Mathematical Simulation of Polymer Flooding in Complex Reservoirs

1972 ◽  
Vol 12 (05) ◽  
pp. 369-382 ◽  
Author(s):  
P.L. Bondor ◽  
G.J. Hirasaki ◽  
M.J. Tham
Keyword(s):  
Finite Difference ◽  
Aqueous Phase ◽  
Flow Behavior ◽  
Polymer Flooding ◽  
Gravity Drainage ◽  
Two Phase ◽  
Polymer Injection ◽  
Well Spacing ◽  
Three Phase ◽  
Polymer Flood

Abstract Simulation of polymer flooding in many complex reservoirs has requirements that preclude the use of either three-phase stream tube or two-phase finite-difference simulators. The development of a polymer flooding model used in a three-phase, polymer flooding model used in a three-phase, four-component, compressible, finite-difference reservoir simulator that allows the simulation of a variety of complex situations is discussed. The polymer model represents the polymer solution as a fourth component that is included in the aqueous phase and is fully miscible with it. Adsorption of polymer is represented, as is both (1) the resulting permeability reduction of the aqueous phase and (2) the resulting lag of the polymer injection front and generation of a stripped polymer injection front and generation of a stripped water bank. The effects of fingering between the water and polymer are taken into account using an empirical "mixing parameter" model. The resulting simulator is capable of modeling reservoirs with nonuniform dip, multiple zones, desaturated zones, gravity segregation, and irregular well spacing and reservoir shape. Two examples are presented. The first illustrates the polymer flooding of a multizone dipping reservoir with a desaturated zone due to gravity drainage. The second illustrates the flooding of a reservoir with a gas cap and an oil rim with polymer injection near the oil-water contact. In this example, the effects of nonuniform dip, irregular well spacing and field shape, and gravity segregation of the flow are all taken into account. The two examples presented illustrate the versatility of the simulator presented illustrate the versatility of the simulator and its applicability to a wide range of problems. Introduction The design of a polymer flood for a complex reservoir requires a model that represents the reservoir features that have a significant effect on the performance of the flood. These features may include the presence of a gas cap or a desaturated zone due to gravity drainage in a dipping formation, the presence of an aquifer, irregular well spacing and reservoir boundaries, multiple zones, reservoir heterogeneities, and a well performance that is limited by state proration, injectivity, and productivity. These reservoir features are being productivity. These reservoir features are being represented by most compressible, three-phase, three-dimensional simulators. However, to model polymer flood projects, it is necessary to include a polymer flood projects, it is necessary to include a conservation equation for the polymer, and to represent the adsorption of polymer, the reduction of be rock permeability to the aqueous phase after contact with the polymer, the dispersion of the polymer slug, and the non-Newtonian flow behavior polymer slug, and the non-Newtonian flow behavior of the polymer solution. PREVIOUS SIMULATOR DEVELOPMENT PREVIOUS SIMULATOR DEVELOPMENT Previous simulator development of polymer flooding has been reported in two different general categories: three-phase stream tube models and one- or two-phase, incompressible, finite-difference simulators. Jewett and Schurz developed a two-phase, multilayer Buckley-Leverett displacement simulator capable of modeling either linear or five-spot patterns. A mobile gas saturation also could be patterns. A mobile gas saturation also could be specified, but this was treated as void space and did not affect the flow characteristics of the system. Gravitational and capillarity effects were neglected. The residual resistance of the brine following a water slug was modeled as an increase in its viscosity; the viscous fingering of the brine through the polymer slug was treated by altering empirical relative permeability relationships to specify a more adverse mobility ratio. Slater and Farouq-Ali modeled five-spot patterns with a two-phase, two-dimensional, finite-difference simulator, neglecting gravity and capillarity. They obtained an empirical expression for the resistance factor of the porous medium as a function of a time-dependent mobility ratio. SPEJ P. 369

Review of Practical Experience by Polymer Flooding at Daqing

2009 ◽  
Vol 12 (03) ◽  
pp. 470-476 ◽  
Author(s):  
Dongmei Wang ◽  
Huanzhong Dong ◽  
Changsen Lv ◽  
Xiaofei Fu ◽  
Jun Nie
Keyword(s):  
Oil Production ◽  
Polymer Flooding ◽  
Oil Field ◽  
High Permeability ◽  
Sweep Efficiency ◽  
Molecular Weights ◽  
Well Spacing ◽  
Polymer Flood ◽  
Daqing Oil Field ◽  
Water Cut

