Integration of machine learning and data analysis for the SAGD production performance with infill wells

There have been numerous studies on predicting the production performance of the steam assisted gravity drainage (SAGD) process by data-driven models with different machine learning algorithms since their introduction into industry. Similar efforts on SAGD infill wells, nevertheless, remain rare for this advanced alteration in improving the classical SAGD performance. On the other hand, predictive tools to optimize an infill well start time is useful in maximizing bitumen production and minimizing its costs. In this paper, a series of SAGD infill well models are constructed with selected ranges of operational conditions. Three SAGD infill well production performance indicators, namely, an increased ratio ($R_{\text{increase}}$), a total steam–oil ratio (SOR_total), and a stolen ratio ($R_{\text{Stolen}}$) for each SAGD infill well, are calculated based on simulated infill well cases and control models. Five different machine learning algorithms (an artificial neural network [ANN] algorithm, three gradient boosting decision tree [GBDT] algorithms, and a support vector machine [SVM] algorithm) are trained, tested, and evaluated for their effectiveness in predicting those three indicators as output parameters, given seven SAGD relevant parameters as input parameters. Comparisons of different data sets show that the ANN is the best in predicting all three performance indicators under different infill well start times among all the above machine learning algorithms, while the GBDT algorithms have a better ability to learn a variation trend in the SAGD infill well performance.     

Numerical simulation of solvent and water assisted electrical heating of oil sands including aquathermolysis and thermal cracking reactions

Simulations of bitumen recovery using solvent‐ and water‐assisted electrical heating of oil sands are presented to evaluate the process and to study gas generation. Aquathermolysis and thermal cracking and dissolution of acid‐gases in water are included. Steam‐assisted gravity drainage (SAGD) is also simulated for comparison. Results show that gas generation negatively impacts SAGD. However, in electrical heating dissolution of gases into solvent weakens their negative impact. Results indicate that SAGD generates a larger gas volume than electrical heating. In both processes, methane is found to be the major species in the produced gas and H₂S concentration can reach high values. While the effect of acid–gas solubility in water on oil recovery is not evident its effect on generated gas volume is significant. Simulation results demonstrate that electrical heating is more energy efficient than SAGD. These results find application in design of experiments and pilot and field‐scale implementation of the process. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4243–4258, 2017     

Modelling temperature dynamics of the SAGD process in an oil reservoir by the discovery of parametric partial differential equations

Many chemical and industrial processes are complex, and the dynamics of such processes cannot be explained using a partial differential equation (PDE) or a system of PDEs with constant coefficients. Parametric PDEs, that is, PDEs with their coefficients varying across time or space, are utilized for this purpose. The non-availability of data at all spatial locations and partially available process knowledge add to the complexity of modelling such processes. This paper proposes a framework to discover parametric PDEs using data-driven and hybrid modelling approaches with the temperature dynamics of steam-assisted gravity drainage (SAGD) process in an oil reservoir as the system under study. We utilize an ensemble of 200 realizations of the temperature dynamics generated using the variogram for the PDE discovery. Permeability, which is one of the oil reservoir's petrophysical properties, is used to develop the hybrid models. We infer that utilizing partial process knowledge aids in improving the model's accuracy.     

Spontaneous imbibition of liquid in glass fiber wicks,Part II: Validation of a diffuse‐front model

In Part I (Zarandi MAF, Pillai KM. Spontaneous Imbibition of Liquids in Glass‐Fiber Wicks. Part I: Usefulness of a Sharp‐Front Approach. AIChE J, 64: 294–305, 2018), a model based on sharp liquid‐front was proposed where a good match with the experimental data was achieved. However, the model failed to account for partial saturations in the wicks. Here, Richard's equation to predict liquid saturation is tried where the equation is solved numerically in 3D using COMSOL and analytically in 1D using Mathematica for glass‐fiber wicks after treating them as transversely‐isotropic porous media. As a novel contribution, relative permeability and capillary pressure are determined directly from pore‐scale simulations in wick microstructure using the state‐of‐the‐art software GeoDict. The saturation along the wick length is determined experimentally through a new liquid‐N₂ based freezing technique. After including the gravity effect, good agreements between the numerical/analytical predictions and experimental results are achieved in saturation distributions. We also validated the Richard's equation based model while predicting absorbed liquid‐mass into the wick as function of time. © 2017 American Institute of Chemical Engineers AIChE J, 63: 306–315, 2018     

