}56,57{]}. SPN fluids are able to recover oil with IFT values in the
desired optimal range and sweep crude oil with greater efficacy as
compared to surfactant-nanoparticle and surfactant formulations.
Henceforth, interfacial behavior of SPN aqueous solutions contribute
beneficially in EOR studies.

\textbf{Fig. 4.} Interfacial tension plots for 14-6-14 GS and \{14-6-14
GS + PHPA\} systems, presented as a function of silica concentration at
303 K.

\textbf{Influence of polymer/nanoparticle on fluid rheology}

An EOR fluid must possess favorable rheological properties to achieve
favorable displacement of crude oil through porous rock formations. The
influence of addition of surfactant (14-6-14 GS), polymer (PHPA) and
nanoparticle (SiO\textsubscript{2}) on the viscosity of chemical fluids
are studied to identify flow behavior and predict oil mobilization
ability. Figs. 5(a), 5(b) and 5(c) show plots of viscosity versus
concentration at shear rate of 10 s\textsuperscript{-1}. It is evident
that apparent viscosity increases with increasing concentration. Aqueous
chemical fluids showed shear thinning or pseudoplastic flow behavior,
which is considered as desirable attributes to achieve good injectivity
and oil mobilization control. Fig. 5(d) shows the viscosity versus shear
stress plots for different aqueous fluid compositions at 303 K. With
application of increasing shear rate, hydrophobic associations are
weakened which decrease the strength of inter-molecular and
intra-molecular interactions. Viscosity of aqueous solution was observed
to be 4.93 mPa.s at 0.02\% 14-6-14 GS concentration, which subsequently
increased to 6.63 mPa.s at 0.05\%, 11.24 mPa.s at 0.10\%, 13.84 mPa.s at
0.20\% and 14.29 mPa.s at 0.35\% concentrations (refer to Fig. 5(a)).
With increase in 14-6-14 GS concentration, surfactant molecules form
super-micelles or vesicles in bulk solution, which reduces the available
``free'' volume and enhances fluid viscosity. Addition of polymer as
well as nanoparticle also exhibited similar behavior in terms of
viscosity for 0.10\% 14-6-14 GS containing fluids. With addition of
0.05\% PHPA, viscosity increased to value as high as 27.69 mPa.s, as
depicted in Fig. 5(b). This is attributed to the increased degree of
entanglement of polymer chains and formation of a network structure
consisting of ``larger'' mixed micelle associations {[}58{]}. Fig. 5(c)
shows further increase in aqueous solution viscosity in the presence of
SiO\textsubscript{2} nanoparticle due to their ability to effectively
strengthen the mechanical barrier (electrostatic repulsion + steric
effects) around dispersed micelles/aggregates formed within \{14-6-14 GS
+ PHPA + SiO\textsubscript{2}\} solution {[}56,59{]}. This leads to more
pronounced network structure with longer mixed micelle entanglements and
consequent increase in viscosity. Surfactant-polymer-nanoparticle (SPN)
fluids showed a sharp increase in viscosity (42.82 mPa.s) until
concentration limit of 0.025\% SiO\textsubscript{2}, beyond which it
increased gradually. In fact, viscosities of SPN nanoemulsions were
measured in the 34-45 mPa.s range, which is attributed to the formation
of enhanced \{14-6-14 GS + PHPA + SiO\textsubscript{2}\} network
structure. Hence, SPN aqueous fluids act as beneficial oil mobility
control agents for EOR studies.

\textbf{Fig. 5.} Viscosity profiles as function of temperature for
different aqueous formulations containing \textbf{(a)} 14-6-14
GS;\textbf{(b)} 14-6-14 GS + PHPA; and \textbf{(c)} 14-6-14 GS + PHPA +
SiO2. \textbf{Fig 5(d)} shows the pseudoplastic character of aqueous
fluids, evident from viscosity versus shear rate plots at 303 K.