Summary This paper describes successful practices applied during polymer flooding at Daqing that will be of considerable value to future chemical floods, both in China and elsewhere. On the basis of laboratory findings, new concepts have been developed that expand conventional ideas concerning favorable conditions for mobility improvement by polymer flooding. Particular advances integrate reservoir-engineering approaches and technology that is basic for successful application of polymer flooding. These include the following:Proper consideration must be given to the permeability contrast among the oil zones and to interwell continuity, involving the optimum combination of oil strata during flooding and well-pattern design, respectively;Higher polymer molecular weights, a broader range of polymer molecular weights, and higher polymer concentrations are desirable in the injected slugs;The entire polymer-flooding process should be characterized in five stages--with its dynamic behavior distinguished by water-cut changes; -Additional techniques should be considered, such as dynamic monitoring using well logging, well testing, and tracers; effective techniques are also needed for surface mixing, injection facilities, oil production, and produced-water treatment; andContinuous innovation must be a priority during polymer flooding. Introduction China's Daqing oil field entered its ultrahigh-water-cut period after 30 years of exploitation. Just before large-scale polymer-flooding application, the average water-cut was more than 90%. The Daqing oil-field is a large river-delta/lacustrine facies, multilayered with complex geologic conditions and heterogeneous sandstone in an inland basin. After 30 years of waterflooding, many channels and high-permeability streaks were identified in this oil field (Wang and Qian 2002). Laboratory research began in the 1960s, investigating the potential of enhanced-oil-recovery (EOR) processes in the Daqing oil field. After a single-injector polymer flood with a small well spacing of 75 m in 1972, polymer flooding was set on pilot test. During the late 1980s, a pilot project in central Daqing was expanded to a multiwell pattern with larger well spacing. Favorable results from these tests--along with extensive research and engineering from the mid-1980s through the 1990s--confirmed that polymer flooding was the preferred method to improve areal- and vertical-sweep efficiency at Daqing and to provide mobility control (Wang et al. 2002, Wang and Liu 2004). Consequently, the world's largest polymer flood was implemented at Daqing, beginning in 1996. By 2007, 22.3% of total production from the Daqing oil field was attributed to polymer flooding. Polymer flooding boosted the ultimate recovery for the field to more than 50% of original oil in place (OOIP)--10 to 12% OOIP more than from waterflooding. At the end of 2007, oil production from polymer flooding at the Daqing oil field was more than 10 million tons (73 million bbl) per year (sustained for 6 years). The focus of this paper is on polymer flooding, in which sweep efficiency is improved by reducing the water/oil mobility ratio in the reservoir. This paper is not concerned with the use of chemical gel treatments, which attempt to block water flow through fractures and high-permeability strata. Applications of chemical gel treatments in China have been covered elsewhere (Liu et al. 2006).

Key Aspects of Project Design for Polymer Flooding at the Daqing Oilfield

2008 ◽  
Vol 11 (06) ◽  
pp. 1117-1124 ◽  
Author(s):  
Dongmei Wang ◽  
Randall S. Seright ◽  
Zhenbo Shao ◽  
Jinmei Wang
Keyword(s):  
Molecular Weight ◽  
Polymer Concentration ◽  
Oil Production ◽  
Polymer Flooding ◽  
Oil Field ◽  
Polymer Injection ◽  
Polymer Flood ◽  
Daqing Oil Field ◽  
Water Cut ◽  
Injection Rates

