Jun 17, 2017 - Evaluation in Baker Hughes, Inc. supporting Drilling. Systems, Wireline Systems, and Drill Bit divisions. Currently, he has responsibility over ...
SPWLA 58th Annual Logging Symposium, June 17-21, 2017
INVERSION OF DIELECTRIC LOGGING USING MIXING MODEL AS A REGULARIZATION FUNCTION Babak Kouchmeshky, Baker Hughes, Alberto Mezzatesta, Baker Hughes, Roberto Arro, Baker Hughes, Otto Fanini, Baker Hughes
Copyright 2017, held jointly by the Society of Petrophysicists and Well Log Analysts (SPWLA) and the submitting authors. This paper was prepared for presentation at the SPWLA 58th Annual Logging Symposium held in Oklahoma City, Oklahoma, USA, June 17-21, 2017.
regularization of the petrophysical parameters, and structure the electromagnetic properties of the formation using mixing models.
ABSTRACT
In order to compare the two inversion methods, their performance is put into test using an example. For a realistic example experimental data on dispersive electromagnetic properties of a core is used. The experimental real and imaginary part of dielectric dispersion are further used to obtain the relative magnitude and phase of an electromagnetic wave travelling in the formation and picked up by two receivers. This synthetic tool response is then perturbed by noise. Monte Carlo method is used to study the effect of the noise on the inverted petrophysical properties of the formation. The probability distribution of the inverted petrophysical parameters obtained from the noisy data using two different inversion methods are compared to each other. It is shown that the proposed method is more tolerant to the noise, and provides a probability distribution for each petrophysical parameter that leads to an expected value for these parameters that is very close to the actual values set in the lab, and also results in a much smaller standard deviation in comparison with the classical inversion method.
Dielectric log can be used to obtain petrophysical properties of a formation like water saturation, water resistivity at DC, and formation texture. Dielectric tool operates at a wide frequency range from a few MHz to 1 GHz. Since the gathered data is inevitably contaminated with noise, studies that quantify the effect of noise on the interpretation of the dielectric log are very useful. This work provides an overview of inversion methods used for interpretation of dielectric log. First the classical method of inversion is introduced in which the task of quantifying petrophysical parameters is divided into two steps. The first step involves inverting for the electromagnetic properties of the formation (permittivity and conductivity) from magnitude and phase of electromagnetic wave recorded at the receiver. These electromagnetic properties are obtained for each frequency of operation to obtain their variation with respect to frequency (dispersion). It is this dispersive behavior of permittivity and conductivity that is used in the second step to obtain petrophysical properties of the formation. For this step, valid mixing models are required to relate petrophysical parameters of formation and dispersive electromagnetic properties. It is shown that the presence of noise in the data can lead to ill-posed inverse problems where multiple answers can be present.
INTRODUCTION Dielectric log can provide invaluable information on the petrophysical parameters of a formation. It measures the magnitude and phase of the electromagnetic wave propagating through the formation. This data is used to infer electromagnetic properties of a formation (Cox and Warren 1983, Rau et. al. 1991, Hizem et. al. 2008). Usually the magnetic permeability is assumed to be that of vacuum (μr = 1) while the relative permittivity is generally a complex value and is related to the real permittivity and conductivity of a formation through the following equation.
In order to avoid having an ill-posed inverse problem, use of regularization method is suggested. An inversion methodology is proposed that combines the two steps of inversion into one. In doing so, only one inversion problem needs to be solved that directly obtains the petrophysical parameters. It is shown that the new inversion method can seamlessly take advantage of the 1
SPWLA 58th Annual Logging Symposium, June 17-21, 2017
ε̃r (ω) = ε′r (ω) + iε′′ r (ω) = εr (ω) + i
σ(ω) ωε0
and receivers where investigation are studied.
(1)
where ε̃r is the complex value representing relative permittivity, εr is the real part of relative dielectric property, σ is electrical conductivity, ω is angular frequency, and ε0 is dielectric constant of vacuum.
multiple
depths
of
The structure of the paper is as follows. First, two different inversion methods for interpretation of dielectric log are explained in detail. The differences between the two methods are highlighted, emphasizing the advantage of onestep inversion method in incorporating regularization. Next, these two methods are applied in an example with synthetic data perturbed by noise. Finally, the ability of the methods to provide accurate petrophysical parameters from a noisy input data is discussed.
