Geochemical evaluation of low salinity hot water injection to enhance heavy oil recovery from carbonate reservoirs

Abstract

Although low salinity water injection (LSWI) has recovered residual oil after the conventional waterflood, highly viscous oil has remained in heavy oil reservoirs. Hot water injection is an economic and practical method to improve oil mobility for viscous oil reservoirs. It potentially controls temperature-dependent geochemical reactions underlying the LSWI mechanism and oil viscosity. Therefore, this study has modeled and evaluated a hybrid process of low salinity hot water injection (hot LSWI) to quantify synergistic effects in heavy oil reservoirs. In comparison to seawater injection (SWI) and LSWI, hot LSWI results in more cation ion-exchange (Ca²⁺ and Mg²⁺) and more wettability modification. Hot LSWI also reduces oil viscosity. In core-scaled systems, it increases oil recovery by 21% and 6% over SWI and LSWI. In a pilot-scaled reservoir, it produces additional oil by 6% and 3% over SWI and LSWI. Probabilistic forecasting with uncertainty assessment further evaluates the feasibility of hot LSWI to consider uncertainty in the pilot-scaled reservoir and observes enhanced heavy oil production. This study confirms the viability of hot LSWI due to synergistic effects including enhanced wettability modification and oil viscosity reduction effects.

1 Introduction

Conventional waterflood has been widely deployed to maintain pressure of reservoirs and pressurize depleted reservoirs. While it typically recovers 35% of original oil in place (OOIP) from conventional reservoirs, heterogeneity, unfavorable mobility, and wettability limitations serve to retain the remaining oil in the reservoir (Lake et al. 2014). Enhanced oil recovery (EOR) methods have been developed to overcome unfavorable conditions. Low salinity water injection (LSWI), which is based on tuning the ionic composition of brine, has emerged as a substitute for expensive EOR. Many experiments have observed that wettability modification is a primary contribution to the LSWI effect (Austad et al. 2005; Zhang et al. 2006, 2007; Lager et al. 2008; Yousef et al. 2011). The studies have observed carboxylic acid in crude oil is the main factor for oil-wetness of chalk. They have found an influence of complex geochemical reactions on the carboxylic acid modifying wetness of chalk. The EOR research group at University of Stavanger (Austad et al. 2005; Zhang et al. 2006, 2007) has carried out chromatographic wettability tests, spontaneous imbibition tests, and coreflood experiments. They used various oil-wet chalk cores, evaluated with the chromatographic wettability test. A chromatographic wettability test tracked the non-adsorbing tracer and injected ions and determined a wettability index of the chalk cores. They injected various compositions of brines into the oil-wet chalk cores and evaluated oil recovery. Using the observations, they have proposed a mechanism that adsorption of SO₄²⁻ and co-adsorption of Ca²⁺ and Mg²⁺ are responsible for wettability modification of chalk cores. The study also concluded that the mechanism is sensitive to temperature and a high temperature (above 70 °C) is a favorable condition to observe the mechanism. Yousef et al. (2011) conducted various experiments of IFT (interfacial tension), NMR (nuclear magnetic resonance) measurement, and coreflood. The study observed an IFT reduction when low salinity water is injected. From the NMR measurement, change of pore distribution was observed and attributed to mineral dissolution. Based on the experiments, the study concluded there is a wettability modification effect to enhance oil recovery and proposed that an alteration of surfaces of carbonate rock alters reservoir wettability. Further work of Ayirala et al. (2018) constructed a coreflooding system with zeta potential measurement and measured zeta potential when different diluted brines were injected into cores. They also simulated the experiments at different temperatures (25, 60 °C) to reveal the relationship between temperature and zeta potential. Hiorth et al. (2010) proposed another mechanism with rock dissolution, rather than rock surface charge, is responsible for the wettability modification effect. Yutkin et al. (2018) examined the proposed mechanisms of LSWI by calculating surface charge potential using experimental results. Their findings of rapid dissolution of carbonate rock, pH buffering by rock dissolution, diffuse double layer collapse, and instantaneous equilibrium between aqueous species and mineral dissolution are at variance with the proposed mechanisms except for MIE (multicomponent ionic exchange) theory (Lager et al. 2008) and ligand-ion-exchange oil release. While the exact mechanism is still unclear, it is obvious that LSWI contributes to wettability modification and geochemical reactions are responsible for the LSWI effect.

A few studies have constructed a numerical LSWI model by implementing its mechanism (Qiao et al. 2015; Awolayo et al. 2017). Qiao et al. (2015) proposed a mechanism modeling approach using the surface complexation model and the electrical diffuse layer calculation in carbonate core systems. The surface complexation model describes surface reactions that adhere aqueous ions and carboxylic groups to the surface of calcite in aqueous, oleic, and solid phases. An additional extensive experimental database of carbonate reservoirs is required for the approach. The experimental difficulties associated with the acquisition and interpretation of electro-kinetic measurements and surface titration data as well as complex surface chemistry of carbonate minerals are barriers to the approach (Wolthers et al. 2008). In addition, this approach is not practical in pilot-scaled modeling because of the various unclear parameters. Another numerical study by Awolayo et al. (2017) developed a LSWI model coupled with aqueous reactions, mineral reactions, ion-exchange reactions of Ca²⁺ and Mg²⁺, and adsorption reaction of SO₄²⁻. It modeled the underlying mechanism of LSWI using the concept of MIE (multicomponent ionic exchange) theory (Lager et al. 2008). Therefore, this study adapted the approach of Awolayo et al. (2017) to formulate LSWI mechanism.

