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Numerical simulation on ferrofluid flow in fractured porous media based on discrete-fracture model

  • Tao Huang , Jun Yao EMAIL logo , Zhaoqin Huang EMAIL logo , Xiaolong Yin , Haojun Xie and Jianguang Zhang
Published/Copyright: June 16, 2017
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Open Physics
From the journal Open Physics Volume 15 Issue 1

Abstract

Water flooding is an efficient approach to maintain reservoir pressure and has been widely used to enhance oil recovery. However, preferential water pathways such as fractures can significantly decrease the sweep efficiency. Therefore, the utilization ratio of injected water is seriously affected. How to develop new flooding technology to further improve the oil recovery in this situation is a pressing problem. For the past few years, controllable ferrofluid has caused the extensive concern in oil industry as a new functional material. In the presence of a gradient in the magnetic field strength, a magnetic body force is produced on the ferrofluid so that the attractive magnetic forces allow the ferrofluid to be manipulated to flow in any desired direction through the control of the external magnetic field. In view of these properties, the potential application of using the ferrofluid as a new kind of displacing fluid for flooding in fractured porous media is been studied in this paper for the first time. Considering the physical process of the mobilization of ferrofluid through porous media by arrangement of strong external magnetic fields, the magnetic body force was introduced into the Darcy equation and deals with fractures based on the discrete-fracture model. The fully implicit finite volume method is used to solve mathematical model and the validity and accuracy of numerical simulation, which is demonstrated through an experiment with ferrofluid flowing in a single fractured oil-saturated sand in a 2-D horizontal cell.

At last, the water flooding and ferrofluid flooding in a complex fractured porous media have been studied. The results showed that the ferrofluid can be manipulated to flow in desired direction through control of the external magnetic field, so that using ferrofluid for flooding can raise the scope of the whole displacement. As a consequence, the oil recovery has been greatly improved in comparison to water flooding. Thus, the ferrofluid flooding is a large potential method for enhanced oil recovery in the future.

Keywords: ferrofluid flow; fractured porous media; discrete fracture model; numerical simulation; enhance oil recovery
PACS: 47.11.Df; 47.54.Bd; 47.65.Cb

1 Introduction

Ferrofluids are stable colloids composed of small (3–15 nm) solid, magnetic, single-domain particles coated with a molecular layer of a dispersant and suspended in a liquid carrier. Thermal agitation keeps the particles suspended because of Brownian motion, and the coatings prevent the particles from sticking to each other [1]. Ferrofluid has been the subject of various experimental and numerical studies. Ghasemian et al. investigated the cooling of a water-based ferrofluid with non-coated magnetic nanoparticles in a mini channel under the influence of both constant and alternating magnetic fields [2]. Hayat et al. studied the flow of ferrofluid between two parallel rotating stretchable disks with different rotating and stretching velocities [3]. Yasmeen et al. analyzed the two dimensional ferrofluid flow with magnetic dipole and homogeneous-heterogeneous reactions [4]. Rahimi et al. measured the surface tension of a ferrofluid usingsessiledrop and falling drop method [5]. Odenbach and Thurm studied the magneto-viscous effects in ferrofluids [6].

As a new kind of functional material, ferrofluid exhibits the characteristics of a general fluid that its motion follows the hydrodynamic law. Secondly, it is a magnetic substance which receives the magnetic body force in the presence of a gradient in the magnetic field strength, so that the attractive magnetic forces allow the ferrofluid to be manipulated to flow in any desired direction through control of the external magnetic field without any direct physical contact [7]. Therefore, a ferrofluid has many industrial applications [8, 9], such as dynamic sealing, heat dissipation, inertial and viscous damper. In recent years, a controllable ferrofluid has caused the extensive concern in oil industry as a new functional material [10–15], many scholars studied its potential application in enhanced oil recovery, fracture detection, etc.

As we know, water flooding is an efficient approach to maintain reservoir pressure and has been widely used to enhance oil recovery. However, the strongly heterogeneous reservoirs can significantly decrease the sweep efficiency. Therefore, the utilization ratio of injected water is seriously affected [16–18]. In this paper, the potential application of using the ferrofluid as a new kind of displacing fluid for flooding in fractured porous media has been studied. The results showed, that using ferrofluid with the magnetic field for flooding can raise the scope of the whole displacement, as a consequence, the oil recovery has been greatly improved in comparison to water flooding.

