Beyond Carbon Steel: Detecting Wellbore Shape and Cavities, and Cement Imperfections in Cased Wells

Abstract

The displacement of drilling fluid from high-angle and horizontal wellbores is complicated, and cement integrity is uncertain and often impaired [7]. [...]an exposed horizontal well casing may be subject to most of the corrosion mechanisms described above. Signals are obtained from a solution of the Helmholtz equation in cylindrical coordinates (r, φ , z): 1r∂∂rr∂Az∂r+1r2∂2 Az∂φ2+∂2 Az∂z2+k2 Az=0, Hz=k2 Az+∂2 Az∂z2,Hr=∂2 Az∂r∂z,Eφ=iωμ∂Az∂r, km2=-iωμm(σm-iωϵm), where Az is the vector potential; ω is the angular frequency; μm=μr,m μ0 , the magnetic permeability ( μr,m —relative, μ0 —permeability of vacuum, m–the layer index); σm is the electrical conductivity; and ϵm is the dielectric permittivity ( ϵm=ϵr ϵ0 , r—relative, 0—permittivity of vacuum). Since at low frequencies, the contribution of the dielectric constant is negligible, the relative permittivity of all layers is set to 1. In this case, there is no significant effect of the imaginary part of the magnetic field. [...]we propose the use of frequencies ranging from 0.1 to 10 kHz, typical of magnetic susceptibility logging. [...]short tools are more sensitive to the magnetic properties of cement. 3.1.

1. Introduction

According to the National Association of Corrosion Engineers ((NACE) https://www.nace.org/home), the total annual cost of corrosion in the oil and gas production industry is estimated to be $1.372 billion, broken down into $589 million in surface pipeline and facility costs, $463 million annually in downhole tubing expenses, and another $320 million in capital expenditures related to corrosion. As the oil and gas industry matures and it demands to sequester carbon dioxide at a massive scale, these corrosion costs may skyrocket. Luckily today, carbon steel casing tubulars can be replaced where appropriate with non-corrosive fiberglass composites.

Carbon steel casing corrodes quickly in a wet CO ₂ environment [1,2] encountered in carbon capture and storage (CCS) and in CO ₂ -based improved and enhanced oil recovery processes. If a casing cement annulus is faulty or breaks down, the carbon steel corrodes when exposed to concentrated formation brine.

Talabani et al. [3], Alcántara et al. [4], Sherar et al. [5], and Choi et al. [6] have found out that carbon steel casing may corrode by several mechanisms that act in series or in parallel. Most of these mechanisms are activated by the absence or imperfections of casing cement annulus or annuli for concentric casing strings.

1. Erosion corrosion = wear/abrasion occurs at the casing surface during drilling and/or insertion of casing. Salts and oxides deposit or form at the casing surface, increasing localized corrosion;

2. Hydrogen damage = hydrogen evolves on the cathodes on a chemically nonuniform steel casing and diffuses into the steel, leading to embrittlement and casing failure;

3. Biological corrosion = local colonies of bacteria change chemistry across some regions of a casing surface; for example, sulfate reducing bacteria (SRB) form H ₂ S that corrodes the steel;

4. Environmental corrosion = cement is absent and steel is exposed to concentrated chlorides in a formation brine or across overlying aquifers;

5. Galvanic corrosion = cement is absent and electrolyte is present between two dissimilar casings which connect electrically and one becomes the anode.

A special case is the corrosion of cased horizontal well laterals. The displacement of drilling fluid from high-angle and horizontal wellbores is complicated, and cement integrity is uncertain and often impaired [7]. Therefore, an exposed horizontal well casing may be subject to most of the corrosion mechanisms described above. In addition, with poor cement quality, horizontal well refracturing is problematic [8].