Gachuz-Muro and Sohrabi (2013, 2014) investigated this promising LSWI for heavy oil recovery. Normally, crude oil is classified as light (higher than 31.1° API), medium (from 31.1° API to 22.3° API), heavy (less than 22.3° API), and extra heavy (less than 10° API). The experiments used heavy oil (14.12° API, 53,484 cP at 20 °C). The heavy crude oil production has several technical issues of wettability, highly viscous oil, asphaltene precipitation, etc. (Gachuz-Muro and Sohrabi 2014; Guo et al. 2016). Gachuz-Muro and Sohrabi (2013, 2014) described the properties of oil and brines used in the coreflooding experiments. Ionic composition of SW is equivalent to the brine composition from the Gulf of Mexico. Compositions of formation water (FW), seawater (SW), and low salinity water (LSW) are indicated in Table 1. The heavy crude oil viscosity decreases as temperature increases from 20 to 115 °C, as shown in Fig. 1. Gachuz-Muro and Sohrabi (2014) conducted LSWI experiments with limestone cores. In the coreflooding experiment, SW and LSW (10 times-diluted SW) were injected at a relatively high temperature (92 °C). They reported that SW injection (SWI) of 15 pore volume (PV) obtained an oil recovery up to 36.8% and successive LSW injection (LSWI) of 15 PV after SWI produced additional oil recovery of 15.3%. The enhanced oil recovery proved the potential LSWI effect and wettability modification in heavy oil reservoirs.

Table 1 Properties and compositions of brines

Fig. 1

Temperature-dependent oil viscosity

A study (Lapham 2012) reported that the global oil reserves are estimated to contain 35% light oil, 29% medium oil, 26% heavy oil, and 10% extra heavy oil. Though the heavy oil reserve is potentially huge in the world, especially South America, the heavy oil recovery factor still remains low (Meyer et al. 2003). In addition, heavy oil in fractured carbonate reservoirs represents 25%–30% of the total oil in place in the Middle East (Saidi 1988). The thermal EOR has a potential to enhance the heavy oil recovery. The Wafra oil field in Oman already shows the huge potential for thermal EOR in at least a portion of the field. Lapham evaluated the extensive EOR projects and concluded that hybrid thermal EOR combining with other EOR is efficient to recover the heavy oil. Therefore, thermal EOR with LSWI can be a promising hybrid EOR for heavy oil reservoirs. When this hybrid EOR technology is developed and secures practical feasibility, it will expand the heavy oil market. One of the great candidate thermal EORs for the hybrid EOR is hot water injection. It is a waterflood-based EOR similar to LSWI. The field tests and experiments already have confirmed that hot water injection reduces heavy oil viscosity and improves heavy oil production (Kovscek et al. 2000; Alajmi et al. 2009; Duval et al. 2015). Additionally, it potentially influences pore connectivity because of temperature-dependent mineral reactions (Kovscek et al. 2000). The geochemical reactions are known to be sensitive to both temperature and pressure (Appelo and Postma 2005), so hot water injection significantly affects geochemical reactions.

This study proposes the hybrid EOR technology combining hot water injection and LSWI, hereafter referred to as low salinity hot water injection (hot LSWI) for heavy oil recovery. Previously, Abass and Fahmi (2013) conducted hot LSWI experiments using intermediate heavy oil (1700 cP at 65 °C) and sandstone cores from the BAW oil field in Sudan. Its results proved the enhanced heavy oil production and synergistic effects of the hybrid hot LSWI, however, the study lacked investigations of temperature-dependent geochemical reactions and carbonate rock during hot LSWI. Therefore, this study simulates hybrid hot LSWI considering temperature-dependent geochemical reactions and evaluates the heavy oil recovery of hot LSWI from carbonate reservoirs. The heavy oil production and synergistic effects of hot LSWI are compared to those of SWI and LSWI in core- and pilot-scaled systems.

2 Basic theories

Transportation modeling of multi-phases and -components is coupled with multiple modeling of geochemical reactions and Henry’s law. The geochemical reactions involve aqueous reactions, mineral dissolution/precipitation, and ion exchange and they are sensitive to temperature. In geochemical reactions, ion activity, equilibrium constant, selectivity coefficient, and reaction rate are all a function of temperature and are determined by various experiments (Wolery and Daverler 1992; Appelo and Postma 2005). Viscosity and density of brine depend on temperature and ion activity as well.

2.1 Aqueous reactions

Ionic concentration in the aqueous phase is determined when the reaction quotient or ion activity product (IAP) reaches the temperature-dependent equilibrium constant at a specific temperature. The temperature-dependent equilibrium constant is obtained from Kharaka et al. (1988) and Delany and Lundeen (1991).

$$Q_{\alpha } - K_{{{{\rm eq,}}\alpha }} = 0$$

(1)

$$Q_{\alpha } = \prod\limits_{k = 1}^{{n_{{\rm aq}} }} {a_{k}^{{v_{k,\alpha } }} }$$

(2)

$$\log K_{{{{\rm eq,}}\alpha }} = A_{1} + A_{2} T + A_{3} T^{2} + A_{4} T^{3}$$

(3)

where $\alpha$ is the aqueous reaction, $K_{{{{\rm eq,}}\alpha }}$ is the temperature-dependent equilibrium constant at a specific temperature, $Q_{\alpha }$ is the IAP, $k$ is the component, $n_{{\rm aq}}$ is the number of aqueous reactions, $a_{k}$ is the ionic activity, $v_{k,\alpha }$ is the stoichiometry coefficients of an aqueous reaction, A₁, A₂, A₃, and A₄ are the fitting parameters to determine the equilibrium constant at a specific temperature, and T denotes temperature.