The electromagnetic properties of the formation exhibit a variation with respect to frequency that is called dispersion. It is this dispersive behavior that can be used in inferring petrophysical properties of a formation. Dielectric log uses contrast in the permittivity of water and the other elements present in the formation to obtain information on water saturation, water resistivity at DC, and formation texture. Dielectric log interpretation provides an advantage over traditional resistivity logging in formations where the water resistivity is unknown or varies significantly over short distances.
TWO-STEP INVERSION METHOD In this method the inversion of dielectric log is divided into two steps (Hizem et. al., 2008). The first step involves inverting for the electromagnetic properties of the formation, namely permittivity and conductivity, using the magnitude and phase response of the tool. The inversion is done at multiple frequencies. At each frequency the output of inversion is permittivity and conductivity of the formation. This step can be summarized by the following equation.
The accuracy of the petrophysical parameters obtained from this log is affected by noise level. The aim of this paper is to study the possibility of increasing the noise tolerance by modifying the inversion methods. The current paper addresses the effect of noise in the recorded dielectric log data on the inverted petrophysical parameters. The existence of noise in the recorded data leads to an ill-posed inverse problem. In order to address this problem and make the inverse problem at hand more tolerant to noise, usually some sort of regularization is performed.
𝑎𝑟𝑔𝑚𝑖𝑛𝜀𝑟(𝜔),𝜎(𝜔) ‖𝑴(𝜔) − 𝒇(𝜀𝑟 (𝜔), 𝜎(𝜔))‖2
(2)
where ‖. ‖2 is ℓ2 norm, M is a vector containing the measured magnitude and phase at each frequency, and f is a vector containing the calculated magnitude and phase at each frequency as a function of permittivity, ε, and conductivity, σ, of formation. Usually constraints are added to the inversion such that the obtained values for permittivity and conductivity have the following conditions.
Two different inversion methods are presented in this paper. The major difference between the methods is reflected in their ability to take advantage of the regularization methods and hence their tolerance to the level of noise. The first method presented is the classical method used in inversion of dielectric log (Hizem et. al., 2008). This method divides the task of inversion into two steps. The first step inverts for electromagnetic properties of the formation using the recorded relative magnitude and relative phase of electromagnetic wave. The results of this step at different frequencies are used as an input to the second step of inversion where petrophysical properties are obtained. The second method combines these two steps into one and in the process enables the use of regularization leading to an inversion problem that is more tolerant to noise level. It should be noted that the methods deployed in this paper can be easily applied to an array distribution of sensors with multiple transmitters
𝜀𝑟 (𝜔) > 1 , 𝜎(𝜔) > 0
(3)
Collecting the inverted electromagnetic properties of formation at multiple frequencies results in a dispersive relation obtained for both permittivity and conductivity. This dispersive relation is used as the input for the second step of inversion where the petrophysical properties of formation are obtained as follows 𝑎𝑟𝑔𝑚𝑖𝑛𝑿 ‖𝑷 − 𝒈(𝑿, 𝜑)‖2
(4)
where P is a 2 × N vector with N being number of 2
SPWLA 58th Annual Logging Symposium, June 17-21, 2017
recorded frequencies and contains permittivity and conductivity obtained for each frequency from the first step
petrophysical parameters.
𝑷 = [𝜀𝑟 (𝜔1 ), 𝜎(𝜔1 ), 𝜀𝑟 (𝜔2 ), 𝜎(𝜔2 ), … , 𝜀𝑟 (𝜔𝑁 ), 𝜎(𝜔𝑁 )]
Prior knowledge about formation or petrophysical values obtained from adjacent depth can be used in selecting values for elements of X0 . It should be noted that selecting a large value for α would lead to an optimal value of X satisfying above equation that is very close to X0 . Conversely, selecting a very small value for α reduces the effect of regularization and results in the optimal value of X satisfying only the noisy data presented in P (Eq. 5).