The evaluation of cement integrity is of primary importance to the oil and gas industry [9]. Poor cementation can lead to costly accidents and serious damage to the environment. According to a BP report [10], one of the reasons for the Macondo well blowout on 20 April 2010, was poor zonal isolation with a foam cement. Thus, cement placement and the evaluation of cement quality must both be improved. Magnetic particles are used in different applications. They enable various tasks to be performed remotely. In medicine, these particles are used for drug delivery systems, cancer diagnosis, or bioseparation [11]. In the oil industry, they are used for hydraulic fracture evaluation, EOR, and other applications [12]. The magnetorheological approach can be used to inject cement slurry uniformly into an annular space between the casing and borehole wall. Magnetic cement slurry can be displaced into regions where it would not otherwise flow when pumped conventionally [13]. Magnetic properties of cement change with time because of heating and aging. Electrical properties of a cement-based magnetorheological fluid differ from those of common cement. The presence of conductive particles increases the magnetic permeability of the cement [14] and, because of the proximity of the cement-filled annulus to casing, one can use the magnetic susceptibility logging method to determine cement quality. It is necessary to estimate the magnitude of the useful signal and quantify appropriate measurement methods. This leads to an accuracy assessment of the sensors or magnetometers that should be installed in the magnetic cement sensing tool. A thorough analysis of the available sensors and frequency ranges helped us compile Figure 1. Measurement of electromagnetic fields for geophysical purposes covers a wider range than those required by most of the other fields. For example, when performing cross-well EM exploration, the noise level was estimated as 0.5×^10-5 nT [15]. The magnitudes of magnetic fields used in cardiac or brain medical research are also very small and require precise and expensive equipment. We do not need such a high accuracy for assessing the quality of magnetic cement as flux-gate magnetometers, Hall-effect sensors, or solenoid type sensors are quite sufficient.

Measuring electrical properties through casing was a great challenge in the second part of the last century. The complex effects of casing were captured long ago and solutions were found [16,17], providing two methods of logging in cased wells. Due to the high conductivity of steel casing relative to the surrounding formation, the expected measurements are to be made in the nanovolt range [18]. Technical and computing capabilities of the industry in the 1940s were insufficient for such precise measurements. Kaufman [19] developed a theory of measuring formation resistivity in a cased borehole with a sufficient accuracy for practical applications. Schlumberger has implemented the theory and provides the formation resistivity log in a cased borehole called CHFR [18,20]. This log takes about 12 h to run, with each measurement consuming about 2 min. There are theoretical preconditions for logging through the casing on the basis of magneto-acoustic effects [21,22]. It is proposed to estimate electrical properties from an acoustic signal generated by a sensor responding to acoustic waves at a metal surface in communication with an earth formation. The metal surface is exposed to a constant magnetic field normal to it and a harmonic magnetic field of variable frequency along the surface. Further development of this method requires additional laboratory experiments.

Existing methods of estimating electrical properties behind casing are not suitable for the assessment of electrical properties of cement. These methods evaluate the integral electrical formation properties at a distance away from the casing or are currently underdeveloped. In this paper, we propose a tool to measure and control the integrity of a weakly magnetic cement behind non-conductive fiberglass casing. The objective is to verify cement quality in a borehole environment by computing the tool parameters such as distance between coils and operating frequencies. Borehole environment is magnetized by a low frequency induction tool. Measurements can be made with a set of coils or sensors. The alternating magnetic field provides necessary noise immunity for logging and excludes the influence of the geomagnetic field [24]. Significant work has been devoted to studying the influence of borehole media’s electrical properties on electromagnetic logging signals, for example the dielectric permeability and its distribution [25], or change of electrical resistivity of the invaded zone [26]. The effect of magnetic permeability on the inductive response has been studied for metal detector applications [27] and logging applications [28,29]. However, cement detection and the measurement of cement integrity have not been studied sufficiently for weakly magnetic cements. Here we focus on detecting small changes in the magnetic permeability of a cement-filled annulus behind a non-conductive casing.

2. Theory and Method

To simulate magnetic susceptibility logging, we solved the Maxwell equations of electromagnetism [30] in cylindrical coordinates. Transmitter coil generates a primary magnetic field that produces an eddy current in the formation, see Figure 2. The primary and secondary magnetic fields induce an electromotive force in the receiver coil. Only the vertical component, _Hz , of the magnetic field is considered. Key model assumptions are:

1. The system consists of 4 concentric cylinders—wellbore, casing, cement, and formation – with constant electrical properties along the z-axis;

2. All layers are isotropic and homogeneous;

3. The wellbore is an infinite column of liquid and its axis coincides with the common axis of all cylinders;

4. Coil axes coincide with the wellbore axis, and;

5. Compared with the tool size, coils are small and can be approximated by point dipoles.

Signals are obtained from a solution of the Helmholtz equation in cylindrical coordinates (r, φ , z):