In geochemical reactions, effective ionic concentration is considered rather than molality, because of electrostatic interactions among ions in the aqueous phase. The effective ionic concentration is represented by ion activity, which is determined by the activity coefficient and molality. The activity coefficient is a function of temperature and ionic strength. Davies, Debye–Hückel, and modified Debye–Hückel (B-dot) models can calculate activity coefficient. The modified Debye–Hückel (B-dot) model determines reasonable activity coefficient of ions when ionic strength varies up to 1 molality (Bethke 2007). In addition, various geochemical software EQ3/EQ6, CHILLER, SOLMINEQ, and SPECE8 and REACT use the model. Therefore, this study uses the modified Debye–Hückel model to calculate temperature-dependent activity coefficient of ions. In this study, Bethke (2007) is used to calculate them.

$$a_{k} = \gamma_{k} m_{k}$$

(4)

$$\log \gamma_{k} = - \frac{{A_{\gamma } z_{k}^{2} \sqrt I }}{{1 + \dot{a}_{k} B_{\gamma } \sqrt I }} + \dot{B}I$$

(5)

$$I = \frac{1}{2}\sum\limits_{k = 1}^{{n_{{\rm aq}} }} {m_{k} z_{k}^{2} }$$

(6)

where $\gamma_{k}$ defines the activity coefficient, $m_{k}$ is the molality, $A_{\gamma }$ and $B_{\gamma }$ are temperature-dependent coefficients, and $\dot{B}$ is the temperature-dependent coefficients (m⁻¹), I is the ionic strength, $\dot{a}_{k}$ is the ion-size parameter (m), and $z_{k}$ is the charge number of ions.

2.2 Mineral dissolution/precipitation

In this study, calcite (CaCO₃) and dolomite (CaMg(CO₃)₂) are assumed to be the main minerals. The dissolution or precipitation of minerals is characterized by heterogeneous, non-equilibrium, and slow reactions. The mineral dissolution or precipitation is a kinetic reaction and the rate of the mineral reaction is affected by mineral type, ionic composition, temperature, and, pH (Bethke 2007; Morse and Arvidson 2002; Soulaine et al. 2017). This study simulates the rate-dependent kinetic reaction following the rate law (Bethke 2007) and the rate law does not take account of the effect of pH directly. Kharaka et al. (1988) and Delany and Lundeen (1991) simulated the mineral reactions of calcite and dolomite.

$${\text{CaCO}}_{ 3} + {\text{H}}^{ + } \leftrightarrow {\text{Ca}}^{ 2+ } + {\text{HCO}}_{ 3}^{ - }$$

(7)

$${\text{CaMg(CO}}_{ 3} )_{ 2} + 2 {\text{H}}^{ + } \leftrightarrow {\text{Ca}}^{ 2+ } + 2 {\text{HCO}}_{ 3}^{ - } + {\text{Mg}}^{ 2+ }$$

(8)

$$r_{\beta } = \hat{A}_{\beta } k_{\beta } \left( {1 - \frac{{Q_{\beta } }}{{K_{{{\text{eq}},\beta }} }}} \right)$$

(9)

$$Q_{\beta } = \prod\limits_{k = 1}^{{n_{\text{aq}} }} {a_{k}^{{v_{k,\beta } }} }$$

(10)

where $\beta$ indicates mineral type, calcite or dolomite, $r_{\beta }$ is the reaction rate (mol m⁻³ s⁻¹), $k_{\beta }$ is the reaction rate constant, $\hat{A}_{\beta }$ is the reactive surface area of a mineral (m⁻¹), $K_{{{\text{eq}},\beta }}$ is the solubility product constant at a specific temperature, $Q_{\beta }$ is the IAP, and $v_{k,\,\beta }$ is the stoichiometric coefficients of a mineral reaction.

Dissolution/precipitation of minerals provides/consumes aqueous ionic species in brine. The rate of generation/consumption is closely related to the rate of mineral change. Reaction rate and stoichiometric coefficients of mineral dissolution/precipitation determine the rate of mineral generation/consumption in brine.

$$\gamma_{k,\beta } = v_{k,\beta } r_{\beta }$$

(11)

where $\gamma_{k,\beta }$ indicates the reaction rate (consumption/production) of ionic aqueous components (mol m⁻³ s⁻¹).

Temperature influences the solubility product constant, activity, and kinetic reaction rate in mineral reactions. The solubility product constant is determined by the empirical polynomial formulation.

$$\log K_{{{\text{eq}},\beta }} = B_{0} + B_{1} T_{1} + B_{2} T^{2} + B_{3} T^{3} + B_{4} T^{4}$$

(12)

where B₀, B₁, B₂, B₃, and B₄ represent fitting parameters. The temperature-dependent activity coefficient has been explained in Eqs. (4)–(6). Lastly, the kinetic reaction rate is adjusted at an elevated temperature in terms of the Arrhenius equation.

$$k_{\beta } = k_{{{\text{o}}\beta }} \exp \left[ { - \frac{{E_{a\beta } }}{R}\left( {\frac{1}{T} - \frac{1}{{T_{\text{o}} }}} \right)} \right]$$

(13)

where $k_{{{\text{o}}\beta }}$ indicates reaction rate constant at the reference temperature (mol m⁻² s⁻¹), $E_{a\beta }$ is the activation energy (8.314 J/(mol K)), R is the universal gas constant, and T_o is the reference temperature (K).