Summary This paper describes the design procedures that led to favorable incremental oil production and reduced water production during 12 years of successful polymer flooding in the Daqing oil field. Special emphasis is placed on some new design factors that were found to be important on the basis of extensive experience with polymer flooding. These factors include (1) recognizing when profile modification is needed before polymer injection and when zone isolation is of value during polymer injection, (2) establishing the optimum polymer formulations and injection rates, and (3) time-dependent variation of the molecular weight of the polymer used in the injected slugs. For some Daqing wells, oil recovery can be enhanced by 2 to 4% of original oil in place (OOIP) with profile modification before polymer injection. For some Daqing wells with significant permeability differential between layers and no crossflow, injecting polymer solutions separately into different layers improved flow profiles, reservoir sweep efficiency, and injection rates, and it reduced the water cut in production wells. Experience over time revealed that larger polymer-bank sizes are preferred. Bank sizes grew from 240-380 mg/L·PV during the initial pilots to 640 to 700 mg/L·PV in the most recent large-scale industrial sites [pore volume (PV)]. Economics and injectivity behavior can favor changing the polymer molecular weight and polymer concentration during the course of injecting the polymer slug. Polymers with molecular weights from 12 to 35 million Daltons were designed and supplied to meet the requirements for different reservoir geological conditions. The optimum polymer-injection volume varied around 0.7 PV, depending on the water cut in the different flooding units. The average polymer concentration was designed approximately 1000 mg/L, but for an individual injection station, it could be 2000 mg/L or more. At Daqing, the injection rates should be less than 0.14-0.20 PV/year, depending on well spacing. Introduction Many elements have long been recognized as important during the design of a polymer flood (Li and Niu 2002; Jewett and Schurz 1970; Sorbie 1991; Vela et al. 1976; Taber et al. 1997; Maitin 1992; Koning et al. 1988; Wang et al. 1995; Wang and Qian 2002; Wang et al. 2008). This paper spells out some of those elements, using examples from the Daqing oil field. The Daqing oil field is located in northeast China and is a large river-delta/lacustrine-facies, multilayer, heterogeneous sandstone in an inland basin. The reservoir is buried at a depth of approximately 1000 m, with a temperature of 45°C. The main formation under polymer flood (i.e., the Saertu formation) has a net thickness ranging from from 2.3 to 11.6 m with an average of 6.1 m. The average air permeability is 1.1 µm2, and the Dykstra-Parsons permeability coefficient averages 0.7. Oil viscosity at reservoir temperature averages approximately 9 mPa·s, and the total salinity of the formation water varies from 3000 to 7000 mg/L. The field was discovered in 1959, and a waterflood was initiated in 1960. The world's largest polymer flood was implemented at Daqing, beginning in December 1995. By 2007, 22.3% of total production from the Daqing oil field was attributed to polymer flooding. Polymer flooding should boost the ultimate recovery for the field to more than 50% OOIP--10 to 12% OOIP more than from waterflooding. At the end of 2007, oil production from polymer flooding at the Daqing oil field was more than 11.6 million m3 (73 million bbl) per year (sustained for 6 years). The polymers used at Daqing are high-molecular-weight partially hydrolyzed polyacrylamides (HPAMs). During design of a polymer flood, critical reservoir factors that traditionally receive consideration are the reservoir lithology, stratigraphy, important heterogeneities (such as fractures), distribution of remaining oil, well pattern, and well distance. Critical polymer properties include cost-effectiveness (e.g., cost per unit of viscosity), resistance to degradation (mechanical or shear, oxidative, thermal, microbial), tolerance of reservoir salinity and hardness, retention by rock, inaccessible pore volume, permeability dependence of performance, rheology, and compatibility with other chemicals that might be used. Issues long recognized as important for polymer-bank design include bank size (volume), polymer concentration and salinity (affecting bank viscosity and mobility), and whether (and how) to grade polymer concentrations in the chase water. This paper describes the design procedures that led to favorable incremental oil production and reduced water production during 12 years of successful polymer flooding in the Daqing oil field.

Laboratory Investigations of Factors Influencing Polymer Flood Performance

1975 ◽  
Vol 15 (04) ◽  
pp. 338-346 ◽  
Author(s):  
M.T. Szabo
Keyword(s):  
Oil Recovery ◽  
Polymer Solutions ◽  
Polymer Concentration ◽  
Polymer Flooding ◽  
Mobility Control ◽  
Sweep Efficiency ◽  
Experimental Conditions ◽  
Polymer Injection ◽  
Polymer Flood