Multiphase flow at the edge of a steam chamber

The use of steam‐assisted gravity drainage (SAGD) to recover bitumen from Athabasca deposits in Alberta has been growing. Butler [Butler, J. Can. Pet. Tech. 1985;24:42–51] derived a simple theory to calculate the production rate of oil during SAGD in an ideal reservoir. This simple and useful theory made several assumptions about the properties of the reservoir and operating conditions of the process. The theory also assumed that the highest mobility oil is at the edge of the steam chamber and that the oil phase velocity is highest at the chamber edge and reduces with distance into the oil sand. This research examines flow conditions at the edge of the steam chamber. Specifically, a new theory is derived that takes into account the impact of oil saturation and relative permeability on the oil mobility profile at the edge of a steam chamber. It is shown that the flow behaviour at the edge of a steam chamber is more complex and is not fully represented by Butler's theory. Contrary to Butler's theory, the oil mobility has its maximum some distance away from the edge of the steam chamber. The results reveal that the higher the thermal diffusivity of the oil sand, the deeper the location where the oil phase velocity is maximum. The developed model has been validated against published experimental and field data.     

Steam fingering at the edge of a steam chamber in a heavy oil reservoir

The steam‐assisted gravity drainage (SAGD) process is one of the key in situ recovery processes being used today to recover heavy oil and bitumen. In this process, steam injected through a horizontal well, flows convectively towards the outer edges of a depletion chamber. At the edges of the depletion chamber, the steam releases its latent heat to the cool oil sand and raises its temperature. The heated oil is mobile and flows under the action of gravity to a horizontal production well located several metres below the injection well. It remains unclear what is the exact mechanism of chamber growth. Some have suggested that in addition to heat conduction, it is by convective steam flow in the form of pointed fingers at the edges of the chamber which penetrate the oil sand. In theory published by Butler [Butler, J. Can. Petroleum Technol. 1987;26(3):70–75], it was determined that the fingers can be as long as 6 m for Athabasca bitumen reservoirs. In this research, a new theory is derived and provides predictions of the rise rate which compare better to estimates derived from field thermocouple data and physical model experimental observations than values obtained from Butler's theory. The results suggest that in the absence of mobile water, heat conduction rather than steam fingers at the chamber edge is the dominant heat transfer mechanism.     

A Rule of Thumb for Binary Isotope Separations in a Gas Centrifuge

Abstract

A simple hypothetical model of the binary isotope separation process in a modern countercurrent Gas Centrifuge is proposed. Like the usual Cohen-Onsager separation theory, internal fluid dynamics are obviously involved. But unlike that theory it completely obviates the flow integrals for Cohen's E, thereby allowing an immediate estimate of the flow efficiency of a given design by visual inspection of the flow field. At times this should be checked later by the usual analyses. To shed some light on this idea, derivations for two simple assumed idealized hydrodynamics are given, but a rigorous proof remains an open question. Then our hypothesis is tested against a battery of about 10 new “exact” formulas for E based upon analytical solutions to several variants of Onsager's pancake equation and is found to be “reasonably” accurate and surprisingly robust. Finally, some limitations of our rule are explored.     