1r∂∂rr∂_Az∂r+1^r2∂2 _Az∂^φ2+^∂2 _Az∂^z2+^k2 _Az=0,

_Hz=^k2 _Az+^∂2 _Az∂^z2,_Hr=^∂2 _Az∂r∂z,_Eφ=iωμ∂_Az∂r,

^_km2=-iω_μm(_σm-iω_ϵm),

where _Az is the vector potential; ω is the angular frequency; _μm=_{μr,m μ0} , the magnetic permeability ( _μr,m —relative, _μ0 —permeability of vacuum, m–the layer index); _σm is the electrical conductivity; and _ϵm is the dielectric permittivity ( _ϵm=_{ϵr ϵ0} , r—relative, 0—permittivity of vacuum). Since at low frequencies, the contribution of the dielectric constant is negligible, the relative permittivity of all layers is set to 1.

The vector potential in the wellbore is:

_Az,1(r,z)=M4π^e-i_k1RR+2π_{∫0∞ C1 I0}(_λ1r)cosλzdλ,

_λm=^λ2+i_{σm μm}ω,R=^r2+^z2>0.

Here M is the magnetic moment of the coil; λ is the separation variable; r the radial distance; z the axial distance; _k1 is the wave number corresponding to the borehole; and _C1 is a constant that carries information about the borehole environment and is obtained from the boundary conditions that require the continuity of the tangential components of the electric, _Eφ , and magnetic, _Hz , field. Using these conditions, we solve a system of linear Equation (2). The solution allows us to determine the distribution of the electromagnetic field in the wellbore and translate this field into measured signals.

The measured signals are the phase, _φm , and the amplitude, _Am , of the electromotive force induced by the magnetic field in the receiving coil:

a=Re(_Hz),b=Im(_Hz),

_φm=arctanba,_Am=^a2+^b2.

The logging signals are often displayed in apparent resistivity that itself is a well-known physical property of the rock. In Section 3.3 we show that measuring apparent resistivity allows us to detect cement solidification using a 200 MHz induction tool. We use a homogeneous medium approximation to calculate the apparent electrical resistivity from signal amplitude. The apparent resistivity calculation algorithm was described in [31]. There are many ways to transform signals into apparent resistivities, e.g., the pallet method, optimization methods, and asymptotic formulæ. To convert signals into apparent resistivities, we chose the Newton method for efficiency. A good initial guess is necessary to ensure convergence in a small number of iterations when using this method. The exact formulæ for calculating induction logging signals, Equation (7), have been transformed, and a good initial guess has been constructed. The apparent resistivity calculation algorithm used here is accurate to at least six significant digits.

The electrical properties of the media are listed in Table 1. Wellbore, which passes through a carbonate formation, was filled with a fresh water-based mud. The well was cased with a fiberglass casing. The magnetic permeability of cement depends on the concentration of iron powder in it. Using an analytical solution, we varied the frequency, f, magnetic moment of the source, M, the electrical conductivity of the drilling mud and the surrounding rock, σ , and the magnetic permeability of cement, μ . The magnetic permeabilities varied between 1 and 2. This variation corresponds to the magnetic particle content from 0% to 15% as a volume fraction, according to [32]. In addition, we varied the distance between the receiver and the source, z, in order to choose the most optimal configuration of the magnetic logging tool.

We have confirmed the analytical solution by the finite element method using COMSOL Multiphysics^® 5.2. Unlike the analytical solution, in which there are no boundaries perpendicular to the wellbore, COMSOL allowst the study of the influence of such heterogeneities on the logging signals. We considered various logging scenarios detailed in Section 3.3: Incomplete lift of cement, cement debonding, cavities, fractures, and other inhomogeneities. We used parameters from Table 1 and varied the position of the transmitter by a step of 1 cm down the wellbore. The distance between the transmitter and receivers remains unchanged.

Apparent Magnetic Permeability

Our calculation of apparent magnetic permeability is based on the assumption of the medium’s homogeneity. A change in the real part of magnetic field is proportional to the change of medium’s magnetic permeability. It is worth describing the calculation of geometrical and demagnetization coefficients, as they determine the conditions of measurements. In a homogeneous environment, these coefficients are expressed as [24]:

G^æ′=_ξz,s+_ξz,pξz,p,^æ′=^æ′(1+Næ).