\textbf{Flooding experiment results}

Core-flooding experiments are necessary to determine secondary and
tertiary recoveries with different formulated (aqueous) chemical slugs
{[}60{]}. In this study, gemini surfactant concentration greater than
CMC was chosen to account for adsorption losses. PHPA +/
SiO\textsubscript{2} were introduced in 14-6-14 GS based injection
fluids as EOR performance enhancers to achieve better oil displacement
data. Cumulative oil recoveries for different fluid systems were
investigated as a function of injection pore volume, as presented in
Fig. 6. During water-flooding process, 45-47\% of the original oil in
place (OOIP) was extracted. However, residual oil remained trapped
within reservoir pore-throats owing to gravity effect, inertia and
capillary forces. Once [?] 95\% water cut was achieved, recovery profile
flattened. Thereafter, gemini surfactant/polymer/silica slug was
injected as the first stage of EOR to improve oil production efficiency.
The second stage of EOR incorporated flooding with chase water to
maintain pressure differential and ensure continuous displacement of
forward-moving oil bank. Tertiary oil recoveries of \textasciitilde{}15
\% was achieved during \{14-6-14 GS + chase water\} flooding, which
subsequently improved to \textasciitilde{}17\% and \textasciitilde{}18\%
for \{14-6-14 GS + PHPA + chase water\} and \{14-6-14 GS + PHPA +
SiO\textsubscript{2} chase water\} systems respectively. The secondary
and tertiary flooding data results were employed as input data for
(CMOST) assisted history-matching functions, discussed in subsequent
sections {[}18,19,27,37{]}.

\textbf{Fig. 6.} Oil recovery performance of aqueous
surfactant/polymer/nanoparticle solution in core-flooding systems.

\begin{enumerate}
\tightlist
\item
  \textbf{STARS Modelling approach for Coreflood Simulation}
\item
  \textbf{Core Model Building}
\end{enumerate}

The STARS (CMG) tool replicates a cylindrical sandstone core with volume
of 91.952 cm\textsuperscript{3}. A Cartesian system was developed with
single porosity model, as shown in Fig. 7. A rectangular grid with 100
blocks (each length 0.0874 cm) in I-direction, height (3.243 cm) and
width (3.243 cm) was created initially such that its volume is equal to
that of laboratory core. The grid pattern was mapped as centroid
function along X-axis to obtain appropriate STARS model. In subsequent
studies, Case scenarios I, II and III refer to core-flooding simulation
models pertaining to \{water-flood + surfactant EOR\}, \{water flood +
surfactant-polymer EOR\}, and \{water flood +
surfactant-polymer-nanoparticle EOR\} systems respectively.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image12/image12}

\end{center}
\end{figure}

\textbf{Fig. 7.} Cartesian grid (centroid X) pattern for flooding
simulation.

\textbf{Rock-Fluid Properties and Well Completion}

After building the reservoir grid model in STARS, the input/output
frequency control was set and different variables relevant to our
prescribed reservoir model were chosen. Fig. 8 depicts the porosity map
in case of surfactant/polymer/nanoparticle flooding. Porosity in each
case were measured in the range 17-18\%. Formation pore volume of core
samples were measured during brine saturation, and observed as 16.00
cm\textsuperscript{3}, 16.22 cm\textsuperscript{3} and 16.51
cm\textsuperscript{3} for I, II and III respectively. Liquid
permeabilities were obtained in the range 350-400 mD, as calculated from
flow-meter tests. Thereafter, liquid saturation values were incorporated
in a well-sorted consolidated sandstone rock. Initial oil saturation
values were inputted as 79.76\%, 80.08\% and 80.25\% prior to secondary
and tertiary recovery tests; for surfactant, surfactant-polymer and
surfactant-polymer-nanoparticle flooding models respectively in
CMG-STARS model. It was assumed that no solvent gas was present within
the core before and during recovery tests. The injector well was created
at the node {[}1 1 1{]}, whereas the producer well was situated at
{[}100 1 1{]}. The well-bore radius was fixed at 1 cm (0.01 m) in
K-direction. Datasets related to grid formation, formation pore volume,
oil phase volume, temperature, initial saturation, and temperature are
shown in Table 3.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image13/image13}

\end{center}
\end{figure}

\textbf{Fig. 8.} Porosity map for each flooding systems. Rock porosities
were measured in the range 17-18\%, showing similar profiles/contour
maps.

