Modeling of oil–water flow using energy minimization concept

A new model is developed to predict flow behaviors including flow pattern, pressure gradient and holdup for oil–water flow in horizontal and slightly inclined pipes. The model is based on the universal principle that a system stabilizes to its minimum total energy. The structural configurations observed in two-phase flow systems can be interpreted in terms of total energy minimization. Performance of the developed model is tested against several experimental data, and comparisons with existing models are presented. It is evident from the results and comparisons that the model estimates the pressure gradient and flow pattern very well. The model provides extensive information about oil–water flow characteristics.     

Bingham’s model in the oil and gas industry

Yield stress fluid flows occur in a great many operations and unit processes within the oil and gas industry. This paper reviews this usage within reservoir flows of heavy oil, drilling fluids and operations, wellbore cementing, hydraulic fracturing and some open-hole completions, sealing/remedial operations, e.g., squeeze cementing, lost circulation, and waxy crude oils and flow assurance, both wax deposition and restart issues. We outline both rheological aspects and relevant fluid mechanics issues, focusing primarily on yield stress fluids and related phenomena.     

Flow of oil–water emulsions through a constricted capillary

The flow of oil-in-water emulsions through quartz micro-capillary tubes was analyzed experimentally. The capillaries were used as models of connecting pore-throats between adjacent pore body pairs in high-permeability media. Pressure drop between the inlet and outlet ends of the capillary was recorded as a function of time, for several values of the volumetric flow rate. Several distinct emulsions were prepared using synthetic oils in deionized water, stabilized by a surfactant (Triton X-100). Two oils of different viscosity values were used to prepare the emulsions, while two distinct drop size distributions were obtained by varying the mixing procedure. The average oil drop size varied from smaller to larger than the neck radius. The results are presented in terms of the extra-pressure drop due to the presence of the dispersed phase, i.e. the difference between the measured pressure drop and the one necessary to drive the continuous phase alone at the same flow rate. For emulsions with drops smaller than the capillary throat diameter, the extra-pressure drop does not vary with capillary number and it is a function of the viscosity ratio, dispersed phase concentration and drop size distribution. For emulsions with drops larger than the constriction, the large oil drops may partially block the capillary, leading to a high extra pressure difference at low capillary numbers. Changes in the local fluid mobility by means of pore-throat blockage may help to explain the additional oil recovery observed in laboratory experiments and the sparse data on field trials.     

Influx of oil to a gallery of water‐plugged wells

Within the framework of the Buckley–Leverett scheme, a solution is obtained for the problem of organization of an influx to a gallery of wells whose nearwell zone is contaminated for some reasons by the water phase. A method of engineering estimates is developed for the moment of penetration of the front of water displacing oil into the plugged zone of production wells with simultaneous determination of oil recovery in the reservoir. The results obtained may be used in constructing a mathematical model of optimized development of oil fields.     

NaOH–ball-milled co-modified magnetic biochar and its oil adsorption properties

A magnetic biochar adsorbent (BM–OH–BC) was prepared through NaOH–ball milling co-modification with walnut shells as the raw material, and its oil adsorption characteristics were investigated. The adsorption properties of oil pollutants were compared before and after the NaOH-ball-milling co-modification, and the mechanism of NaOH-ball-milling on oil pollutants was investigated by scanning electron microscope-energy dispersive X-ray spectroscopy, BET, X-ray photoelectron spectroscopy and Fourier transform infrared spectroscopy. The experimental results showed that the oil adsorption capacity of BM–OH–BC can reach 2.75 g/g, which is 129% higher than that of unmodified biochar. Moreover, after five adsorption and desorption cycles, the adsorption rate of BM–OH–BC only decreased by 5.9%, which was because the oil adsorption of BM–OH–BC is mainly chemical adsorption. The adsorption processes involving single layer, heterogeneous phase and multilayer made BM–OH–BC have excellent adsorption properties. After biochar co-modification, the specific surface area of BM–OH–BC increased to 466 m²/g, the total pore volume increased to 0.245 cm³/g, the average pore size decreased to1.90 nm, and the number of hydrophobic non-polar functional groups increased, leading to the enhancement of its oil absorption capacity. This study provides a reference for the treatment of oil-contaminated water bodies.     