2 Magnetic body force

Ferrofluid’s macroscopic magnetic properties come from its internal magnetic solid particles. When there is no external magnetic field present, the magnetic moments of particles (that is, the tiny magnetic field) are disordered, due to the influence of thermal motion and cancel each other; when an external magnetic field is applied, the magnetic moments are arranged neatly in the direction of the external magnetic field, so that the ferrofluid exhibits magnetism at the macroscopic level, as shown in Figure 1.

Figure 1 The components and magnetization of a ferrofluid. (a) Particle coated with a molecular layer of a dispersant; (b) Magnetization process; (c) TEM micrograph of a ferrofluid sample [19]; (d) A bottle of ferrofluid Hinano-FFW
Figure 1

The components and magnetization of a ferrofluid. (a) Particle coated with a molecular layer of a dispersant; (b) Magnetization process; (c) TEM micrograph of a ferrofluid sample [19]; (d) A bottle of ferrofluid Hinano-FFW

With the increase of the external magnetic field strength H, the magnetization M of the ferrofluid increases and reaches a maximum value, that is, the saturation magnetization Mmax. In this paper, the water-based ferrofluid Hinano-FFW has been studied experimentally and theoretically by numerical simulation. The saturation magnetization Mmax = 1.596 × 104 A/m, and the magnetization curve are shown in Figure 2.

Figure 2 Magnetization versus magnetic field strength for Hinano-FFW
Figure 2

Magnetization versus magnetic field strength for Hinano-FFW

Magnetization curves can be approximated by simple two-parameter arctangent functions of the form [20]:

M=α×arctan⁡(β×H)(1)

For the Hinano-FFW ferrofluid, α = 1 × 104, β = 3.5 × 10−5, besides, in the case of the immiscible two-phase flow in porous media, assuming ferrofluid magnetization increases linearly with its saturation:

M(Sff)=M(Sff=1)Sff(2)

In this paper, the external magnetic field is provided by the NdFeB magnets. The specific parameters of the magnet are shown in Table 1, and the three-dimensional magnetic field strength H = (Hx, Hy, Hz) can be calculated by analytic equations [21]:

Hd=Gd(x,y,z)−Gd(x+L,y,z),d=x,y,z(3)

Where,

Gxx,y,z=Br4πμ0⋅arctany+az+bxy+a2+z+b2+x21/2+arctany−az−bxy−a2+z−b2+x21/2−arctany+az−bxy+a2+z−b2+x21/2−arctany−az+bxy−a2+z+b2+x21/2(4)
Gyx,y,z=Br4πμ0⋅lnz+b+z+b2+y−a2+x21/2z−b+z−b2+y−a2+x21/2×z−b+z−b2+y+a2+x21/2z+b+z+b2+y+a2+x21/2(5)
Gzx,y,z=Br4πμ0⋅lny+a+z−b2+y+a2+x21/2y−a+z−b2+y−a2+x21/2×y−a+z+b2+y−a2+x21/2y+a+z+b2+y+a2+x21/2(6)
Table 1

The properties of permanent magnet used for experiment and numerical simulation

MagnetSymbolValue
PM1Residual flux density Br1.19 T
Length L0.0254 m
Width 2a0.0191 m
Height 2b0.0191 m
PM2Residual flux density Br1.19 T
Length L0.127 m
Width 2a0.0508 m
Height 2b0.0508 m

Where Br is magnet residual flux density and 2a, 2b, L, are the lengths of the magnet in three directions, respectively, as shown in Figure 3.