\textbf{Table 3.} Summary of petrophysical data for sandstone core model
using CMG-STARS\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
\textbf{Model parameters} & \textbf{\{14-6-14 GS\} flood} &
\textbf{\{14-6-14 GS + PHPA\} flood} & \textbf{\{14-6-14 GS + PHPA +
Silica\} flood}\tabularnewline
\midrule
\endhead
Number of Grids & 100 \selectlanguage{ngerman}× 1 × 1 & 100 \selectlanguage{ngerman}× 1 × 1 & 100 \selectlanguage{ngerman}× 1 × 1\tabularnewline
Sandpack length (I-axis) & 8.74 cm & 8.74 cm & 8.74 cm\tabularnewline
Grid dimensions (J, K axes) & 3.24, 3.24 cm & 3.24, 3.24 cm & 3.24, 3.24
cm\tabularnewline
Porosity & 0.1740 & 0.1764 & 0.1796\tabularnewline
Formation pore volume & 16.00 cm\textsuperscript{3} & 16.22
cm\textsuperscript{3} & 16.51 cm\textsuperscript{3}\tabularnewline
Permeability & 375 mD & 381 mD & 390 mD\tabularnewline
Oil phase volume & 12.76 cm\textsuperscript{3} & 12.98
cm\textsuperscript{3} & 13.25 cm\textsuperscript{3}\tabularnewline
Aqueous phase volume & 3.24 cm\textsuperscript{3} & 3.24
cm\textsuperscript{3} & 3.26 cm\textsuperscript{3}\tabularnewline
Temperature & 303 K & 303 K & 303 K\tabularnewline
Initial oil saturation (s\textsubscript{oi}) & 0.7976 & 0.8008 &
0.8025\tabularnewline
Solvent Gas present & No & No & No\tabularnewline
Injector well node {[}x y z{]} & {[}1 1 1{]} & {[}1 1 1{]} & {[}1 1
1{]}\tabularnewline
Producer well node {[}x y z{]} & {[}100 1 1{]} & {[}100 1 1{]} & {[}100
1 1{]}\tabularnewline
Well-bore radius (direction) & 1 cm, K-axis & 1 cm, K-axis & 1 cm,
K-axis\tabularnewline
\bottomrule
\end{longtable}

\textbf{Chemical fluid component and Injection Strategy}

After finalizing well pattern and rock-fluid parameters, injection
parameters were set in the simulator. Initially, the secondary
water-flood injection stage continued for a period of 0.1444 days (208
min) at a flow rate of 0.00024 m\textsuperscript{3}/day. This was
followed by chemical flood injection, in which
surfactant/polymer/nanoparticle based aqueous fluids were injected at
the same rate to recover additional oil trapped within pore-throat
regions. This process continued for 86 min duration until cumulative
period of 0.2041 day. Finally, chase water was injected during
0.2041-0.3083 day period (\textasciitilde{}150 min) to maintain pressure
gradient. Earlier researchers developed simulation models using
CMG-STARS and CMOST for core-scale flooding studies {[}61-63{]}. This is
advantageous in understanding reservoir and fluid properties, and
accurately simulate enhanced flooding performance parameters
{[}62,63{]}. Table 4 shows the flooding model comparisons for different
injection schemes employed during displacement experiments.