Abstract Numerous polymer floods were performed in unconsolidated sand packs using a C14-tagged, cross-linked, partially hydrolyzed ployacrylamide, and the data are compared with brine-flood performance in the same sands. performance in the same sands. The amount of "polymer oil" was linearly proportional to polymer concentration up to a proportional to polymer concentration up to a limiting value. The upper limit of polymer concentration yielding additional polymer oil was considerably higher for a high-permeability sand than for a low-permeability sand. It is shown that a minimum polymer concentration exists, below which no appreciable polymer oil can be produced in high-permeability sands. The effect of polymer slug size on oil recovery is shown for various polymer concentrations, and the results from these tests are used to determine the optimum slug size and polymer concentration for different sands. The effect of salinity was studied by using brine and tap water during polymer floods under similar conditions. Decreased salinity resulted in improved oil recovery at low, polymer concentrations, but it had little effect at higher polymer concentrations. Polymer injection that was started at an advanced stage of brine flood also improved the oil recovery in single-layered sand packs. Experimental data are presented showing the effect of polymer concentration and salinity on polymer-flood performance in stratified reservoir polymer-flood performance in stratified reservoir models. Polymer concentrations in the produced water were measured by analyzing the radioactivity of effluent samples, and the amounts of retained polymer in the stratified models are given for each polymer in the stratified models are given for each experiment. Introduction In the early 1960's, a new technique using dilute polymer solutions to increase oil recovery was polymer solutions to increase oil recovery was introduced in secondary oil-recovery operations. Since then, this new technique has attained wide-spread commercial application. The success and the complexity of this new technology has induced many authors to investigate many aspects of this flooding technique. Laboratory and field studies, along with numerical simulation of polymer flooding, clearly demonstrated that polymer additives increase oil recovery. polymer additives increase oil recovery. Some of the laboratory results have shown that applying polymers in waterflooding reduces the residual oil saturation through an improvement in microscopic sweep efficiency. Other laboratory studies have shown that applying polymer solutions improves the sweep efficiency in polymer solutions improves the sweep efficiency in heterogeneous systems. Numerical simulation of polymer flooding, and a summary of 56 field applications, clearly showed that polymer injection initiated at an early stage of waterflooding is more efficient than when initiated at an advanced stage. Although much useful information has been presented, the experimental conditions were so presented, the experimental conditions were so variable that difficulties arose in correlating the numerical data. So, despite this good data, a systematic laboratory study of the factors influencing the performance of polymer flooding was still lacking in the literature. The purpose of this study was to investigate the effect of polymer concentration, polymer slug size, salinity in the polymer bank, initial water saturation, and permeability on the performance of polymer floods. The role of oil viscosity did not constitute a subject of this investigation. However, some of the data indicated that the applied polymer resulted in added recovery when displacing more viscous oil. The linear polymer-flood tests were coupled with tests in stratified systems, consisting of the same sand materials used in linear flood tests. Thus, it was possible to differentiate between the role of polymer in mobility control behind the flood front in each layer and its role in mobility control in the entire stratified system through improvement in vertical sweep efficiency. A radioactive, C14-tagged hydrolyzed polyacrylamide was used in all oil-recovery tests. polyacrylamide was used in all oil-recovery tests. SPEJ P. 338

Sandstone and Carbonate Two- and Three-Phase Relative Permeability Characteristics

1970 ◽  
Vol 10 (01) ◽  
pp. 75-84 ◽  
Author(s):  
F.N. Schneider ◽  
W.W. Owens
Keyword(s):  
Relative Permeability ◽  
Oil Recovery ◽  
Flow Behavior ◽  
Water Injection ◽  
Phase System ◽  
Phase Flow ◽  
Two Phase ◽  
Permeability Characteristics ◽  
Three Phase ◽  
Three Phase Flow