Figure 3 Local coordinate system for the magnetic field produced by a permanent magnet
Figure 3

Local coordinate system for the magnetic field produced by a permanent magnet

When an external magnetic field is applied, the secondary magnetic field produced by the magnetic particles inside the ferrofluid interacts with the external magnetic field, which causes the ferromagnetic fluid to be affected by the magnetic field force. As a result, the ferrofluid is affected by the magnetic body force [22]:

Fm=μ0M⋅∇H(7)

where μ0 = 4π × 10−7 T m/A is the magnetic permeability of free space. Generally, the direction of magnetization of a ferrofluid element is always in the direction of the local magnetic field, then

Fm=μ0MHH⋅∇H=μ0MH12∇H⋅H−H×∇×H(8)

Assuming the ferrofluid is electrically non-conducting and that the displacement current is negligible, so that ∇ × H = 0, we can obtain

Fm=μ0M∇H(9)

3 Discrete-Fracture Model

Usually, fractures have complicated geometric configuration due to the various generation environment, such as stress, deposition, erosion, effloresce, etc. Thus, it is necessary to simplify the fractures for convenience. For a laminar flow conditions, velocity distribution along the fracture aperture can be obtained. Rewriting the flux in the form of equivalent Darcy’s law gives the fractures’ equivalent permeability. Evidently, the flow parameters and correlative physical quantities are kept constant along the direction of the fracture aperture, so reducing its dimension is feasible. In this paper, we use discrete-fracture model to simplify the fractures geometric configuration [23]. For the 2-D problem, Delaunay triangular mesh is employed to subdivide the whole research region and 1-D line element is employed to represent fracture. For the 3-D problem, Delaunay triangular mesh is used to subdivide the fracture surface; the entire research region is subdivided by relevant tetrahedron or hexahedron, as shown in Figure 4.

Figure 4 Mesh schematics of discrete-fracture model [23]; (a) the 2-D problem; (b) the 3-D problem
Figure 4

Mesh schematics of discrete-fracture model [23]; (a) the 2-D problem; (b) the 3-D problem

The matrix system comprising of micro-fissure and rock mass is regarded as an equivalent porous continuum and the macroscopic fractures are manifestly represented as discrete fractures. Therefore, the whole fractured porous media consist of a matrix system and fracture system. The research region is Ω = Ωm + ∑ αi × (Ωf)i, where m represents matrix, f represents fracture, and αi is the aperture of the i-th fracture. Assuming the representative element volumes of both matrix and fracture system, the flow equations (FEQ) are applicable to the entire research area. Then, for the discrete-fracture model, the integral form of the flow equation can be expressed as:

∫ΩFEQdΩ=∫ΩmFEQdΩm+∑iαi×∫ΩfiFEQdΩfi(10)

4 Numerical simulation of ferrofluid flow in porous media

4.1 Flow equations

For simplicity, we only consider isothermal flow of impressible fluid and neglect capillary pressure in this paper, which is similar to the analysis of other flow problems. From the law of mass conservation, we know that a fluid in a control volume should meet:

∫∂V−ρβvβ⋅ndA+∫VqmβdV=∫V∂∂t(ρβϕSβ)dV(11)

where ρβ is fluid density, vβ is seepage velocity, n is the outer normal unit vector of outer boundary ∂ V, qmβ is the source term which represents mass change in time unit and volume unit, ϕ is porosity of porous media, Sβ is saturation.

According to Darcy’s law, the seepage velocity is written as:

vβ=−krβμβk⋅(∇pβ−ρβg∇D)(12)

where k is permeability tensor which changes into scalar k in isotropic porous media, krβ is the relative permeability, μβ is fluid viscosity, pβ is fluid pressure, D denotes highness, which is positive on the upward side, g is gravitational acceleration. Particularly, for a ferrofluid affected by an external magnetic field a body force is produced, so that an additional magnetic force term appears in the Darcy’s Equation [20]:

vff=−krffμffk⋅∇pff−ρffg∇D−μ0M∇H(13)

where the subscript ffstands for ferrofluid.