\textbf{Table 4. Secondary and tertiary flood model comparisons and
Injection schemes}\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
\begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
\textbf{Core-flood (laboratory) Parameters for different EOR
techniques}\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
\textbf{Core-flood (laboratory) Parameters for different EOR
techniques}\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
\textbf{Core-flood (laboratory) Parameters for different EOR
techniques}\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
\textbf{Core-flood (laboratory) Parameters for different EOR
techniques}\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
\textbf{Core-flood (laboratory) Parameters for different EOR
techniques}\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\textbf{Aqueous fluid injected @ 0.00024 m\textsuperscript{3}/day}
\textbf{STW (surface water rate)}\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\textbf{Aqueous fluid injected @ 0.00024 m\textsuperscript{3}/day}
\textbf{STW (surface water rate)}\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\textbf{First Slug}\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\textbf{Second Slug}\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\textbf{Third Slug}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0 - 0.1444 day\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.1444 - 0.2041 day\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.2041 -- 0.3083 day\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Gemini surfactant flooding}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Injected Fluid composition\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{1.0\% NaCl brine (Injected Water)}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Chemical fluid}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{1.0\% NaCl brine (Injected Water)}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Simulation run time\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
208 min\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
86 min\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
150 min\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Time-step (min)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
EOR model\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Water-flood\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Chemical flood\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Chase water-flood\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Wetting phase parameter (DTRAPW)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-5\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-4 to -2\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-2.5 to -0.5\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Number of CMOST runs\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1500\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2000\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2000\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{\{Gemini surfactant + Polymer\} flooding}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Injected Fluid composition\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{1.0\% NaCl brine (Injected Water)}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{0.10\% 14-6-14 GS + 0.05\% PHPA}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{1.0\% NaCl brine (Injected Water)}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Simulation run time\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
208 min\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
86 min\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
150 min\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Time-step (min)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Process model\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Water-flood\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Chemical flood\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Chase water-flood\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Wetting phase parameter (DTRAPW)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-5\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-4 to -2\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-2.5 to -0.5\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Corey exponent\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1500\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2000\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2000\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{\{Gemini surfactant + Polymer + Nanoparticle\} flooding}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Injected Fluid composition\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{1.0\% NaCl brine (Injected Water)}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{0.10\% 14-6-14 GS + 0.05\% PHPA + 0.025\%
SiO\textsubscript{2}}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{1.0\% NaCl brine (Injected Water)}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Simulation run time\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
208 min\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
86 min\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
150 min\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Time-step (min)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
EOR Process\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Water-flood\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Chemical flood\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Chase water-flood\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Wetting phase parameter (DTRAPW)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-5\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-4 to -2\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-2.5 to -0.5\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
Corey exponent\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1500\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2000\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2000\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

\begin{enumerate}
\tightlist
\item
  \textbf{Simulation run and History-Matching with CMOST}
\item
  \textbf{Oil saturation images/maps at different stages of simulation}
\end{enumerate}

Core-scale simulation runs were conducted to investigate the potential
of secondary and tertiary recovery processes in qualitative aspects.
Based on history matching of experimental data conducted during
different flooding techniques, maps showing oil saturation
(s\textsubscript{oi}) were generated at different time intervals, as
presented in Figs. 9(a), 9(b) and 9(c). As mentioned earlier, case
scenarios I, II and III refer to flooding studies in the presence of
\{0.10\% 14-6-14 GS\}, \{0.10\% 14-6-14 GS + 0.05\% PHPA\} and \{0.10\%
14-6-14 GS + 0.05\% PHPA +0.025\% SiO\textsubscript{2}\} respectively.
At initial time (t = 0), the porous rock model was saturated with crude
oil. At this stage, initial oil saturation (s\textsubscript{oi})
percentages were measured as 79.76\% for case I, 80.08\% for case II,
and 80.25\% for case III. This represents the original oil in place
(OOIP). In each case scenario, same brine solution containing 1.0\% NaCl
was injected at constant flow rate (0.00024 m\textsuperscript{3}/day or
10 ml/h) as a form of secondary recovery process. During this process,
the oil saturation within porous model gradually decreased over time
{[}17,27,64{]}. This is evident from the evolution of Cartesian grid
images from brown/red (previously) to a yellow/green hue, which is
indicative of decreasing oil saturation. For case I, oil saturation
values decreased from 79.76\% (initial time) to 59.12\%, 53.44\% and
43.97\% at the end of 30 min, 60 min and 208 min respectively.
Similarly, respective oil saturation percentages after 30, 60 and 208
min were observed to be 59.78\%, 54.13\% and 44.69\% for case II; and
59.79\%, 54.07\% and 44.35\% for case III. Time-dependent data at 208
min represents the end of secondary (water-flood) recovery. It is
pertinent to note that water-flooding exhibited oil saturation levels in
the 43-45\% range, thereby resulting in similar saturation profiles.
However, main findings of the study lie in the evaluation of enhanced
oil recovery results, during which \{aqueous chemical fluid + chase
water\} were injected successively {[}18,64,65{]}. Aqueous chemical
flooding was introduced at the onset of 208 and was stopped at 294 min.
During the 86 min time-period of the first stage of EOR, oil saturation
percentages were found as 36.93\%, 35.62\% and 35.06\% for cases I, II
and III respectively. This was followed by chase water (with 1.0\% NaCl)
injection until a cumulative time-period of nearly \textasciitilde{}7 h
22 min, wherein the residual oil saturation (s\textsubscript{or}) was
investigated. The s\textsubscript{or} values corresponding to I, II, and
III were determined from history-match results as 31.96\%, 30.68\% and
29.30\% respectively. In summary, analyses of oil saturation profiles
prove that analyzed chemical fluids improve the sweep efficiency by
moving the oil far away from the injector well, and extract oil from
producer well.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image14/image14}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image15/image15}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image16/image16}