2.3 Ion-exchange

Following the approach of Awolayo et al. (2017), this study models wettability modification due to ion-exchange reactions. The ion-exchangeable cations (H⁺, Na⁺, Ca²⁺, and Mg²⁺) interact with the rock surface. This ion-exchange is a reversible reaction. The state of adsorbed cations and ion-exchanged cation is determined when the IAP becomes the selectivity coefficient. The activities of the exchangeable species follow the Gaines-Thomas convention. The number of ion-exchanged ions is generally expressed with an equivalent fraction. The amount of positive charge that adheres to a mineral surface is defined with cation exchange capacity (CEC).

$${\text{H}}^{ + } + {\text{Na}} - {\text{X}} \leftrightarrow \left( {{\text{H}} - {\text{X}}} \right) + {\text{Na}}^{ + }$$

(14)

$${\text{Na}}^{ + } + \frac{ 1}{ 2}\left( {{\text{Ca}} - {\text{X}}_{ 2} } \right) \leftrightarrow \left( {{\text{Na}} - {\text{X}}} \right) + \frac{ 1}{ 2}{\text{Ca}}^{ 2+ }$$

(15)

$${\text{Na}}^{ + } + \frac{ 1}{ 2}\left( {{\text{Mg}} - {\text{X}}_{ 2} } \right) \leftrightarrow \left( {{\text{Na}} - {\text{X}}} \right) + \frac{ 1}{ 2}{\text{Mg}}^{ 2+ }$$

(16)

$$K_{{\rm H}/{\rm Na}} = \frac{{\left[ {\alpha \left( {{\text{Na}}^{ + } } \right)} \right]\alpha \left( {{\text{H}} - {\text{X}}} \right)}}{{\alpha \left( {{\text{H}}^{ + } } \right)\left[ {\alpha \left( {{\text{Na}} - {\text{X}}} \right)} \right]}}$$

(17)

$$K_{{{\rm Na}}/{{\rm Ca}}} = \frac{{\left[ {\alpha \left( {{\text{Ca}}^{ 2+ } } \right)} \right]^{0.5} \alpha \left( {{\text{Na}} - {\text{X}}} \right)}}{{\alpha \left( {{\text{Na}}^{ + } } \right)\left[ {\alpha \left( {{\text{Ca}} - {\text{X}}_{ 2} } \right)} \right]^{0.5} }}$$

(18)

$$K_{{{\rm Na}}/{{\rm Mg}}} = \frac{{\left[ {\alpha \left( {{\text{Mg}}^{ 2+ } } \right)} \right]^{0.5} \alpha \left( {{\text{Na}} - {\text{X}}} \right)}}{{\alpha \left( {{\text{Na}}^{ + } } \right)\left[ {\alpha \left( {{\text{Mg}} - {\text{X}}_{ 2} } \right)} \right]^{0.5} }}$$

(19)

$$\beta_{{{\text{H}} - {\text{X}}}} = \frac{{N_{{{\text{H}} - {\text{X}}}} }}{{N_{{{\text{Na}} - {\text{X}}}} + 2N_{{{\text{Ca}} - {\text{X}}_{ 2} }} + 2N_{{{\text{Mg}} - {\text{X}}_{ 2} }} + N_{{{\text{H}} - {\text{X}}}} }}$$

(20)

$$\beta_{{{\text{Na}} - {\text{X}}}} = \frac{{N_{{{\text{Na}} - {\text{X}}}} }}{{N_{{{\text{Na}} - {\text{X}}}} + 2N_{{{\text{Ca}} - {\text{X}}_{ 2} }} + 2N_{{{\text{Mg}} - {\text{X}}_{ 2} }} + N_{{{\text{H}} - {\text{X}}}} }}$$

(21)

$$\beta_{{{\text{Ca}} - {\text{X}}_{ 2} }} = \frac{{N_{{{\text{Ca}} - {\text{X}}_{ 2} }} }}{{N_{{{\text{Na}} - {\text{X}}}} + 2N_{{{\text{Ca}} - {\text{X}}_{ 2} }} + 2N_{{{\text{Mg}} - {\text{X}}_{ 2} }} + N_{{{\text{H}} - {\text{X}}}} }}$$

(22)

$$\beta_{{{\text{Mg}} - {\text{X}}_{ 2} }} = \frac{{N_{{{\text{Mg}} - {\text{X}}_{ 2} }} }}{{N_{{{\text{Na}} - {\text{X}}}} + 2N_{{{\text{Ca}} - {\text{X}}_{ 2} }} + 2N_{{{\text{Mg}} - {\text{X}}_{ 2} }} + N_{{{\text{H}} - {\text{X}}}} }}$$

(23)

$$CEC = \frac{{N_{{{\text{Na}} - {\text{X}}}} + 2N_{{{\text{Ca}} - {\text{X}}_{ 2} }} + 2N_{{{\text{Mg}} - {\text{X}}_{ 2} }} }}{\varphi }$$

(24)

where X indicates the surface of carbonate rock, $K_{{{\rm H}}/{{\rm Na}}}$, $K_{{{\rm Na}}/{{\rm Ca}}}$, and $K_{{{\rm Na}}/{{\rm Mg}}}$ are the selectivity coefficients, $\beta_{{{\text{H}} - {\text{X}}}}$, $\beta_{{{\text{Na}} - {\text{X}}}}$, $\beta_{{{\text{Ca}} - {\text{X}}_{ 2} }}$ and $\beta_{{{\text{Mg}} - {\text{X}}_{ 2} }}$ are the equivalent fractions, $N_{{{\text{H}} - {\text{X}}}}$, $N_{{{\text{Na}} - {\text{X}}}}$, $N_{{{\text{Ca}} - {\text{X}}_{ 2} }}$, and $N_{{{\text{Mg}} - {\text{X}}_{ 2} }}$ are the number of moles of ion-exchanged H⁺, Na⁺, Ca²⁺, and Mg²⁺, $CEC$ is the cation exchange capacity (meq/kg rock).