Here ^æ′ is the apparent magnetic susceptibility, ( _μapparent=1+æ ); G, the geometrical coefficient; ξ , the electromotive force; N, the demagnetization factor; and p and s denote the primary and secondary field indices. The imaginary part for the preferred frequency range in Figure 3 is negligible when compared with the real part. In this case, the amplitude is equal to the modulus of the real part of the magnetic field, see Equation (7).

Magnetic susceptibility can be expressed as:

æ1+Næ=_ξz,s+_ξz,pG_ξz,p,ξ=iωμσ_Hz.

where æ is the magnetic susceptibility of the medium. From a general solution of the boundary value problem, and in accordance with Equation (8), we obtain the geometrical and demagnetization coefficients:

G=limæ→0_ξz,s+_ξz,pæ_ξz,p,N=G_ξz,pξz,s+_ξz,p-1æ.

These coefficients can be calculated from experimental data by solving a system of linear equations:

_ξz,s+_ξz,pæ_ξz,p(1+N_æi)=G_æi,i=1,2,…

Here i is the subscript of the medium with the magnetic susceptibility _æi .

3. Results

To understand the signals that should be used to extract magnetic properties of a composite medium, it is necessary to analyze the magnetic field itself, as well as the response of the medium under study. We assume that the tool is properly calibrated, i.e., the primary magnetic field has been excluded from the measurements. Figure 3 shows that the real part of the secondary field, _Hz,s , is three orders of magnitude stronger than the imaginary part. Smaller spacings between coils enhance the detection of the magnetic permeability of the cement and the distance between the coils ought to be 25–60 cm (dashed line) to optimize this detection.

We have modeled the magnetic tool responses to changes in the drilling fluid resistivity, formation resistivity, cement hardening, and magnetic permeability of the cement (amount of magnetic particles). The amount of magnetic powder in the cement has a strong influence on the real part of the secondary field, _Hz,s , i.e., useful information about cement integrity can be extracted from it. Curves for the different resistivities of cement, mud, and formation overlap. Changes in the frequency of the transmitter coil in the lower part of the kHz range do not significantly affect the real part of _Hz,s . At the same time, changes in frequency affect the imaginary part of _Hz,s more strongly in the upper kHz range. With an increasing frequency, the amplitude of the imaginary part of _Hz,s grows and becomes the same order as that of the real part. To simplify measurements and processing, we suggest using the lower part of the kHz range. In this case, there is no significant effect of the imaginary part of the magnetic field. Therefore, we propose the use of frequencies ranging from 0.1 to 10 kHz, typical of magnetic susceptibility logging. A typical pattern of _Hz,s vs. tool length is presented in Figure 3.

Figure 4 shows that the signal amplitude is suitable for extracting magnetic properties of cement. Simulation results presented in Figure 3 and Equation (7) support this conclusion. The signal amplitude is insensitive to cement resistivity, i.e., to cement rheology in the frequency range from 0.1 to 10 kHz. Signal simulations for different configurations of borehole geometry show that the singularities of the signal phase are caused by the magnetized cement and its distance from the measurement point.

Apparent magnetic permeability in Figure 5 differs from the actual permeability of magnetic cement because only a part of the medium is magnetic. In Figure 4b, the apparent magnetic permeability has been calculated from the signal amplitude. Finally, short tools are more sensitive to the magnetic properties of cement.

3.1. Sensing Solidification of Concrete

It is known that the electrical resistance of cement depends on the degree of its solidification. The electrical resistivity of cement grows as it solidifies [33]. The rate of resistivity increase depends on water fraction in the cement paste or foam, water conductivity, and other parameters. These questions go beyond our research objectives, because here we only need to know the aggregate state of cement. For simplicity, it can be said that the cement paste has an electrical resistance below 5 Ohm·m. Cement with a resistivity >50 Ohm·m might be considered solid. It reaches this resistance in several hours and with time the resistance slowly grows [34]. This raises the following question: How can one detect a relatively conductive cement-filled annulus behind a non-conducting casing? Methods for measuring DC resistance are not suitable for this task. Fiberglass casing is a resistor and current will not flow through it. To measure cement resistance, one can use a high frequency induction method. The high frequency EM field weakly damps in the insulator and penetrates into the cement annulus. The best results can be achieved by pressing the tool against the casing wall. This is necessary to minimizes signal losses in drilling mud.