𝑿0 = [𝜀𝑚0 , 𝜎𝑤0 , 𝑆𝑤0 , 𝑅𝑎𝑏0 ]
(5)
Alternatively, X is a vector containing petrophysical parameters of the formation. These properties include water saturation, Sw , water conductivity at DC, σw , relative permittivity of dry rock, εm , and in more detailed models, the texture of formation is included as aspect ratio of inclusions, R ab . As it can be seen porosity, φ, is also needed but not included as a parameter of inversion as it needs to be measured independently from other logging tools. If porosity is included as a parameter of inversion for dielectric log, it can lead to an ill-posed problem as shown by Kouchmeshky and Fanini (2016 a). In Equation 4, g is a 2 × N vector that contains permittivity and conductivity values calculated for a formation with petrophysical parameters X and following a predetermined mixing model. For calculating the elements of vector g from petrophysical parameters represented by vector X and porosity φ knowledge of the mixing model appropriate for the formation is required. This information can be obtained through lab measurement on rock cores from the formation under study. As shown by Kouchmeshky et. al. (2016 b) using the quality of fit to logged data at frequency range of operation for dielectric tool is not sufficient as an indicator to choose the appropriate mixing model. For a better judgment on the performance of a mixing model, access to a wider frequency range through lab measurements is required. The inversion in the second step is subjected to the following constraints 𝜀𝑚 > 1 , 𝜎𝑤 > 0, 0 ≤ 𝑆𝑤 ≤ 1
One drawback of this method of inversion is that separate inversions are needed for the aforementioned steps. This can lead to less noise tolerance as the inherent errors associated with numerical convergence of multiple inverse problems add up. As noted, the results of first step above are electromagnetic properties at different frequencies that will be used for the inversion problem in the second step. As such, no regularization at the first step is recommended because enforcing any arbitrary regularization function at step 1 would effectively alter the shape of dispersive function, representing variation of electromagnetic properties with respect to frequency. It is precisely this dispersion function that is used in the second step to obtain petrophysical properties. The most natural choice for regularization function for the first step would be the same mixing model that is used in the second step. The difficulty with this approach is that to be able to use the mixing model one would require determination of the petrophysical properties which are only taken into account in the second step of inversion. Following this discussion, we propose a one-step inversion method for dielectric logging in the following section.
(6)
In reality, the collected data is subjected to noise. This can lead to an ill-posed inversion problem. In order to avoid this scenario, regularization methods are typically used. Inversion for the second step can be modified to include regularization of the petrophysical parameters as follows 𝑎𝑟𝑔𝑚𝑖𝑛𝑿 (‖𝑷 − 𝒈(𝑿, 𝜑)‖2 + 𝛼‖𝑿 − 𝑿0 ‖2 )
(8)
ONE-STEP INVERSION METHOD As discussed in the previous section, the presence of noise in collected data makes application of regularization methods very appealing. These methods increase the tolerance to noise and ensure unique answers to an otherwise ill-posed inverse problem. We saw in the previous section that the natural choice for regularization functions for the first step of inversion, was the same function used
(7)
where α is the regularization coefficient and X0 is a vector that contains expected values of 3
SPWLA 58th Annual Logging Symposium, June 17-21, 2017
as mixing model for the second step. This led to the following procedure for the inversion 𝑎𝑟𝑔𝑚𝑖𝑛𝑿 (‖𝑴∗ (𝝎) − 𝒉(𝑿, 𝜑, 𝝎)‖2 + 𝛼‖𝑿 − 𝑿0 ‖2 )
conductivity values is needed. The petrophysical parameters obtained from the inversion can be used with the selected mixing model to generate the electromagnetic properties of the formation (dispersive relation).
(9)
where h is a 2 × N vector that contains the calculated magnitude and phase at each frequency, M ∗ is a 2 × N vector that contains the measured magnitude and phase for all frequencies present in vector ω = [ω1 , ω2 , … , ωN ], vector X contains petrophysical parameters of formation, φ is porosity, vector X0 contains expected values of petrophysical parameters and α is the regularization coefficient.
It should be noted that prior knowledge on the formation or lab studies on the cores obtained from formation may indicate that more than one mixing models are applicable. In that case, both two-step and one-step inversion methods can be repeated for allowable choices of mixing model, and the best fit to the recorded data can be selected to represent the formation.