\end{center}
\end{figure}

\textbf{Fig. 9.} Oil saturation profiles for different stages of
flooding at the end of 0, 30, 60, 208, 294, 444 min in case
of:\textbf{(a)} 14-6-14 GS; \textbf{(b)} 14-6-14 GS + PHPA;
and\textbf{(c)} 14-6-14 GS + PHPA + SiO\textsubscript{2}.

\textbf{Relative permeability curve analysis}

In the presence of multiple fluid systems such as oil and water,
relative permeability describes the alteration in flow behavior with
saturation change. This is commonly observed during secondary and
tertiary flooding studies involving chemical induced displacement of
oil/water in porous media applications. Wettability alteration, pore
morphology, fluid distribution and saturation data are primary
parameters that influence relative permeability measurements
{[}66,67{]}. Figs. 10(a), 10(b) and 10(c) show the water/oil relative
permeability plots obtained during different flooding simulations. Solid
lines represent experimental data curves, wherein adjusted curves
obtained after CMOST assisted history matching are represented with help
of dotted lines. Initially, the core reservoir is in intermediate-wet
state, in which rock pore surfaces are wetted with oil and water exists
within the central regions between the pores. It is evident that
relative permeabilities for oil and water phases vary significantly with
increasing water saturation, which is brought about during
brine/chemical injection {[}67{]}. In summary, simulation studies prove
that the wetting nature of rock is altered to strongly water-wet state.

\textbf{Fig. 10.} Relative permeability curves of different case
scenarios involving: \textbf{(a)} 14-6-14 GS; \textbf{(b)} 14-6-14 GS +
PHPA; and \textbf{(c)} 14-6-14 GS + PHPA + SiO\textsubscript{2}flooding.

\textbf{Cumulative oil production during secondary and tertiary
flooding}

The oil recovery performance of surfactant, surfactant-polymer and
surfactant-polymer-nanoparticle based aqueous chemical fluids were
corroborated by history matching of experimental data. In previous
section, the laboratory results of flooding studies were discussed for
different chemical formulations (see Fig. 6). However, it is important
to study the validity of these results with compositional fluid flow
simulations such as CMG {[}17,18{]}. Fig. 11 shows a good match between
experimental and simulated outcomes of different flooding scenarios.
Experimental analyses revealed that water-flooding processes extracted
respective volumes of 5.73 cm\textsuperscript{3}, 5.74
cm\textsuperscript{3} and 5.93 cm\textsuperscript{3} of initial oil
content in case scenarios I, II and II respectively. Simulation studies
showed water-flood recoveries of 44.86\%, 44.31\% and 44.99\%
respectively at the end of secondary recovery, which is in close
agreement with experimental results. Simulation studies on tertiary
flooding studies showed crude oil recoveries of 7.65
cm\textsuperscript{3}, 8.01 cm\textsuperscript{3} and 8.41
cm\textsuperscript{3} in the presence of \{14-6-14 GS + chase water\},
\{14-6-14 GS + PHPA + chase water\} and \{14-6-14 GS + PHPA +
SiO\textsubscript{2} chase water\} respectively.

\textbf{Fig. 11.} Cumulative oil production versus time plots
for:\textbf{(a)} 14-6-14 GS; \textbf{(b)} 14-6-14 GS + PHPA;
\textbf{(c)}14-6-14 GS + PHPA + SiO\textsubscript{2} showing match
between experimental and CMG-STARS results.

