Nonlinear Double-Log Mixing Rule for Viscosity Calculation of Bitumen/Solvent Mixtures Applicable for Reservoir Simulation of Solvent-Based Recovery Processes

Summary Various solvent-based recovery processes for bitumen and heavy-oil reservoirs have gained much interest in recent years. In these processes, viscosity reduction is attained not only because of thermal effects, but also by dilution of bitumen with a solvent. Accurate characterization of the oil/solvent-mixture viscosity is critical for accurate prediction of recovery and effectiveness of such processes. There are varieties of models designed to predict and correlate the mixture viscosities. Among them, the linear log mixing (Arrhenius) model is the most commonly used method in the oil industry. This model, originally proposed for light oils, often show poor performance (40 to 60% error) when applied to highly viscous fluids such as heavy oil and bitumen. The modified Arrhenius model, called the nonlinear log mixing model, gives slightly better predictions compared with the original Arrhenius model. However, the predictions still might not be acceptable because of large deviations from measured experimental data. Calculated mixture-phase viscosity has a significant effect on flow calculations in commercial reservoir simulators. Underestimation of mixture viscosities leads to overprediction of oil-production rates. Using such mixing models in reservoir simulation can lead to inaccuracy in mixture viscosities and hence large uncertainty in model results. In the present study, different correlations and mixing rules available in the literature are evaluated against the mixture-viscosity data for a variety of bitumen/solvent systems. A new form (nonlinear) of the double-log mixing rule is proposed, which shows a significant improvement over the existing models on predicting viscosities of bitumen/solvent mixtures, especially at high temperatures.

A predictive group-contribution model for the viscosity of aqueous organic aerosol

The viscosity of primary and secondary organic aerosol (SOA) has important implications for the processing of aqueous organic aerosol phases in the atmosphere, their involvement in climate forcing, and transboundary pollution. Here we introduce a new thermodynamics-based group-contribution model, which is capable of accurately predicting the dynamic viscosity of a mixture over several orders of magnitude (∼10-3 to >1012 Pa s) as a function of temperature and mixture composition, accounting for the effect of relative humidity on aerosol water content. The mixture viscosity modelling framework builds on the thermodynamic activity coefficient model AIOMFAC (Aerosol Inorganic–Organic Mixtures Functional groups Activity Coefficients) for predictions of liquid mixture non-ideality, including liquid–liquid phase separation, and the calorimetric glass transition temperature model by DeRieux et al. (2018) for pure-component viscosity values of organic components. Comparing this new model with simplified modelling approaches reveals that the group-contribution method is the most accurate in predicting mixture viscosity, although accurate pure-component viscosity predictions (and associated experimental data) are key and one of the main sources of uncertainties in current models, including the model presented here. Nonetheless, we find excellent agreement between the viscosity predictions and measurements for systems in which mixture constituents have a molar mass below 350 g mol−1. As such, we demonstrate the validity of the model in quantifying mixture viscosity for aqueous binary mixtures (glycerol, citric acid, sucrose, and trehalose), aqueous multicomponent mixtures (citric acid plus sucrose and a mixture of nine dicarboxylic acids), and aqueous SOA surrogate mixtures derived from the oxidation of α-pinene, toluene, or isoprene. We also use the model to assess the expected change in SOA particle viscosity during idealized adiabatic air parcel transport from the surface to higher altitudes within the troposphere. This work demonstrates the capability and flexibility of our model in predicting the viscosity for organic mixtures of varying degrees of complexity and its applicability for modelling SOA viscosity over a wide range of temperatures and relative humidities.

Estimation of Viscosity of the N-Alkane (C1-C 4) in Bitumen System Using Adaptive Neuro-Fuzzy Interference System (ANFIS)

One of the important mechanisms in solvent-aided thermal recovery processes is viscosity reduction. Light n-alkane hydrocarbons are among the potential solvents for solvent-aided thermal recovery processes. In this study, the viscosity of C1- C4 n-alkanes in bitumen was investigated. Adaptive neuro-fuzzy interference system (ANFIS) was used for this aim. The result obtained by the ANFIS model analyzed with the statistical parameters (i.e., MSE, MEAE, MAAE, and R2) and graphical methods. Results show that the ANFIS has high capability to the prediction of solvent/bitumen mixture viscosity.