4.2 Finite volume discretization

Using the cell center point value to represent the average value of physical quantities, Eq. (11) can be further described as:

∂∂t(ρβϕSβVi)=−∑j∈ηinij⋅(ρβvβ)Aij+qmβVi(14)

where j is the adjacent cell of i, nij is the outer normal unit vector of interface between i and j, Aij is the interface area. Substituting Eq. (12) for (14), we can obtain:

∂∂t(ρβϕSβVi)=∑j∈ηinij⋅ρβkrβμβk⋅∇ΦβAij+qmβVi(15)

Herein, we define the flow potential as follows:

Φβ=pβ−ρβgD(16)

In particular, from Eq. (13) we know the ferrofluid flow potential can be written as:

Φff=pff−ρffgD−μ0MH(17)

Using the first order difference for time discretization and central difference for space discretization, the Eq. (15) can be further written as:

1Δt(ρβSβϕV)in+1−(ρβSβϕV)in=∑j∈ηi(ρβλβ)ij+1/2n+1γijΦβjn+1−Φβin+1+Qβin+1(18)

where (ρβ)ij+1/2n+1=(ρβ)in+1+(ρβ)jn+1/2 is the average density at interface between i and j, γij = Aijkij+1/2/(di+dj) is the conductivity, kij+1/2 is the harmonic average of permeability ki and kj, di and dj is the vertical distance from interface to the center point of i and j, respectively. Source term Qβin+1=(qmβ)in+1=ρβqβin+1Vi,λβ = krβ/μβ is the mobility coefficient and the upstream calculation formula is implemented as follows:

(ρβλβ)ij+1/2n+1=(ρβλβ)in+1if(Φβjn+1−Φβin+1)≤0(ρβλβ)jn+1if(Φβjn+1−Φβin+1)>0(19)

4.3 Solving the discrete equation

The Newton-Raphson iterative method is used to solve the numerical discrete equation in this paper. The numerical discretized mass conservation Equation (18) is written in the following residual form:

Rβin+1=1Δt(ρβSβϕV)in+1−(ρβSβϕV)in−∑j∈ηi(ρβλβ)ij+1/2n+1γij(Φβjn+1−Φβin+1)−ρβqβin+1Vi(20)

Expanding to the first order in the primary variables and introducing an iteration index p, we can obtain

∑l∂Rβin+1(xp)∂xlpδxlp+1=−Rβin+1(xp)(21)

where xlp is the l-th primary variable at p-th iteration level, time step n+1,δxlp+1=xlp+1−xlp is the increment of primary variable at iteration level p + 1. Solution of the Jacobian matrix system of equations is obtained with the last iteration level, resulting in an updated estimation of the primary variables. Iteration continues until the latest residuals are reduced to a small value,

|Rβip+1,n+1|<ε(22)

In this paper, convergence criterion ε = 1 × 10−5.

5 Examples and discussions

(1) Single fractured porous media model

Considering the single fractured porous media model in Figure 5a, the porosity of the homogeneous isotropic matrix ϕ = 0.2, permeability km = 1.38 × 10−12 m2, fracture aperture α = 1 mm, and permeability kf = α2/12 = 8.33 × 10−8 m2. Viscosity of ferrofluid μff = 5.8 mPa•s, viscosity of oil μo = 22.1 mPa⋅s. Density of ferrofluid ρff = 1187 kg/m3, density of oil ρo = 850 kg/m3, ferrofluid phase relative permeability krff=Sff2, oil phase relative permeability kro = (1 − Sff)2; we assumed irreducible ferrofluid saturation and residual oil saturation are equal zero. Initial oil saturation is equal 1, both injection and producing speeds are q = 0.01Vp/min, where Vp is the total pore volume. The triangular meshes consist of 603 nodes and 1124 elements as shown in Figure 5b. Before the injection of the ferrofluid, a magnet PM1 was put on the upper and the right side of the model and the magnetic field, as shown in Figure 5c.

Figure 5 Single fractured porous media model; (a) Model geometry; (b) Triangular meshes; (c) Distribution of magnetic field H in units of Gs
Figure 5

Single fractured porous media model; (a) Model geometry; (b) Triangular meshes; (c) Distribution of magnetic field H in units of Gs

The ferrofluid saturation distribution of flow experiment and numerical simulation on the single fractured model are shown in Figures 6 and 7. There are some differences between calculated and experimental results, because it is impossible to make extreme homogeneous isotropic matrix. However, it still can be seen that the calculation result is basically consistent with the experimental result, which verifies the validity and accuracy of the mathematical model and numerical algorithm.