The error between experimental and simulated results for cumulative
flooding studies was obtained with the help of CMG-DECE (Designed
Exploration Controlled. Evolution) engine with 2000 experiments. Figs.
12(a), 12(b) and 12(c) presents the global history match (HM) error
versus experiment ID plots for cases I, II and III respectively. It is
evident that the simulation models were tailored during history match to
achieve optimized result(s) in the search direction of minimal error.
Error percentages with values [?] 6.00\% between the history matched and
experimental models was achieved during the simulation run. Cases I, II
and III registered the most optimal results for experiment ID nos. 1791
(within \selectlanguage{ngerman}± 5.85\% error), 1017 (± 4.38 \% error) and 1753 (± 5.23\%
error) respectively. This optimized model was validated to match imput
fluid and rock conditions, and used as the best-fitted model to explain
flooding performances of different fluid systems. Table 5 shows the
rock-fluid parameters and flooding results for different case scenarios.
The parametric results were obtained from careful analysis of histogram
plots over significant number of simulation runs. The recovery rates,
oil/water permeability curves, rock-wetting properties and fluid flow
parameters were tuned during the history matching process. The study
ultimately presents the success of surfactant flood, surfactant-polymer
flood and surfactant-polymer-nanoparticle flood models in simulating the
experimental outcomes, and confirms their relative efficiencies
{[}17,18,26,27,35{]}.

\textbf{Fig. 12.} History matching error between experimental and
simulated models, showing the base case, general solutions and optimal
solution for cumulative flooding characterized by : \textbf{(a)} 14-6-14
GS; \textbf{(b)} 14-6-14 GS + PHPA; \textbf{(c)} 14-6-14 GS + PHPA +
SiO\textsubscript{2}

\textbf{Table 5. Petrophysical properties and Flooding Simulation
Results from history matching}\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
\begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
\textbf{Flooding performance}\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
\textbf{Flooding performance}\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
Surfactant flood\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
Surfactant-Polymer (SP) Flood\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
Surfactant-Polymer-Nanoparticle flood\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Injection Fluid composition}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Injection Fluid composition}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Brine + \{0.10\% 14-6-14 GS + Chase water\}}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Brine + \{0.10\% 14-6-14 GS + 0.05\% PHPA + Chase water\}}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Brine + \{0.10\% 14-6-14 GS + 0.05\% PHPA + 0.025\%
SiO\textsubscript{2} + Chase water\}}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Pore volume (PV)}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Pore volume (PV)}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
16.00 cm\textsuperscript{3}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
16.22 cm\textsuperscript{3}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
16.51 cm\textsuperscript{3}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Initial Oil Volume}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Initial Oil Volume}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
12.76 cm\textsuperscript{3}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
12.99 cm\textsuperscript{3}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
13.25 cm\textsuperscript{3}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Initial oil saturation (S\textsubscript{oi})}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Initial oil saturation (S\textsubscript{oi})}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.7976\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.8008\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.8025\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Residual oil saturation (Sor)}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Residual oil saturation (Sor)}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.3196\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.3068\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.2930\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\textbf{Secondary recovery} \textbf{(\% OOIP)}\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\textbf{Experimental}\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
46.33\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
45.46\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
45.91\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Simulation}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
44.86\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
44.27\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
44.99\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Global HM Error (\%)}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\selectlanguage{ngerman}± 8.83\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\selectlanguage{ngerman}± 11.03\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\selectlanguage{ngerman}± 10.21\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\textbf{Tertiary recovery} \textbf{(\% OOIP)}\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\textbf{Experimental}\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
15.29\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
17.40\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
18.15\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Simulation}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
15.06\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
17.42\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
18.49\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Global HM Error (\%)}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\selectlanguage{ngerman}± 5.85\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\selectlanguage{ngerman}± 4.38\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\selectlanguage{ngerman}± 5.23\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Cumulative recovery (\% OOIP)}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\textbf{Cumulative recovery (\% OOIP)}\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
59.92\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
61.69\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
63.48\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