The imaginary part of the magnetic field intensity detects changes of cement resistivity. Figure 6 shows the imaginary part of the secondary magnetic field versus distance between the transmitter and receiver. The source is a point dipole oscillating at the frequency of 200 MHz. The geometric and electric parameters are listed in Table 1. The relative magnetic permeability of the cement is 1.5. In this case, a two-coil tool and a three-coil tool can be used. It is recommended that tools with a separation between coils ranging from 0.3 to 0.4 m are used. We conclude that soft cement can be detected at a high frequency.

3.2. The Analytic Solution Versus the Finite Element Method

COMSOL software calculations and analytic solutions were identical, see Figure 7a. We considered a point magnetic dipole, oscillating at the frequency of 1 kHz. The dipole was located at the origin, the length of the well was 3 m, the diameter of the model was 3 m, and the geometric and electrical parameters of the model are from Table 1. The nonuniform mesh parameters used in the modeling are: the maximum element size =1 cm and the minimum one =8×^10-5 m. Maxwell’s equations are solved in the frequency domain, and the number of degrees of freedom is 1,199,956. The external boundary is assumed to be a magnetic and electric insulator. Due to the short length of the probes relative to the model size, the influence of the external boundary can be neglected. Simulations were carried out in two environments to obtain the secondary magnetic field, i.e., air and the medium under study. The response in the air was subtracted, i.e., the tool response was calibrated. The signals were calculated using Equation (7). The signals computed with the finite element method were less smooth than those from the analytical calculations. Despite the very fine mesh, the COMSOL-computed signals were rough, see Figure 7a. Increasing the element sizes further reduced the accuracy of the calculation. The magnetic field strength scale was amplified in Figure 7b to improve visualization of the field distribution. Relative to a non-magnetic medium, a magnetic cement with μ = 2 is practically a “magnetic conductor”.

3.3. Logging Signal Modeling

To test the technology being developed, we performed numerical testing of magnetic logging for five scenarios: (1) Incomplete lift of cement, (2) cavity, (3) crack filled with magnetic cement, (4) 2 cm cement debonding, and (5) progress of cement solidification along the borehole. The 2D axisymmetric simulations were performed using the AC/DC module in COMSOL. The source of electromagnetic waves was a point dipole with the magnetic moment = 1 A·m ² . The dipole oscillates was at the frequency of 1 kHz for scenarios 1–4. The magnetic moment was 0.1 A·m ² and the frequency was 200 MHz for the 5th scenario. Probes with the lengths of 30, 35, 40, and 50 cm passed through a wellbore interval with inhomogeneities. The geometric and electric parameters are listed in Table 1. The relative magnetic permeability of the cement was 1.5. Response in the air was subtracted. For the 5th scenario, six different cement resistivities were used to depict its solidification: 1, 5, 20, 50, 100, and 1000 Ohm·m. In this case, cement tubes that were 1 m high lay on top of each other, and the space above 1 Ohm· m tube was filled with air. For the cement solidification state, an additional 25 cm long tool was considered because at high frequencies the skin depth, (δ=2σμω , σ being the electrical conductivity) significantly decreased.

Figure 8a,b show that an incomplete rise of cement could be determined by an abrupt decrease of amplitude of the secondary magnetic field. Figure 8c,d and Figure 9a,b demonstrate that the proposed tool was capable of detecting cement inhomogeneities and it was more sensitive to the near wellbore region. The shape and intensity of magnetic logging curvesweare determined by the shapes of heterogeneities filled with cement. Cement adjacent to the well casing generated the strongest tool response. An absence of cement resulted in a sharp decrease of magnitude of the secondary magnetic field observed in Figure 9c,d.