In the thermodynamic system, the van’t Hoff equation introduces a temperature effect on the selectivity coefficient of ion-exchange reactions (SenGupta 2017). The temperature-dependent selectivity coefficient is calculated with a standard enthalpy change and reference selectivity coefficient. The data of standard enthalpy change and reference selectivity coefficient is provided from the PHREEQC (pH Redox Equilibrium) software database (Appelo and Postma 2005).

$$\log K_{{{\rm Na}/{\rm Ca}},T_{1}} = \log K_{{{\rm Na}/{\rm Ca}},T_{2}} - \frac{{\Delta H_{{\rm r}}^{{\rm o}} }}{2.303R}\left( {\frac{1}{{T_{1} }} - \frac{1}{{T_{2} }}} \right)$$

(25)

$$\log K_{{{\rm Na}/{\rm Mg}},T_{1}} = \log K_{{{\rm Na}/{\rm Mg}},T_{2}} - \frac{{\Delta H_{{\rm r}}^{{\rm o}} }}{2.303R}\left( {\frac{1}{{T_{1} }} - \frac{1}{{T_{2} }}} \right)$$

(26)

where $K_{{{\rm Na}/{\rm Ca}},T}$ and $K_{{{\rm Na}/{\rm Mg}},T}$ indicate the selectivity coefficients at a specific temperature, and $\Delta H_{\text{r}}^{\text{o}}$ is the reaction enthalpy of the system (kJ mol⁻¹).

3 Numerical simulation

Numerical modeling of hot LSWI is developed using a series of LSWI experiments (Gachuz-Muro and Sohrabi 2013, 2014) targeting heavy oil reservoirs. Using these experiments, LSWI coreflooding coupled with geochemical modeling is simulated with GEM developed from CMG. The software is a fully-coupled geochemical and compositional simulator (Nghiem et al. 2004). It is a multiphase and multicomponent flow simulator with phase and chemical equilibrium and rate-dependent mineral dissolution/precipitation. Using the adaptive implicit method, a few grid blocks are solved fully implicitly and the other blocks are solved explicitly according to the blocks’ implicitness. In terms of the stability criterion, Courant-Friedrichs-Lewy (CFL) is used to determine the degree of implicitness and the criterion can be used for switching both from explicit to implicit and from implicit to explicit discretizations of a block. In addition, this simulator offers Newton’s method to solve the nonlinear systems of reservoir simulation. This study selects the recommended convergence criteria for Newton’s method and the tolerances of the criteria follow: pressure change with 3.55 kPa; temperature change with 0.001 °C; relative change of hydrocarbon component molar density with 0.01; and relative change of water component molar density with 0.01. In terms of the phase and geochemical equilibrium calculations, the tolerance of the criterion is the sum of square residual with 1 × 10⁻¹⁰.

The 1-D numerical core model representing a carbonate core is composed of 20 grid blocks. The properties of the core model are summarized in Table 2. The brine compositions of FW, SW, and LSW (10 times-diluted SW) to be modelled are indicated in Table 1. The ionic strengths of the brines are calculated using PHREEQC software and also described in Table 1. The temperature-dependent oil viscosity (Gachuz-Muro and Sohrabi 2013) is modeled with modified Pedersen’s equation (Pedersen and Fredenslund 1987) and depicted in Fig. 1. When temperatures are above 40 °C, the viscosity of the modeled oil has error less than 6% compared to experiments. In this coreflooding model, SW injection (SWI) of 15 PV and LSW injection (LSWI) of 15 PV after SWI are simulated corresponding to the experimental design (Gachuz-Muro and Sohrabi 2014).

Table 2 Properties of limestone core in the experiment (Gachuz-Muro and Sohrabi 2014) and simulation

The LSWI effect modifies the wettability of reservoirs. The wettability is a complex characteristic of a reservoir and characterized with relative permeability and residual oil saturation. For the modeling of the LSWI effect, this study attributes wettability modification to ion-exchange of cations following the approach of Awolayo et al. (2017). During LSWI, increasing equivalent fractions of Ca²⁺ is assumed to modify wettability changing the relative permeability and residual oil saturation. The change of the relative permeability and residual oil saturation is quantified through a history-matching process. The history matching is carried out with CMOST software and uses the production data of successive SWI-LSWI coreflooding (Gachuz-Muro and Sohrabi 2014) to determine a modification of relative permeability and residual oil saturation. The history-matching process applies a DECE (Designed Exploration and Controlled Evolution) algorithm, an interactive process of designed exploration stage (experimental design and Tabu search) and controlled evolutionary stage.