Experimental study on interfacial waves in stratified horizontal oil–water flow

Interfacial wave characteristics were studied experimentally in horizontal oil–water pipe flows during stratified flow and at the transition to dual continuous flow, where drops of one phase appear into the other (onset of entrainment). The experimental investigations were carried out in a stainless steel test section with 38 mm ID with water and oil (density 828 kg/m³and viscosity 5.5 mPas) as test fluids. Wave characteristics were obtained with a high speed video camera and a parallel wires conductivity probe that measured the instantaneous fluctuations of the interface. Experiments were conducted at 2 m and at 6 m from the inlet. Visual observations revealed that no drops are formed when interfacial waves are absent. It was also found that waves have to reach a certain amplitude before drops can detach from their crests. Wave amplitudes are increased as the superficial velocities of both phases increase. In the stratified region, the mean wave amplitude decreases by increasing the oil–water input ratio while mean wavelength increases as the slip velocity between the two-phase decreases. At the onset of entrainment, the mean amplitude and length are found to be a function of the relative velocity between the oil and water layers and of the turbulence in each layer.     

Effect of drag reducing polymers on oil–water flow in a horizontal pipe

Measurements of drag-reduction are presented for oil–water flowing in a horizontal 0.0254 m pipe. Different oil–water configurations were observed. The injection of water soluble polymer solution (PDRA) in some cases produced drag reduction of about 65% with concentration of only 10–15 ppm. The results showed a significant reduction in pressure gradient due to PDRA especially at high mixture velocity which was accompanied by a clear change in the flow pattern. Phase inversion point in dispersed flow regime occurred at a water fraction range of (0.33–0.35) indicated by its pressure drop peak which was disappeared by injecting only 5 ppm (weight basis) of PDRA. Effect of PDRA concentration and molecular weight on flow patterns and pressure drops are presented in this study. Influence of salt content in the water phase on the performance of PDRA is also examined in this paper.     

Single-beam gamma densitometry measurements of oil–water flow in horizontal and slightly inclined pipes

Gamma densitometry is a frequently used non-intrusive method for measuring component volume fractions in multiphase flow systems. The application of a single-beam gamma densitometer to investigate oil–water flow in horizontal and slightly inclined pipes is presented. The experiments are performed in a 15 m long, 56 mm diameter, inclinable stainless steel pipe using Exxsol D60 oil (viscosity 1.64 mPa s, density 790 kg/m³) and water (viscosity 1.0 mPa s, density 996 kg/m³) as test fluids. The test pipe inclination is changed in the range from 5° upward to 5° downward. Experimental measurements are reported at three different mixture velocities, 0.25, 0.50 and 1.00 m/s, and the inlet water cut is varied from 0 to 1. The gamma densitometer is composed of radioactive isotope of Am-241 with the emission energy of 59.5 keV, scintillation detector [NaI(Tl)] and signal processing system. The time averaged cross-sectional distributions of oil and water phases are measured by traversing the gamma densitometer along the vertical pipe diameter. Based on water volume fraction measurements, water hold-up and slip ratio are estimated. The total pressure drop over the test section is measured and frictional pressure drop is estimated based on water hold-up measurements. The measurement uncertainties associated with gamma densitometry are also discussed. The measured water hold-up and slip ratio profiles are strongly dependent on pipe inclination. In general, higher water hold-up values are observed in upwardly inclined pipes compared to the horizontal and downwardly inclined pipes. At low mixture velocities, the slip ratio decreases as the water cut increases. The decrease is more significant as the degree of inclination increases. The frictional pressure drop for upward flow is slightly higher than the horizontal flow. In general, there is a marginal difference in frictional pressure drop values for horizontal and downwardly inclined flows.     

Numerical simulation and experimental verification of silicone oil flow over magnetic fluid under applied magnetic field

Two-layer flow of magnetic fluid and non-magnetic silicone oil was simulated numerically. The continuity equation, momentum equations, kinematic equation, and magnetic potential equation were solved in two-dimensional Cartesian coordinate. PLIC （piecewise linear integration calculation） VOF （volume of fluid） scheme was employed to track the free interface. Surface tension was treated via a continuous surface force （CSF） model that ensures robustness and accuracy. The influences of applied magnetic field, inlet velocity profile, initial surface disturbance of interface and surface tension were analyzed. The computed interface shapes at different conditions were compared with experimental observation.     