When logging at 200 MHz, see Figure 10 and Figure 11, one can observe a stair-step change of the real and imaginary part of _Hz,s . It is important to note that in this particular case, magnitudes of the imaginary and real parts of _Hz,s were very close and the stair-step changes were opposite for both components. Figure 11 shows that we can easily distinguish a “liquid” cement (1–5 Ohm·m) from a “solidified” cement (50 Ohm·m and more). It is impossible to distinguish a 50 Ohm·m layer from a 100 Ohm·m one, but a trend of solidification can be observed. Short tools are more sensitive to the wellbore and measured the lowest resistivities. Longer tools better sensed the near-wellbore space. Due to the special nature of the electromagnetic field and model complexity, the electrical resistances calculated from the phase, Figure 11b, and amplitude, Figure 11c, differed significantly. For a better display, Figure 11b is plotted as dots because the boundary-related singularities in the resistivity log obtained from the signal phase obscure the tool responses. However, compared with the amplitude, the signal phase was more sensitive to the cement solidification state. The effect of surrounding layers was more significant for the graph generated from amplitude rather than those from the signal phase.

Simulations show that the zones with insufficient cementing could be easily determined using the proposed tools, a high-frequency induction tool could be used to distinguish between the zones of “solidified” and “liquid” cement.

3.4. Detection of Radial Inhomogeneities

Magnetic logging signals were simulated to study the possible detection of radial inhomogeneities: (1) The eccentricity of the cement, and (2) a crack filled with the magnetic cement. The 3D simulations were performed using the AC/DC module in COMSOL. The model was a 1.5 m long cylinder with a diameter of 1.5 m. The complete mesh consisted of 1,387,193 domain elements, 65,048 boundary elements, and 2327 edge elements. The average element quality was 0.7679. The source of electromagnetic waves was a point dipole with the magnetic moment of 1 A·m ² , oscillating at the frequency of 1 kHz in the middle of the borehole. The external boundary was assumed to be a magnetic and electric insulator. The distances between the transmitter and receivers were 30, 35, 40, and 50 cm. The influence of the outer boundary was neglected. The magnetic field was registered by 12 sensors evenly distributed inside the casing, see Figure 12 and Figure 13. The geometric and electric parameters are listed in Table 1. The relative magnetic permeability of the cement was 1.5. The tool response was calibrated by subtracting the system response in the air. Figure 12 shows that an asymmetric distribution of magnetic cement can be detected by the proposed tool. Figure 13 shows that a small radial crack filled with cement was invisible to the tool. The distance to the crack was too large and the contribution to the signal from the anomaly was less than the tool’s measurement error. However, insufficient cementation near the casing could be detected with magnetic logging signals.

4. Conclusions

We optimized an induction logging tool for testing the integrity of a weakly magnetic cement behind a non-conductive casing. Tools with the lengths of 0.25–0.6 m were most sensitive to magnetic cement properties. The real part of the secondary magnetic field, _Hz,s , was more sensitive to magnetic cements than the imaginary part. The most suitable frequencies for magnetic cement detection were in the range of 0.1 to 10 kHz, typical of magnetic susceptibility logging. Amplitude could be used to infer the integrity of the magnetic cement behind the casing, but to obtain information about cement rheology, it was necessary to perform the high-frequency resistivity measurements. Logging at 200 MHz distinguished solid cement from liquid and quantified the cement solidification state. Signal phase at a high frequency was more sensitive to cement solidification, rather than amplitude. Cavities and cracks filled with magnetic cement were visible on the logs. The proposed tool could be used for the determination of the zones of cement debonding. Casing eccentricity and radial inhomogeneities could be detected using the radially distributed sensors. The absence of cement caused a sharp decrease of the magnitude of the secondary magnetic field. The magnetic logging technology proposed in this paper could be used to check cement quality in moderate temperature wells (<150 ^∘ C). The proposed method could determine poor zonal isolation and cement hardening.

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Parameter	Wellbore	Fiberglass Casing	Cement	Formation
Radius, m	0.07	0.10	0.15
Resistivity,Ω·m	2	108	100	50
Magnetic permeability	1	1	1, 1.25, 1.5, 2	1

Author Contributions

Methodology development, computation, data processing, visualization, writing-original draft preparation-T.E.; conceptualization, project administration, review and editing-T.W.P.

Funding

Timofey Eltsov was supported by the KAUST Magnetic Sensor project.

Acknowledgments

We are grateful to COMSOL Multiphysics® for providing the academic software license.

Conflicts of Interest

The authors declare no conflict of interest.

Abbreviations

AC Alternating current

CCS Carbon Capture and Storage

CHFR Cased-hole formation resistivity

DC Direct current

EM Electro-magnetic

EOR Enhanced oil recovery

Imag Imaginary part

SRB Sulfate reducing bacteria

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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