In the modelling of coreflooding, a few assumptions are necessary due to the lack of experimental data (Gachuz-Muro and Sohrabi 2014): (1) The general displacement rate of waterflooding is assumed to be about 1 ft/day. (2) Capillary pressure has been ignored because of the high injection pressure. (3) The cations (K⁺, Ba²⁺, and Sr²⁺) at relatively low concentrations are neglected. Batch simulations using PHREEQC are carried out to validate the assumption. The pH values of the seawater and low salinity water are calculated when the seawater and low salinity water have and do not have the cations. The results of the batch simulations show that the difference of pH is only about 0.01 for both brines. With this assumption, the re-calculated pH values of the brines using PHREEQC are used. (4) The geochemical reactions (aqueous reactions, mineral dissolution/precipitation, and ion-exchange) to be modelled are listed in Table 3 and the database of the geochemical reaction modeling is from Wolery and Daverler (1992) and Appelo and Postma (2005). (5) The density and viscosity of brine are a function of temperature, pressure, and NaCl concentration. They are calculated with Rowe and Chou (1970)’s and Kestin et al. (1981)’s models. (6) The chalk is assumed to contain 95% calcite and 5% dolomite. (7) Heavy oil behavior with asphaltene potentially influences on the performance of hot LSWI due to formation damage. However, the experiments (Gachuz-Muro and Sohrabi 2013, 2014) have a lack of experimental results for asphaltene, so this numerical simulation neglects asphaltene kinetics consideration and formation damage evaluation.

Table 3 Geochemical reactions

4 Results and discussion

Firstly, an unknown relative permeability and modification of relative permeability during successive secondary SWI and tertiary LSWI are quantified through a history-matching process. The history-matching draws multiple history-matched models based on experimental data (Fig. 2). In terms of a best history-matched model, modification of relative permeability due to wettability modification effect is evaluated. We next investigated the coreflooding of secondary SWI, LSWI, and hot LSWI (115 °C), respectively, in terms of oil viscosity, geochemical reactions, and wettability modification. Thermal energy during hot LSWI potentially contributes to additional heavy oil production. It is evaluated in core- and pilot-scaled systems, respectively. Because heat loss is crucial for thermal EOR, the simulation of the pilot-scaled system considers heat loss to over-burden and under-burden shale formations. Lastly, a probabilistic forecast methodology is employed to estimate oil recovery of LSWI and hot LSWI in a pilot-scaled heterogeneous reservoir. While the previous assessments of hot LSWI in the core- and pilot-scaled systems incorporate a best history-matched relative curve, probabilistic forecast analysis assesses multiple relative permeability curves obtained from the history-matching process to reflect inherent uncertainty. In Fig. 2, the multiple history-matched models are indicated with red lines. From the results of probabilistic forecasting using the multiple history-matched models, performance of hot LSWI is compared to that of LSWI considering uncertainty in a pilot-scaled reservoir.

Fig. 2

History matching result for successive SWI-LSWI in terms of oil production (m³)

4.1 SWI-LSWI

In the result of history matching process (Fig. 2), the blue dots and red solid line indicate experimental and history-matched oil production respectively. In an analysis of a best history-matched model, LSWI recovers additional 15% of OOIP after SWI (Fig. 2). The effluent pH values of simulation and experiment are compared to verify the geochemical reaction modeling (Fig. 3). Both simulation and experiment correspondingly show an effluent pH of 7.4 after LSWI. Both SWI and LSWI slightly dissolve calcite and dolomite minerals and increase the pore volume (Fig. 4). Considering total pore volume of the core, the pore volume change is negligible. In comparison to SWI, LSWI results in increased equivalent fractions of Ca²⁺ and Mg²⁺ by 183% and 115%, respectively, and decreased equivalent fraction of Na⁺ by 57%. These results indicate that LSWI leads to more ion-exchange of Ca²⁺ and Mg²⁺ rather than that of Na⁺. As described in Fig. 5, LSWI increasing ion-exchange of Ca²⁺ and Mg² improves wettability modifying relative permeability. LSWI reduces residual oil saturation by 0.12 units. It also increases the end point relative permeability of oil by 58% and decreases the end point relative permeability of water by 41%, respectively.

Fig. 3

Comparison of effluent pH between experiment and simulation

Fig. 4

History of mineral dissolution/precipitation (mole) and pore volume (m³) for successive SWI-LSWI

Fig. 5

Relative permeability curves before (a) and after (b) wettability modification

4.2 Core-scaled system: hot LSWI

Using the history-matched coreflooding model, secondary modes of SWI, LSWI, and hot LSWI are simulated for 10 PV and the results are compared. Figure 6 describes heavy oil productions for SWI, LSWI, and hot SWI, respectively. Secondary SWI recovers only 35% of OOIP after 10 PV injection. LSWI and hot LSWI produce additional heavy oil with 15% and 21% over SWI.

Fig. 6

History of oil recovery (%) for SWI, LSWI, and hot LSWI

In comparison with SWI, LSWI increases the equivalent fractions of Ca²⁺ and Mg²⁺ by 182% and 116%, respectively. The change of effluent concentration of Ca²⁺ also confirms increasing the cation-exchange of Ca²⁺. Figure 7 depicts the concentration of ions (Ca²⁺, Mg²⁺, and Cl⁻) in effluent divided by their concentration in the injection fluid, i.e. the relative concentration of the ions. The Cl⁻ hardly participates in geochemical reactions, so the Cl⁻ is assumed to be a tracer. After breakthrough with 1 PV injection, delay of Ca²⁺, not Cl⁻, is observed and it is the result of cation-exchange of Ca²⁺. In addition, the relative concentration of Ca²⁺ becomes higher than 1 after a 2.5 PV injection. This observation is attributed to substitution of Ca²⁺ by Mg²⁺ in terms of cation-exchange. The increasing equivalent fraction of Ca²⁺ is responsible for wettability modification effect following LSWI. As a result, LSWI produces as much as 15% more heavy oil than SWI due to wettability modification effects (Fig. 6). In terms of mineral reaction, LSWI dissolves more mineral by 16% over SWI (Fig. 8a). The mineral dissolution slightly increases porosity and pore volume (Fig. 8b).