\textbf{Flooding Performance analysis and Decision Criteria}

CMG-STARS is useful in modelling the surfactant/polymer/nanoparticle
flooding experiment, with good agreement between the experimental and
simulated data {[}17,37,65,68{]}. Figs. 13(a), 13(b) and 13(c) show the
oil saturation, water cut and recovery factor profiles for different
chemical fluid compositions respectively. A Cartesian model was
developed with constant injection rate and constant pressure condition
to investigate the EOR performance of analyzed fluids. Oil saturation
curves showed that surfactant-polymer-nanoparticle aqueous fluids are
capable of extracting maximum amount of trapped crude oil in comparison
to other analyzed systems. The residual oil saturation
(s\textsubscript{or}) values for cases I, II and III were found to be
31.96\%, 30.68\% and 29.30\% respectively at the end of simulation
tests. Crude oil was recovered during secondary flooding experiments,
until water cut reaches [?] 95\%. At this stage, tertiary fluids were
introduced to improve oil production and reduce water cut percentages.
All three flooding instances discussed herein showed similar behavior in
terms of water cut versus pore volume plots. In fact, oil displacement
experiment was stopped when the quantity of produced oil was extremely
low from economical aspect. EOR investigations achieved crude oil
recoveries of 15.06\% during \{14-6-14 GS + chase water\} flooding,
17.42\% during \{14-6-14 GS + PHPA + chase water\} flooding, and 18.49\%
during \{14-6-14 GS + PHPA + SiO\textsubscript{2} + chase water\}
flooding. Surfactant-polymer-nanoparticle (SPN) flooding recovered an
additional \textasciitilde{}1.07\% of OOIP over surfactant-polymer
flooding; and 3.43\% over conventional surfactant flooding process. The
simulated results were successfully matched with experimental flooding
data. This may not seem very significant in terms of percentages.
However, if the field-scale data is assumed, additional barrels of crude
oil can be produced. This translates to improved efficacy of
surfactant-polymer-nanoparticle based EOR method.

\textbf{Fig. 13.} Flooding performance versus injected pore volume (PV)
of different aqueous EOR fluids, expressed in terms of \textbf{(a)} oil
saturation; \textbf{(b)} water cut; and \textbf{(c)} recovery factor.

\textbf{Conclusions}

Laboratory core-flood experiments were simulated using CMG-STARS to
investigate the flooding performance of \{14-6-14 GS +/ PHPA polymer +/
SiO\textsubscript{2} nanoparticle\} aqueous fluids. Aqueous chemical
systems exhibited ultra-low IFT, rock-wetting behavior and pseudoplastic
flow character, as evident from experimental analyses. Surfactant fluids
were characterized by micelles/aggregates in bulk phase, which altered
to network structure of dispersed micelles interconnected by entangled
polymer chains in surfactant-polymer solutions. This structural
attribute becomes more pronounced in the surfactant-polymer-nanoparticle
(SPN) fluids, resulting in the formation of supra-molecular network
structure with enhanced oil-attracting properties. Cartesian
single-porosity model was employed to develop a robust numerical
approach to match flooding properties of analyzed fluids. Initially,
water-flood was simulated for 208 min. After secondary oil recovery,
tertiary chemicals were injected to improve oil production and maintain
pressure drop within reservoir pore-throats. This flooding process
involved chemical injection period of 86 min, and \textasciitilde{}150
min chase-water flooding period. Oil saturation maps showed that oil
saturation within core sample decreased to 31.96\%, 30.68\% and 29.30\%
of original liquid content at the end of flooding studies, involving
\{14-6-14 GS\}, \{14-6-14 GS + PHPA\} and \{14-6-14 GS + PHPA +
SiO\textsubscript{2}\} fluids respectively. Relative permeability curves
were adjusted to model flooding results, and proved to be useful in
predicting oil displacement results. Tertiary flooding simulations
revealed EOR percentages of 15.06\%, 17.42\% and 18.49\% of original oil
in place (OOIP) in the presence of \{14-6-14 GS + chase water\},
\{14-6-14 GS + PHPA + chase water\} and \{14-6-14 GS + PHPA +
SiO\textsubscript{2} + chase water\} respectively. In summary, the
analyzed aqueous fluids exhibit favorable recoveries and economic
feasibility for EOR in sandstone rock systems.

\textbf{Acknowledgements}

The authors are grateful to the Department of Petroleum Engineering,
Indian Institute of Technology Dhanbad, India for providing
(educational) licensed version of CMG General Release to perform
reservoir simulation studies.

\textbf{Conflict of Interest}

The authors declare no competing financial interest(s).

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