Optimization strategies and impact of low oil price on long term SAGD projects

Steam assisted gravity drainage (SAGD) has been known as a commercially proven high ultimate recovery process for bitumen and heavy crudes. It is an energy intensive process, which is economical when oil price is above certain value. When the oil price goes below the economic threshold of project, steam injection can be decreased or completely stopped for a certain period of time, and can resume thereafter when the condition alters. The objective of this study is to provide comprehensive information about the effect of steam injection interruptions on thermal project performance. An optimization strategy for the SAGD process, in cases where steam injection interruption occurs, is discussed using actual reservoir models of different geological formations. An economical model is used to evaluate operating strategy effect on the net present value (NPV) of the project. The parameters, like shut-in period, initial steam injection period, etc, are optimized for Athabasca type oil sand reservoirs. The results show several key mechanisms exist in the life cycle of the SAGD process that must be included to reflect the field scale behaviour; otherwise, the mechanistic simplicity of the models could lead to directional and semi-quantitative conclusions. Among the mechanisms, temperature effect on basic petrophysical properties of reservoir rocks was found to have an important role in the oil recovery, and considerably impacts the results of optimization. When the steam injection is interrupted, an optimum shut-in period can be determined to maximize the oil recovery. The optimum length of steam injection interruption depends on the initial steam injection period.     

Prediction and experimental verification of damping in 3-D braided textile structural composites

The material damping characteristics of 3-D braided textile structural composites were investigated in this paper. A model for predicting damping in these materials was developed based upon the classical laminated plate theory. The model modified the existing models for predicting the static moduli of 3-D textile structural composites by using the elastic-viscoelastic correspondence principle. The basic engineering constants were replaced with their corresponding complex forms by applying the elastic-viscoelastic correspondence principle to them. In this study, the basic damping loss factors (i.e. η_L, η_T, η_LT and η_vLT) were obtaiend by a modified Hashin's theory, Rule-of-Mixture Laws, and an indirect method on the basis of empirical works. From complex numerical results, we concluded that axial damping, flexural damping, coupling damping, and in-plane shear damping coefficients were all functions of the yarn orientation angle and fiber volume fraction in 3-D braided textile structural composites. Experimental data supported theoretically predicted results.     

A Flow Time Model for Melt‐Cast Insensitive Explosive Process

Diphasic flows of concentrated suspensions of melt‐cast insensitive explosives exhibit specific rheological properties. In order to limit the handling of pyrotechnical products presenting a risk with respect to the mechanical and thermal shocks, a lot of work has been undertaken for many years in the civil engineering sector. The objective of this study is to propose a predictive model of the flow time of a concentrated suspension through a nozzle located at the bottom of a tank. Similar to our industrial process, the suspension is made out of insensitive energetic materials and flows under gravity. Experimental results are compared to three models (Quemada, Krieger‐Dougherty, and Mooney) predicting the viscosity μ of a suspension as a function of the solid volume fraction ϕ, the maximum packing density ϕ_m and the viscosity μ₀ of the interstitial liquid. De Larrard's model is used to calculate ϕ_m. The value of viscosity measured for the pure liquid is close to the one predicted by the Bernoulli theorem, where liquids are considered as incompressible and inviscid. Finally, it was found that the Quemada's model gives a fair agreement between predictions and experiments.     

The gap between the measured and calculated liquid–liquid interfacial tensions derived from contact angles

We present our new findings about the causes of discrepancies between the measured and calculated liquid-liquid interfacial tensions derived from contact angles. The calculated ones are based on either the equation developed by Fowkes or that by van Oss, Chaudhury and Good (VCG), while the measured ones are based on the sessile drop, weight-volume by Jańzuk et al. and the axisymmetric drop shape analysis (ADSA) by Kwok and Neumann. Indeed, there are deviations between the calculated and measured results. For an immiscible liquid-liquid or liquid-solid interface, we prefer to employ Harkins spreading model, which requires the interfacial tension to be constant. However, for the initially immiscible liquid-liquid pairs, we propose an adsorption model, and our model requires the interfacial tension to be varying and the surface tensions of bulk liquids at a distance from the interface to remain unchanged. Thus, the difference between the initial and final interfacial spreading coefficients (S_i) equals the equilibrium interfacial film pressure (π_i)_e. According to our findings, the calculated interfacial tension represents the initial value (γ₁₂)_o, which differs from the equilibrium value (γ₁₂)_e obtained experimentally after some time delay. This expected gap at a reasonable time frame is chiefly caused by the equilibrium interfacial film pressure between the two liquids. The initial (or calculated) interfacial tension can be positive or negative, while the equilibrium (or measured) one can reach zero. In fact, the former is shown to have more predictive value than the latter. A negative initial interfacial tension is described to favor miscibility or spontaneous emulsification but it tends to revert to zero instantaneously. Thus, a miscible liquid mixture should have zero interfacial tension. In response to recent papers by Kwok et al., we show that the disagreements between the calculated and measured interfacial tensions are definitely not caused by the failure of the VCG approach. Correct interfacial tensions are calculated for liquid pairs containing formamide or dimethyl sulfoxide (DMSO) by using the dispersion components cited in Fowkes et al.'s later publication. With the corrected surface tension components, the equilibrium interfacial film pressures (π_i)_e's for at least 34 initially immiscible liquid pairs have been calculated. These values are generally lower than the corresponding spreading pressures π_e's obtained by others using the Harkins model. Recently, we established a relationship between these two film pressures with the Laplace equation and found a new criterion for miscibility to be (π_i)_e = π_e.     