Fig. 7

History of relative concentrations of Ca²⁺, Mg²⁺, and Cl⁻ for LSWI, and hot LSWI

Fig. 8

History of mineral dissolution/precipitation (mole) and pore volume (m³) for SWI, LSWI, and hot LSWI

When hybrid hot LSWI is simulated into the core-scaled system, hot water injection influences geochemical reactions and reduces oil viscosity. Hot LSWI accelerates mineral dissolution by 235% over SWI and increases pore volume (Fig. 8). The increased porosity by mineral dissolution increases permeability, but the increments of porosity and permeability in the core-scaled system are negligible. In addition, hot LSWI causes a significant cation ion-exchange. In comparison to SWI, hot LSWI increases average equivalent fractions of Ca²⁺ and Mg²⁺ by a factor of three and two, respectively. The relative concentration of Ca²⁺ is also investigated to confirm the cation-exchange (Fig. 7). There is a delay of Ca²⁺ at breakthrough due to cation-exchange and a higher relative concentration of Ca²⁺ than 1 at 2.5 PV injection is observed due to cation-exchange of Mg²⁺. The increased equivalent fraction of Ca²⁺ results in wettability modification. Therefore, hot LSWI could preserve the wettability modification effect. The next compares hot LSWI and LSWI. While both hot LSWI and LSWI inject equivalent ionic composition of brine, almost double the amount of dolomite and calcite are dissolved and pore volume increases more in hot LSWI (Fig. 8). The dolomite dissolution generates both Ca²⁺ and Mg²⁺ and calcite dissolution produces only Ca²⁺. The hot LSWI produces more chemical compounds of Ca²⁺ and Mg²⁺ (CaHCO₃⁺, CaCO₃, CaSO₄, MgHCO₃⁺, MgCO₃, MgOH⁺, MgSO₄) consuming Ca²⁺ and Mg²⁺ (Fig. 9). These results lead to a slightly increased amount of Ca²⁺ and a decreased amount of Mg²⁺ for hot LSWI (Fig. 10). They are also confirmed through the relative concentration of ions. The relative concentration of Ca²⁺ of hot LSWI shows slightly higher value than that of LSWI (Fig. 7). Consequently, hot LSWI slightly increases the average equivalent fraction of Ca²⁺ by 9% and decreases the average equivalent fraction of Mg²⁺ by 3% compared to LSWI. The increased equivalent fraction of Ca²⁺ indicates that the wettability modification effect is enhanced during hot LSWI. The mineral dissolution produces HCO₃⁻ as well as cations. The HCO₃⁻ also generates CO₂ and the CO₂ remains as CO₂ (aq), not CO₂ (gas), due to solubility (Fig. 11). Additionally, hot LSWI reduces the viscosity of heavy oil from 111 cP to 41 cP, as indicated in Fig. 1. As a result, hot LSWI introduces synergistic effects of wettability modification and oil viscosity reduction and increases oil recovery up to 56% (Fig. 6).

Fig. 9

History of the amount (mole) of chemical compounds of Ca-X (CaHCO₃⁺, CaCO₃, CaSO₄) and Mg-X (MgHCO₃⁺, MgCO₃, MgOH⁺, MgSO₄) during LSWI and hot LSWI

Fig. 10

History of the amount (mole) of Ca²⁺ and Mg²⁺ during LSWI and hot LSWI

Fig. 11

History of the amount of CO₂ (aq) (mole) and gas saturation during LSWI and hot LSWI

4.3 Pilot-scaled system: hot LSWI

Next, we evaluated the performance of hot LSWI in a heterogeneous permeable reservoir. The reservoir properties are described in Table 4. The reservoir system has a permeability distribution as depicted in Fig. 12. Another necessary factor to consider in thermal EOR is the heat loss to the over-burden and under-burden shale formations. Table 4 also describes the heat capacity and thermal conductivity of the shale and carbonate formations. The analytical model developed by Vinsome and Westerveld (1980) calculates heat loss from reservoir to over-burden and under-burden formations. Injection of brine is designed with 150 m³/day and total 1.5 PV is injected. Hot LSWI heated to 115 °C before injection is deployed into this reservoir and the production from hot LSWI is compared to that of LSWI.

Table 4 Reservoir properties

Fig. 12

Permeability (mD) distribution of pilot-scaled reservoir

The quarter of five-spot system with one injector and one producer is considered (Fig. 13). When hot LSWI is applied to a pilot-scaled system, the temperature of the reservoir increases up to 114 °C (Fig. 13a) despite of heat loss to over-burden and under-burden formations. It results in a reduction in oil viscosity down to 59 cP improving the mobility ratio (Fig. 13b). The hot LSWI is compared to SWI and LSWI in terms of geochemical reactions and wettability modification effect. Dissolution and precipitation of calcite and dolomite minerals are investigated (Fig. 14). The dissolution/precipitation of minerals change amount of cation in the pilot-scaled reservoir (Fig. 15). In comparison to SWI, LSWI dissolves more calcite minerals by 230%. Hot LSWI dissolves more calcite mineral by 15% over LSWI because geochemical reaction is sensitive to temperature. In comparison to LSWI, more calcite dissolution during hot LSWI leads to an increased amount of Ca²⁺ by 5%. In terms of dolomite mineral reaction, both LSWI and hot LSWI result in precipitation. The precipitation of dolomite during hot LSWI is higher than that during LSWI. The higher dolomite precipitation by 88% decreases the amount of Mg²⁺ in the reservoir by 8%. For both LSWI and hot LSWI, the dissolution of calcite is much higher than the precipitation of dolomite so that overall mineral dissolution rather than precipitation is dominant.