Abstract Three-phase relative permeability characteristics applicable to various oil displacement processes in the reservoir such as combustion and alternate gas-water injection were determined on both outcrop and reservoir core samples. Steady-state and nonsteady-state tests were performed on a variety of sandstone and carbonate core samples having different wetting properties. Some of the tests were performed on preserved samples. Some of the three-phase tests were performed on samples that contained two flowing phases and a third nonflowing phase, either gas or oil. These were classed as three-phase flow tests because the third phase played an important role in the flow behavior which was determined. The three-phase relative permeability test results are directly compared with the results of two-phase gas-oil and water-oil test. Wetting-phase relative permeability was found to be primarily dependent on its own saturation, i.e., relative permeability to the wetting phase during three-phase flow was in agreement with and could be predicted from the tow-phase data. Nonwetting-phase relative permeability-saturation relationships were found to be more complex and to depend in some cases on the saturation history of both nonwetting phases and on the saturation ratio of the second nonwetting phase and the wetting phases. Trapping of a given nonwetting phase or mutual flow interference between the two nonwetting phases when both are flowing accounts for most of the low relative permeabilities observed for three-phase flow tests. However, in special cases nonwetting-phase relative permeabilities at a given saturation are higher than those given by two-phase flow data. Despite these complexities some types of three-phase flow behavior can be predicted from two-phase flow data. Through its effect on the spatial distribution of the phases, wettability is shown to be a controlling factor in determining three-phase relative permeability characteristics. however, despite the importance of wettability the present data shown that for both water-wet and oil-wet systems oil recovery can be improved by several different injection processes, but the additional oil recovery is accompanied by lower fluid mobility. Introduction The increasing emphasis on optimizing recovery and the rapid and extensive development and use of mathematical modes for predicting reservoir performance are together creating a widespread need for reliable basic data on rock flow behavior. The two-phase imbibition or drainage flow relationships common to conventional oil recovery processes (depletion, gas or water injection, gravity drainage) are not applicable to some of the newer secondary and tertiary recovery techniques. This is because the reservoir displacement process may differ from that easily simulated in laboratory relative permeability studies. in some situations, data are needed fro a three-phase system where almost any combination of two fluids or even all three fluids may be flowing. In other, however, only two flowing phases are present, but the saturation history of the system is unique. Leverett and Lewis were the first to collect experimental relative permeability data on a three-phase system. Corey et al. were similarly leaders in efforts to define three-phase flow relationships using empirical approaches. Space does not permit a critical review of these earlier works. For those interested, a recent article by Saraf and Fatt provides a brief discussion of the experimental techniques used by earlier investigators. Suffice it to say that both experimental and empirical approaches have been used, but the applicability of both has been limited because in only one case have three-phase relative permeability data been obtained on reservoir rock material. SPEJ P. 75ˆ

scholarly journals Influence of Sulfate Ions on the Combined Application of Modified Water and Polymer Flooding—Rheology and Oil Recovery

Energies ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 2356 ◽  
Author(s):  
Muhammad Tahir ◽  
Rafael E. Hincapie ◽  
Leonhard Ganzer
Keyword(s):  
Oil Recovery ◽  
Sodium Sulfate ◽  
Water Injection ◽  
Polymer Flooding ◽  
Two Phase ◽  
Sulfate Ions ◽  
Polymer Injection ◽  
Smart Water ◽  
Combined Application ◽  
Core Flood

Oil recovery using modified/smart water technology can be maximized by optimizing the composition of the injected water. Brine optimization is also believed to improve polymer flooding performance. This chapter assesses and defines the potential impact of combining low-salt-modified water with polymer flooding, based on the presence of sulfate in the injection water. Hence, we evaluated the influence of sodium sulfate on (1) polymer viscoelasticity, under the assumption that the phenomena exists, and (2) oil recovery and pressure response. Mainly, a comprehensive rheological evaluation and two-phase core flood experiments are the focus of this work. Composition of injection brine is optimized after having synthetic seawater as a base brine. Core-flood experiments were performed in a secondary, tertiary and a sort of post-tertiary (quaternary) mode to evaluate the feasibility of applying both processes (modified water and polymer flood). Obtained data was subsequently cross-analyzed and as an overall observation, sodium sulfate helped with improving polymer viscosity compared to sodium chloride or divalent cation presence. Moreover, optimized modified water, with the higher amount of sulfate ions, showed an additional oil recovery in both secondary and tertiary mode of about 5.0%. Additionally, polymer injection in tertiary mode, after modified-water injection, showed significant additional oil recovery.

Prediction of Three-Phase Gravity Drainage from Two-Phase Capillary Pressure Curves

2010 ◽  
Author(s):  
Mohammad Mirzaei ◽  
David A. DiCarlo ◽  
Mandana Ashouripashaki ◽  
Hassan Dehghanpour ◽  
Behdad Aminzadeh
Keyword(s):  
Capillary Pressure ◽  
Gravity Drainage ◽  
Two Phase ◽  
Three Phase ◽  
Capillary Pressure Curves

scholarly journals A New Approach to Polymer Flooding: Effects of Early Polymer Injection and Wettability on Final Oil Recovery