Water Diffusivity and Drying Kinetics of Air Drying of Figs

The aim of this study is to evaluate experimentally the effective diffusion coefficient and the drying kinetics of whole unpeeled figs (Ficus carica L. var. tsapela) in terms of drying conditions. Estimation of the effective diffusion coefficient was carried out employing Fick's law for unsteady diffusion, which was solved analytically and numerically. In both methods, shrinkage effect was considered. The results from the two methods were compared and presented together with the limited results from the literature. The estimated effective diffusion coefficient values by both methods were fitted to a modified Arrhenius equation. Finally, a model predicting drying kinetics was developed. The model's coefficients were associated to the experimental conditions.     

Diffusion of dyes in polyester fibers. III. Time delay in establishment of the equilibrium concentration of dye at fiber surface

In the dyeing process of the copolyester fiber Dilana with the disperse dye Synthene Scarlet P3GL, a deviation from the simple model of Fickian sorption occurs. It manifests itself as a time delay in establishment of the equilibrium dye concentration at the fiber surface. As has been stated, the variation of C_s (the surface dye concentration) with time of dyeing fits the equation; C_s = C_∞ (1? e^?βt). Regarding the relation of C_s to t, the diffusion coefficient of the dye in the studied fiber has been calculated by the theoretical equation reported in Crank's monograph. It has been proved that the experimental data on kinetics of dyeing the fiber Dilana with Synthene Scarlet P3GL fit considerably better the tested equation than the classical Hill's equation.     

Modeling of interdiffusion in poly(vinyl acetate)–poly(methyl methacrylate)–toluene multicomponent systems

Work on interdiffusion has been mainly carried out in binary systems in the past, and this work has focused on polymer–solvent (S) systems and polymer blends. To understand and predict the interdiffusion of two solids in the presence of one S, we present a new mathematical model based on the Onsager approach. Within our model, interdiffusion kinetics are described with a modification of the reptation model for long polymer chains, and the chemical potential gradient is used as the driving force behind mass transfer. The chemical potential is calculated with a Flory–Huggins approach. The model was validated with 29 Raman spectroscopy experiments in poly(vinyl acetate)–poly(methyl methacrylate)–toluene systems at 20 °C. Monomer mobilities (L _i,0s) were determined for both polymers to show the independence of L _i,0 from the chain length. The L _i,0s were found to be strongly dependent on the S content. With the knowledge of phase equilibria and L _i,0s, interdiffusion in the ternary polymer–polymer–S system could be predicted by the introduced model. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47092.     

Kinetics of xanthan gum production from whey by constructed strains of Xanthomonas campestris in batch fermentations

Two new constructed strains of X. campestris XLM1521 and XMT1, either alone or in mixed cultures were used for the production of xanthan gum in batch fermentations from whey. Fermentations were carried out at three different pH levels of 6.0, 7.0 and 8.0 and the results were compared with those previously reported for fermentations in Erlenmeyer flasks without controlling the pH. The kinetics of cultures of the strain X. campestris XLM1521 were studied in a batch reactor at constant pH values. A mathematical model, based on the Luedeking-Piret equation, was used and experimental design was employed in order to correlate model's parameters with pH variation. The highest xanthan gum concentration, 17.3 g/l, was observed at pH 8.0. This is the largest amount of xanthan gum reported so far.     