Fig. 13

Distribution of temperature (°C) and oil viscosity (cP) for hot LSWI

Fig. 14

Mineral dissolution/precipitation (mole) for LSWI and hot LSWI

Fig. 15

The amount (mole) of Ca²⁺ (a) and Mg²⁺ (b) for SWI, LSWI, hot LSWI

Next, we evaluated the ion-exchange of Ca²⁺ contributing to wettability modification during SWI, LSWI, and hot LSWI (Fig. 16). The equivalent fraction of Ca²⁺ increases up to 0.16 after SWI of 1.5 PV. LSWI and hot LSWI lead to more ion-exchange of Ca²⁺ increasing the equivalent fractions up to 0.39 and 0.43, respectively. In comparison to SWI, the equivalent fraction during LSWI increases by 240%. In addition, the hot LSWI has a 10% higher average equivalent fraction of Ca²⁺ over LSWI. It means the wettability modification effect is enhanced during hot LSWI compared to LSWI. As a result, LSWI and hot LSWI produce 3% and 6% additional oil over SWI, respectively (Fig. 17). The increased oil recovery during hot LSWI is attributed to synergistic effects of oil viscosity reduction and enhanced wettability modification.

Fig. 16

Equivalent fraction of Ca²⁺ after SWI (a), LSWI (b), and hot LSWI (c)

Fig. 17

History of oil recovery (%) for SWI, LSWI, and hot LSWI

4.4 Probabilistic forecast of hot LSWI

To assess inherent uncertainties in the history matching process, a probabilistic forecast method is employed for LSWI and hot LSWI simulations in a pilot-scaled reservoir. Multiple relative permeability curves from 58 history-matched models containing less than 1.5% matching errors (Fig. 2) are subjected to the assessment of probabilistic forecast. Oil recoveries are calculated from the simulations of LSWI and hot LSWI, respectively (Fig. 18). LSWI produces oil recovery from 30% to 40% and hot LSWI produces oil recovery from 33% to 42%. Uncertainty assessments based on the simulations are carried out using a radial basis function neural network modeling and Monte-Carlo simulation. The assessment has estimated P90, P50, and P10 in cumulative distribution function of oil recovery. The P90, P50, and P10 are defined as the oil recovery corresponding to percentile of 90, 50, and 10, respectively. Figure 19 denotes the results of Monte-Carlo simulation for LSWI and hot LSWI. In LSWI, the P10, P50, and P90 of oil recovery are about 29%, 32%, and 38%, respectively. Estimated P10 and P90 of oil recovery indicate conservative and optimistic oil recoveries. There is approximately 11% of difference between P90 and P10. For hot LSWI, P10, P50, and P90 of oil recovery are 32%, 35%, and 40%, respectively. The optimistic oil recovery has 8% higher than conservative oil recovery in hot LSWI. Despite the uncertainty to predict oil production, hot LSWI enhances heavy oil production by synergistic effects.

Fig. 18

Oil recovery (%) of history-matched models for LSWI (a) and hot LSWI (b)

Fig. 19

Monte-Carlo simulations of LSWI and hot LSWI in terms of oil recovery (%)

5 Conclusions

This study models hot LSWI process and evaluates synergistic effects of hot LSWI to enhance heavy oil production. The synergistic effects of oil viscosity reduction and wettability modification are evaluated during hot LSWI. The wettability modification is investigated in terms of geochemical reactions. This study tests the viability of the hot LSWI in core- and pilot-scaled systems. The following conclusions are drawn from this study.

In comparison to LSWI, the thermal energy of hot LSWI influences geochemical reactions and oil viscosity. In a core-scaled system, both LSWI and hot LSWI lead to ion-exchange of Ca²⁺ and Mg²⁺ modifying wettability. In comparison to SWI, LSWI and hot LSWI increase the equivalent fraction of Ca²⁺ by 182% and 209% as a result of ion-exchange. In comparison to LSWI, the hot LSWI dissolves more mineral and produces Ca²⁺ in the system. The mineral dissolution slightly increases the equivalent fraction enhancing wettability modification for hot LSWI. In an assessment of the pilot-scaled system, LSWI and hot LSWI provide 240% and 268% higher equivalent fraction over SWI and improve wettability. In comparison to LSWI, hot LSWI produces higher equivalent fraction by 10% because of more calcite dissolution. This result also implies the enhanced wettability modification effect during hot LSWI. Another key factor to determine oil recovery is the oil viscosity. While LSWI has favorable wetness to recover oil, the oil recovery increase is 3%. Hot LSWI reduces oil viscosity by 63%. Therefore, 3% more movable oil can be recovered in the hot LSWI process. Finally, a probabilistic forecast with uncertainty assessment evaluates the feasibility of hot LSWI by comparing LSWI. It confirms that hot LSWI enables the production of additional heavy oil due to enhanced wettability modification and oil viscosity reduction effects.