Figure 6 The ferrofluid saturation distribution of flow experiment and numerical simulation at different injection volume; (a)-(a”) respectively show the experimental results at 0.25Vp, 0.75 Vp, 1.5Vp; (b)-(b”) respectively show the calculation results at 0.25Vp, 0.75Vp, 1.5Vp
Figure 6

The ferrofluid saturation distribution of flow experiment and numerical simulation at different injection volume; (a)-(a”) respectively show the experimental results at 0.25Vp, 0.75 Vp, 1.5Vp; (b)-(b”) respectively show the calculation results at 0.25Vp, 0.75Vp, 1.5Vp

Figure 7 The ferrofluid-flooding production index curves of experiment and simulation; (a) Ferrofluid cut curves; (b) Recovery curves
Figure 7

The ferrofluid-flooding production index curves of experiment and simulation; (a) Ferrofluid cut curves; (b) Recovery curves

(2) Complex fractured porous media model

As Figure 6 shows, affected by the attractive magnetic forces, the ferrofluid was manipulated to flow to the magnets. Thus, we designed a complex fractured porous media model which has multiple fractures in the lower part of the model, and a magnet PM2 was put on the left-top of the model, as shown in Figure 8. Next, we simulated water flooding and ferrofluid flooding process on this model, to study the potential by using the ferrofluid as a displacing fluid for flooding in fractured porous media. The viscosity of water μw = 1 mPa⋅s and ρw = 1000 kg/m3, both injection and producing speeds are q= 0.01Vp/min.

Figure 8 Complex fractured porous media model; (a) Model geometry; (b) Distribution of magnetic field H in units of Gs
Figure 8

Complex fractured porous media model; (a) Model geometry; (b) Distribution of magnetic field H in units of Gs

As shown in Figure 9, the most amount of injected water flows into fractures during the water flooding process, because the fractures provide high-conductivity paths. As a result, a portion of the remaining oil has not been displaced (especially in the left-upper part of model) and the flooding sweep area has become smaller. However, the ferrofluid was controlled to flow into the low sweep area, when the magnetic field was applied during the ferrofluid flooding process, leading to the displacement of most amount of the oil.

Figure 9 The saturation distribution at different injection volume during water flooding and ferrofluid flooding process; (a)-(a”) respectively show the water saturation distribution at 0.25 VP, 0.75 VP, 1.5 VP; (b)-(b”) respectively show the ferrofluid saturation distributionat 0.25 VP, 0.75 VP, 1.5 VP
Figure 9

The saturation distribution at different injection volume during water flooding and ferrofluid flooding process; (a)-(a”) respectively show the water saturation distribution at 0.25 VP, 0.75 VP, 1.5 VP; (b)-(b”) respectively show the ferrofluid saturation distributionat 0.25 VP, 0.75 VP, 1.5 VP

As seen above, using ferrofluid with external magnetic field for flooding can expand the sweep area and enhance the displacement efficiency. Thus, the recovery ratio improved from 40% to 62% compared to water-flooding, as shown in Figure 10.

Figure 10 The production index curves of water-flooding and ferrofluid-flooding; (a) Water cut and ferrofluid cut curves; (b) Recovery curves of water-flooding and ferrofluid-flooding
Figure 10

The production index curves of water-flooding and ferrofluid-flooding; (a) Water cut and ferrofluid cut curves; (b) Recovery curves of water-flooding and ferrofluid-flooding

6 Conclusions

  1. In this paper, the potential application of using the ferrofluid as a new kind of displacing fluid for flooding in fractured porous media has been studied for the first time. Using the fully implicit finite volume method to solve mathematical model, the validity and accuracy of numerical simulation is demonstrated through an experiment, in which ferrofluid flows in a single fractured oil-saturated sand in a 2-D horizontal cell. At the end, the displacement effect between water flooding and ferrofluid flooding on a complex fractured porous media has been studied.

  2. The calculation results showed the magnetic force can control ferrofluid flow in desired direction. Therefore, when there is a high conductivity path, such as high permeability zone or fracture, using ferrofluid for flooding, one can raise the scope of the whole displacement. As a consequence, the oil recovery has been greatly improved compared to water flooding. Thus, the ferrofluid flooding is potentially a promising method for enhanced oil recovery in the future.