Measurement and prediction of droplet size in annular gas–liquid flows in aero-engine oil systems

Two-phase gas–liquid annular flows are encountered in ventless aero-engine oil system pipes. The droplet size in the flow has an important impact on the performance of downstream equipment as breathers and de-aerators. However, literature studies present semi-empirical models that are not in the range of operating conditions of the oil system. To investigate the effect of the use of lubrication oil on the droplet sizes, this paper presents experimental results of annular flow with oil flow rates from 160 to 640 l/h and air flow rates from 60 to 120 Nm³/h. Comparison of the Sauter–Mean Diameter predicted by existing correlation show an error of minimum 30% compared to experimental values for higher oil flow rates, which are the most important in oil systems. To address this issue, correlations were adapted to fit experimental results. With the new set of parameters, the Sauter-Mean Diameter is estimated with an error of maximum 18% for higher oil flow rates. Results analysis illustrate that the main difference between existing and new correlations could be due do the surface tension and viscosity of lubrication oil, which are very different from water at low temperature. The results are also consistent with the transition between bag and ligament break-up droplet generation mechanism at a flow rate of 80 Nm³/h.     

Investigation of two-phase flow pattern,liquid holdup and pressure drop in viscous oil–gas flow

An experimental investigation was carried out on viscous oil–gas flow characteristics in a 69 mm internal diameter pipe. Two-phase flow patterns were determined from holdup time-traces and videos of the flow field in a transparent section of the pipe, in which synthetic commercial oils (32 and 100 cP) and sulfur hexafluoride gas (SF₆) were fed at oil superficial velocities from 0.04 to 3 m/s and gas superficial velocities from 0.0075 to 3 m/s.     

Influence of sudden contractions on in situ volume fractions for oil–water flows in horizontal pipes

Oil–water two-phase flow experiments were conducted in horizontal ducts made of Plexiglas® to determine the in situ oil fraction (holdup) by means of the closing valves technique, using mineral oil (viscosity: 0.838 Pa s at 20 °C; density: 890 kg m⁻³) and tap water. The ducts present sudden contractions from 50 mm to 40 mm i.d. and from 50 mm to 30 mm i.d., with contraction ratios of 0.64 and 0.36, respectively. About 200–320 tests were performed by varying the flow rates of the phases. Flow patterns were investigated for both the up- and downstream pipe in order to assess whether relevant variations of the flow patterns across the sudden contraction take place. Data were then compared with predictions of a specific correlation for oil–water flow and some correlations for gas–water flow. A drift-flux model was also applied to determine the distribution parameter.     

Experimental investigation of air–oil slug flow using capacitance probes,hot-film anemometer,and image processing

Despite the importance of air–oil slug flows to many industrial applications, their available data reported in the literature are limited compared to air–water slug flows. The main objective of the present study is to explain how air–oil slug flow parameters can be experimentally investigated using hot-film anemometry, capacitance sensors and image processing. Experiments were performed using air–oil slug flow through a horizontal pipe for air superficial velocities ranged from 0.01 m/s to 0.65 m/s and oil superficial velocities ranged from 0.03 m/s to 2.3 m/s. The signal obtained from the hot-film anemometer was used to determine the time-averaged local void fraction and liquid velocity and turbulence intensity for air–oil slug flow. The capacitance signals along with the data obtained by image processing of the flow were used to determine the elongated bubble length and velocity. The measurements techniques used found to describe in detail the internal structure of the slug flow. Finally, the experimental results were compared to existing models and correlations.     

Characterization of the critical transition from annular to wavy-stratified flow for oil–water mixtures in horizontal pipes

The transition from annular to wavy-stratified oil–water adiabatic flow within horizontal pipes is experimentally analyzed, and a semiempirical model is proposed. The transition is referred to as critical because it occurs suddenly, giving rise to a sharp and strong increase in the pressure drop due to the contact of the high-viscosity oil with the pipe wall. This could lead to a dangerous accident in pipelines. Experimental runs were performed on eight test sections of both Plexiglas^® and Pyrex^® pipes with internal diameters ranging from 21.5 to 50 mm, using tap water and oil with viscosity about 880 times higher than that of water. On the basis of pressure drop measurement and flow pattern visualization, the transition boundary between annular and wavy-stratified flow was analytically determined and compared with flow pattern maps.     