Competitive sorption of water vapor and CO2 in photocrosslinked PVCA film for a capacitive‐type humidity sensor

The sorption behavior of water vapor and CO₂ gas in photocrosslinked poly(vinyl cinnamate) (PVCA) film was examined at 30°C under atmospheric pressure. Both the water sorption isotherm and the CO₂ sorption isotherm obtained with quartz crystal microbalance (QCM) method obeyed the simple Langmuir's equation. Water vapor/CO₂ mixed‐gas sorption isotherms were also obtained. Total amount of sorbed mixed gases was clearly influenced by the partial pressure of water vapor (p_w) and CO₂ gas (p_c) in the atmosphere. A modified Langmuir's equation based on a dual‐site model was employed for predicting the competitive adsorption isotherm, and the isotherm was clearly described by the equation. The theoretically estimated amount of adsorbed water at the constant p_w decreased slightly with increasing p_c. The effect of this phenomenon on the sensitivity of the capacitive‐type relative humidity sensor was examined. As expected, the electrical capacitance of the sensor at the constant relative humidity decreased because of the coexistence of CO₂ gas. However, the influence was quite small in the CO₂ concentration range in the ordinary environment. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 83: 401–407, 2002     

Empirical models for matrix cracking in a CFRP cross‐ply laminate under static‐ and cyclic‐fatigue loadings

This paper presents empirical models for predicting matrix crack density in a carbon fiber reinforced plastic (CFRP) cross‐ply laminate under static‐fatigue and cyclic‐fatigue loadings. First, a modified slow crack growth (SCG) law, that covers the whole range of stress ratio R of tension‐tension fatigue (0 ≤ R ≤ 1), was proposed. The modified SCG law and three conventional SCG laws were then combined with Weibull's probabilistic failure concept for predicting fatigue matrix crack density in a cross‐ply laminate. Matrix crack density was expressed as a function of R, the maximum stress in the transverse ply and the number of cycles. Next, fatigue tests were performed for R of 0, 0.2, 0.4, 0.6, and 1 to determine the applicability of these four models. Finally, constant fatigue life (CFL) diagrams were investigated based on the modified model. POLYM. COMPOS., 2011. © 2011 Society of Plastics Engineers     

Design,construction and operation of lab scale cylindrical steam assisted gravity drainage model for heavy oil recovery

Based on a theoretical background [1,2], a lab scale cylindrical SAGD (steam assisted gravity drainage) model was designed, constructed and operated. There are six different parts in the apparatus: (1) water supplier, (2) steam generator, (3) SAGD cylindrical model, (4) cooling system, (5) constant pressure maintaining system and (6) production system. Temperature, pressure and steam injection rate were controlled by computer, and product (mixture of oil and water) was collected/separated manually. Extra heavy oil (<10 cp at 200 °C) and glass bead (diameter 1.5 mm) were mixed homogeneously for making porosity of 0.3 and applied for simulating oil sand. For obtaining optimum operation conditions of SAGD apparatus, several attempts were made. When the steam at high temperature (160–180 °C), high pressure (8–9 atm) was injected with 20–25 cc/min, cSOR (cumulative steam to oil ratio) of about 5 was obtained with oil recovery of 78.8%.     

New numerical model for solubility of light alkanes in triethylene glycol

A new numerical model, which covers the full range of dehydration-plant operating conditions and wide range of experimental data results, estimates the amount of CH₄, C₂H₆ and C₃H₈ absorbed per volume of triethylene glycol (TEG) circulated vs. the partial pressure of light alkanes and the absorber temperature. This article shows that the proposed numerical approach is more accurate than routine equation of states in predicting the solubility of light hydrocarbons in TEG. This article also provides comparisons between the results of the proposed model with experimental data and an equation of state results.