  3. In this paper, only 2-D problem was discussed. 3-D problem and multiphase problem are the next research projects.

Acknowledgement

The authors would like to express their gratitude to the National Natural Science Foundation of China (No. 51234007, 51490654, 51404292, 41502131) and The Fundamental Research Funds for the Central Universities (No. 16CX06026A) for their support.

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Received: 2016-10-27
Accepted: 2017-1-20
Published Online: 2017-6-16

© 2017 T. Huang et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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https://doi.org/10.1515/phys-2017-0041
Keywords for this article
ferrofluid flow; fractured porous media; discrete fracture model; numerical simulation; enhance oil recovery
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  197. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  198. What If Quantum Theory Violates All Mathematics?
  199. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  200. Relativity, anomalies and objectivity loophole in recent tests of local realism
  201. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  202. The photon identification loophole in EPRB experiments: computer models with single-wing selection
  203. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  204. Bohr against Bell: complementarity versus nonlocality
  205. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  206. Is Einsteinian no-signalling violated in Bell tests?
  207. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  208. Bell’s “Theorem”: loopholes vs. conceptual flaws
  209. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  210. Nonrecurrence and Bell-like inequalities
  211. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  212. Three-dimensional computer models of electrospinning systems
  213. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  214. Electric field computation and measurements in the electroporation of inhomogeneous samples
  215. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  216. Modelling of magnetostriction of transformer magnetic core for vibration analysis
  217. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  218. Comparison of the fractional power motor with cores made of various magnetic materials
  219. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  220. Dynamics of the line-start reluctance motor with rotor made of SMC material
  221. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  222. Inhomogeneous dielectrics: conformal mapping and finite-element models
  223. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  224. Topology optimization of induction heating model using sequential linear programming based on move limit with adaptive relaxation
  225. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  226. Detection of inter-turn short-circuit at start-up of induction machine based on torque analysis
  227. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  228. Current superimposition variable flux reluctance motor with 8 salient poles
  229. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  230. Modelling axial vibration in windings of power transformers
  231. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  232. Field analysis & eddy current losses calculation in five-phase tubular actuator
  233. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  234. Hybrid excited claw pole generator with skewed and non-skewed permanent magnets
  235. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  236. Electromagnetic phenomena analysis in brushless DC motor with speed control using PWM method
  237. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  238. Field-circuit analysis and measurements of a single-phase self-excited induction generator
  239. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  240. A comparative analysis between classical and modified approach of description of the electrical machine windings by means of T0 method
  241. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  242. Field-based optimal-design of an electric motor: a new sensitivity formulation
  243. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  244. Application of the parametric proper generalized decomposition to the frequency-dependent calculation of the impedance of an AC line with rectangular conductors
  245. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  246. Virtual reality as a new trend in mechanical and electrical engineering education
  247. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  248. Holonomicity analysis of electromechanical systems
  249. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  250. An accurate reactive power control study in virtual flux droop control
  251. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  252. Localized probability of improvement for kriging based multi-objective optimization
  253. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  254. Research of influence of open-winding faults on properties of brushless permanent magnets motor
  255. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  256. Optimal design of the rotor geometry of line-start permanent magnet synchronous motor using the bat algorithm
  257. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  258. Model of depositing layer on cylindrical surface produced by induction-assisted laser cladding process
  259. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  260. Detection of inter-turn faults in transformer winding using the capacitor discharge method
  261. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  262. A novel hybrid genetic algorithm for optimal design of IPM machines for electric vehicle
  263. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  264. Lamination effects on a 3D model of the magnetic core of power transformers
  265. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  266. Detection of vertical disparity in three-dimensional visualizations
  267. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  268. Calculations of magnetic field in dynamo sheets taking into account their texture
  269. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  270. 3-dimensional computer model of electrospinning multicapillary unit used for electrostatic field analysis
  271. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  272. Optimization of wearable microwave antenna with simplified electromagnetic model of the human body
  273. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  274. Induction heating process of ferromagnetic filled carbon nanotubes based on 3-D model
  275. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  276. Speed control of an induction motor by 6-switched 3-level inverter
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