Convergence of Lax–Friedrichs and Godunov schemes for a nonstrictly hyperbolic system of conservation laws arising in oil recovery

This paper is devoted to the compactness framework and the convergence theorem for the Lax–Friedrichs and Godunov schemes applied to a \({2 \times 2}\) system of non-strictly hyperbolic nonlinear conservation laws that arises from mathematical models for oil recovery. The presence of a degeneracy in the hyperbolicity of the system requires a careful analysis of the entropy functions, whose regularity is necessary to obtain the result. For this purpose, it is necessary to combine the classical techniques referring to a singular Euler–Poisson–Darboux equation with the compensated compactness method.     

Hydrodynamics and heat transfer characteristics of G–S magnetically stabilized beds consisting of admixtures of shale oil and magnetic particles

The hydrodynamic and heat transfer behavior of a bed consisting of magnetic and shale oil particle admixtures under the effect of a transverse magnetic field is investigated. The phase diagram, bed void fraction are studied under wide range of the operating conditions i.e., gas velocity, magnetic field intensity and fraction of the magnetic particles. It is found that the range of the stabilized regime is reduced as the magnetic fraction decreases. In addition, the bed voidage at the onset of fluidization decreases as the magnetic fraction decreases. On the other hand, Nusselt number and consequently the heat transfer coefficient is found to increase as the magnetic fraction decreases. An empirical equation is investigated to relate the effect of the gas velocity, magnetic field intensity and fraction of the magnetic particles on the heat transfer behavior in the bed.     

Experimental study on the effect of drag reducing polymer on flow patterns and drag reduction in a horizontal oil–water flow

In this study, a HMW anionic co-polymer of 40:60 wt/wt NaAMPS/acrylamide was used as a drag reducing polymer (DRP) for oil–water flow in a horizontal 25.4 mm ID acrylic pipe. The effect of polymer concentration in the master solution and after injection in the main water stream, oil and water velocities, and pipe length on drag reduction (DR) was investigated. The injected polymer had a noticeable effect on flow patterns and their transitions. Stratified and dual continuous flows extended to higher superficial oil velocities while annular flow changed to dual continuous flow. The results showed that as low as 2 ppm polymer concentration was sufficient to create a significant drag reduction across the pipe. DR was found to increase with polymer concentration increased and reached maximum plateau value at around 10 ppm. The results showed that the drag reduction effect tends to increase as superficial water velocity increased and eventually reached a plateau at U_sw of around 1.3 m/s. At U_sw > 1.0 m/s, the drag reduction decreased as U_so increased while at lower water velocities, drag reduction is fluctuating with respect to U_so. A maximum DR of about 60% was achieved at U_so = 0.14 m/s while only 45% was obtained at U_so = 0.52 m/s. The effectiveness of the DRP was found to be independent of the polymer concentration in the master solution and to some extent pipe length. The friction factor correlation proposed by Al-Sarkhi et al. (2011) for horizontal flow of oil–water using DRPs was found to underpredict the present experimental pressure gradient data.     

Experimental flow pattern map,slippage and time–frequency representation of oil–water two-phase flow in horizontal small diameter pipes

We detect the flow structures of a horizontal oil–water two-phase flow in a 20 mm inner-diameter pipe using 8-channels radial mini-conductance probes. In particular, we present an experimental flow pattern map that includes 218 flow conditions and compare this map to the flow pattern transitional boundaries predicted by published models. In addition, using the Adaptive Optimal Kernel Time–Frequency Representation, we analyze the conductance fluctuating signals and characterize the flow pattern in terms of the total energy and dominant frequency. Based on the liquid holdup measurements using the quickly closing valve technology combined with three parallel-wire capacitance probes, we investigate the slip effect between the oil and water phases under various flow conditions. The results show that the flow structures greatly affect the slippage, and the slip ratio is sensitive to flow pattern variations.