SPE Journal ◽  
2018 ◽  
Vol 24 (01) ◽  
pp. 129-139 ◽  
Author(s):  
J. L. Juárez-Morejón ◽  
H.. Bertin ◽  
A.. Omari ◽  
G.. Hamon ◽  
C.. Cottin ◽  
...  
Keyword(s):  
Oil Recovery ◽  
Phase Distribution ◽  
Water Saturation ◽  
Dominant Role ◽  
Polymer Flooding ◽  
Displacement Efficiency ◽  
Sweep Efficiency ◽  
Two Phase ◽  
Polymer Injection ◽  
The Core

Summary An experimental study of polymer flooding is presented here, focusing on the influence of initial core wettability and flood maturity (volume of water injected before polymer injection) on final oil recovery. Experiments were performed using homogeneous Bentheimer Sandstone samples of similar properties. The cores were oilflooded using mineral oil for water-wet conditions and crude oil (after an aging period) for intermediate-wet conditions; the viscosity ratio between oil and polymer was kept constant in all experiments. Polymer, which is a partially hydrolyzed polyacrylamide (HPAM), was used at a concentration of 2,500 ppm in a moderate-salinity brine. The polymer solution was injected in the core at different waterflood-maturity times [breakthrough (BT) and 0, 1, 1.75, 2.5, 4, and 6.5 pore volumes (PV)]. Coreflood results show that the maturity of polymer injection plays an important role in final oil recovery, regardless of wettability. The waterflood-maturity time 0 PV (polymer injection without initial waterflooding) leads to the best sweep efficiency, whereas final oil production decreases when the polymer-flood maturity is high (late polymer injection after waterflooding). A difference of 15% in recovery is observed between early polymer flooding (0 PV) and late maturity (6.5 PV). Concerning the effect of wettability, the recovery factor obtained with water-wet cores is always lower (from 10 to 20%, depending on maturity) than the values obtained with intermediate-wet cores, raising the importance of correctly restoring core wettability to obtain representative values of polymer incremental recovery. The influence of wettability can be explained by the oil-phase distribution at the pore scale. Considering that the waterflooding period leads to different values of the oil saturation at which polymer flooding starts, we measured the core dispersivity using a tracer method at different states. The two-phase dispersivity decreases when water saturation increases, which is favorable for polymer sweep. This study shows that in addition to wettability, the maturity of polymer flooding plays a dominant role in oil-displacement efficiency. Final recovery is correlated to the dispersion value at which polymer flooding starts. The highest oil recovery is obtained when the polymer is injected early.

The generated power of multipole induction generator with secondary winding on the stator

2009 ◽  
Vol 25 (25) ◽  
pp. 31-34
Author(s):  
Guntis Diļevs ◽  
Edgars Jakobsons
Keyword(s):  
Rotation Speed ◽  
Induction Generator ◽  
Two Phase ◽  
Three Phase ◽  
Secondary Winding

The generated power of multipole induction generator with secondary winding on the statorThis paper posses the construction of induction generator, which has the ability to operate at a low rotation speed. This generator can be applied for directly driven turbine without using the gearbox. The generator is multi pole with all of the windings placed on the stator. Rotor is tooth-like and has no windings on it. Primary winding is three phase, secondary winding is two phase.

Inductor Saturation Compensation in Three-Phase Three-Wire Voltage-Source Converters via Inverse System Dynamics-I

2020 ◽  
Author(s):  
Ziya Özkan ◽  
Ahmet Masum Hava
Keyword(s):  
Dynamic Model ◽  
Dynamic Performance ◽  
Current Control ◽  
Inverse System ◽  
Voltage Source ◽  
Voltage Source Converter ◽  
Two Phase ◽  
Inverse Dynamic ◽  
Three Phase ◽  
Steady State Current

In three-phase three-wire (3P3W) voltage-source converter (VSC) systems, utilization of filter inductors with deep saturation characteristics is often advantageous due to the improved size, cost, and efficiency. However, with the use of conventional synchronous frame current control (CSCC) methods, the inductor saturation results in significant dynamic performance loss and poor steady-state current waveform quality. This paper proposes an inverse dynamic model based compensation (IDMBC) method to overcome these performance issues. Accordingly, a review of inductor saturation and core materials is performed, and the motivation on the use of saturable inductors is clarified. Then, two-phase exact modelling of the 3P3W VSC control system is obtained and the drawbacks of CSCC have been demonstrated analytically. Based on the exact modelling, the inverse system dynamic model of the nonlinear system is obtained and employed such that the nonlinear plant is converted to a fictitious linear inductor system for linear current regulators to perform satisfactorily.

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