A predictive group-contribution model for the viscosity of aqueous organic aerosol

The viscosity of primary and secondary organic aerosol (SOA) has important implications for the processing of aqueous organic aerosol phases in the atmosphere, their involvement in climate forcing, and transboundary pollution. Here we introduce a new thermodynamics-based group-contribution model, which is capable of accurately predicting the dynamic viscosity of a mixture over several orders of magnitude (~ 10−3 to > 1012 Pa s) as a function of temperature and mixture composition, accounting for the effect of relative humidity on aerosol water content. The mixture viscosity modelling framework builds on the thermodynamic activity coefficient model AIOMFAC (Aerosol Inorganic–Organic Mixtures Functional groups Activity Coefficients) for predictions of liquid mixture non-ideality, including liquid–liquid phase separation, and the calorimetric glass transition temperature model by DeRieux et al. (2018) for pure-component viscosity values of organic components. Comparing this new model with simplified modelling approaches reveals that the group-contribution method is the most accurate in predicting mixture viscosity, although accurate pure-component viscosity predictions (and associated experimental data) are key and one of the main sources of uncertainties in current models, including the model presented here. Nonetheless, we find excellent agreement between the viscosity predictions and measurements for systems in which mixture constituents have a molar mass below 350 g mol−1. As such, we demonstrate the validity of the model in quantifying mixture viscosity for aqueous binary mixtures (glycerol, citric acid, sucrose, and trehalose), aqueous multicomponent mixtures (citric acid + sucrose and a mixture of nine dicarboxylic acids), and aqueous SOA surrogate mixtures derived from the oxidation of α-pinene, toluene, or isoprene. We also use the model to assess the expected change in SOA particle viscosity during idealized adiabatic air parcel transport from the surface to higher altitudes within the troposphere. This work demonstrates the capability and flexibility of our model in predicting the viscosity for organic mixtures of varying degrees of complexity and its applicability for modelling SOA viscosity over a wide range of temperatures and relative humidities.

Experimental and Simulated Studies of Oil/Water Fully Dispersed Flow in a Horizontal Pipe

The flow of oil/water mixtures in a pipe can occur under different flow patterns. Additionally, being able to predict adequately pressure drop in such systems is of relevant importance to adequately design the conveying system. In this work, an experimental and numerical study of the fully dispersed flow regime of an oil/water mixture (liquid paraffin and water) in a horizontal pipe, with concentrations of the oil of 0.01, 0.13, and 0.22 v/v were developed. Experimentally, the values of pressure drop, flow photographs, and radial volumetric concentrations of the oil in the vertical diameter of the pipe cross section were collected. In addition, normalized conductivity values were obtained, in this case, for a cross section of the pipe where an electrical impedance tomography (EIT) ring was installed. Numerical studies were carried out in the comsolmultiphysics platform, using the Euler–Euler approach, coupled with the k–ε turbulence model. In the simulations, two equations for the calculation of the drag coefficient, Schiller–Neumann and Haider–Levenspiel, and three equations for mixture viscosity, Guth and Simba (1936), Brinkman (1952), and Pal (2000), were studied. The simulated data were validated with the experimental results of the pressure drop, good results having been obtained. The best fit occurred for the simulations that used the Schiller–Neumann equation for the calculation of the drag coefficient and the Pal (2000) equation for the mixture viscosity.

Diffusivity of Gas Into Bitumen: Part II—Data Set and Correlation

Summary The oil-production rate of in-situ heavy-oil-recovery processes involving the injection of gaseous hydrocarbons partly depends on the diffusivity of the gas in the bitumen. Data for gas diffusivities, particularly above ambient temperature, are relatively scarce because they are time consuming to measure. In this study, the diffusion and solubilities of gaseous methane, ethane, propane, and n-butane in a Western Canadian bitumen were measured from 40 to 90°C and pressures from 300 to 2300 kPa, using a pressure-decay method. The diffusivities were determined from a numerical model of the experiments that accounted for the swelling of the oil. In Part I of this study (Richardson et al. 2019), it was found that both constant and viscosity-dependent diffusivities could be used to model the mass of gas diffused and the gas-concentration profile in the bitumen; however, the constant diffusivity was different for each experiment and mainly depended on the oil viscosity. In this study, a correlation for the constant diffusivity to the oil viscosity is developed as a tool to quickly estimate the gas diffusivity. A correlation of diffusivity to the mixture viscosity is also developed for use in more-rigorous diffusion models. The maximum deviations in the mass diffused over time predicted with the constant and viscosity-dependent (mixture viscosity) correlations at each condition are on average 7.4 and 8.7%, respectively.

Some Simulation Results and Parameter Analyses of a Generalized Quasi Two-Phase Bulk Mixture Model

Here, we consider a newly constructed generalized quasi two-phase bulk model for a rapid flow of a debris mixture consisting of viscous fluid and solid particles down a channel. The model is a set of coupled partial differential equations with new mechanical description of generalized bulk and shear viscosities, pressure, velocities and effective friction. The dynamical variables, physical parameters, inertial and dynamical coeffcients and drift factors involved in the equations contain certain important physics of mixture flow. So, we analyze the behaviour of some inertial and dynamical coeffcients involved in the model. These coeffcients strongly depend upon the initial material composition. We also simulate the evolution of the dynamical variables so as to reveal their strong non-linear behaviours. Through simulations, we also analyze the front position of the debris material, bottom-slip velocity and maximum velocity, which show fundamentally different dynamics for varied material compositions, from dilute to dense flows. Generalized mixture viscosity decreases as the ow moves downslope, and the rate at which it decreases depends upon the initial solid-volume fraction. We also compare the effective viscosity and the bulk mixture viscosity with respect to the norm of the strain rate tensors to reveal different non-linear behaviours.