In calculating the elements of vector h the following steps should be taken. First, a predefined mixing model is chosen. Then, the petrophysical parameters assigned to vector X and porosity, φ, are used to find permittivity and conductivity of formation at angular frequencies in ω. The result is the electromagnetic properties of the formation represented as a dispersive relation for permittivity and conductivity calculated for the petrophysical parameters, X. These electromagnetic properties are then passed to the forward model that predicts the behavior of the tool in the formation. This can be a model that simplifies the transmitters and receivers as dipoles and assumes the formation to be homogenous, or it can be a more detailed model taking into account the effect of finite size of the sensor, borehole effect, etc. Using the predicted electromagnetic properties of the formation as inputs to the forward model, leads to calculating values for the tool response in the format of relative magnitude and phase for each frequency. The resulting magnitude and phase populate the 2 × N elements of vector h.
EXAMPLE In this example synthetic data representing a noisy tool response in a formation with known petrophysical properties is used to study the performance of the two different inversion methods outlined in the previous sections. The petrophysical parameters obtained from the application of each of these two inversion methods are compared with the actual petrophysical parameters used to generate the tool response to compare the noise tolerance of each method. To make sure the data represent a realistic situation, experimental data on a rock core are used (Golikov et. al., 2015). Figure 1 shows the real and imaginary part of dielectric dispersion for a sandstone core at a wide frequency range. The core’s porosity was 19% and it was fully saturated with water. A fitted mixing model to the experimental data is also shown in the same figure. Our previous study (Kouchmeshky et. al. 2016b) on this core data showed that Maxwell-Garnett can be used as a mixing model that provides a good fit to the dispersive real and imaginary part of permittivity (or permittivity and conductivity) as well as an accurate estimation of water saturation and water resistivity at DC. Details on this mixing model are provided in the appendix. Hence, this mixing model is selected for the inversion in both of the methods used in the current example.
𝒉 = [𝑚𝑎𝑔𝜔1 , 𝑝ℎ𝑎𝑠𝑒𝜔1 , 𝑚𝑎𝑔𝜔2 , 𝑝ℎ𝑎𝑠𝑒𝜔2 , … , 𝑚𝑎𝑔𝜔𝑁 , 𝑝ℎ𝑎𝑠𝑒𝜔𝑁 ] (10)
where mag ωi and phaseωi are respectively the relative magnitude and relative phase between two receivers at frequency ωi . In this method the petrophysical parameters are directly obtained from one inversion. Reducing the number of inversion problems would increase the tolerance to noise. Additionally, the regularization can be easily applied on the petrophysical parameters and since the mixing models are used in the forward model to generate the electromagnetic properties of the formation from petrophysical properties, no extra regularization on the permittivity and
The dispersive electromagnetic properties of the formation are assumed to follow the results obtained from the core data. Next, the transmitters and receivers of the dielectric tool are simplified as perfect magnetic dipoles in a homogenous space with aforementioned electromagnetic properties. 4
SPWLA 58th Annual Logging Symposium, June 17-21, 2017
Using these assumptions, the tool response can be obtained from the following relation 𝐵𝑟2 𝐵𝑟1
𝑟
= ( 1) 𝑟2
3 𝑘𝑟 +𝑖 2 𝑘𝑟1 +𝑖
𝑒 𝑖𝑘(𝑟2−𝑟1)
The response of the tool at different frequencies from 20 MHz to 1 GHz are obtained from previous equation and subjected to noise as below.
(11)
where transmitter and receivers are represented by points in space, k = ω(με̃)0.5 is the complex wave number with ω as angular frequency and μ and ε̃ as magnetic permeability and complex permittivity respectively, rm is the magnitude of the vector 𝐫m connecting transmitter and receiver m, and Brm is the component of magnetic field along vector 𝐫m at receiver m. It is assumed that all transmitter and receivers can be represented by collinear points and that magnetic moments of transmitter and receivers are all parallel to the direction of vector connecting the transmitter and receivers, 𝐫m .
∗ = 𝑚𝑎𝑔 × (1 + 𝑢 ) 𝑚𝑎𝑔𝜔 𝜔𝑖 𝑖 𝑖
(12)
∗ = 𝑝ℎ𝑎𝑠𝑒 × (1 + 𝑣 ) 𝑝ℎ𝑎𝑠𝑒𝜔 𝜔𝑖 𝑖 𝑖
(13)
where mag ωi and phaseωi are the magnitude and phase of the tool at frequency ωi , while mag ∗ωi and phase∗ωi are the tool response perturbed by the noise. ui and vi are independent random variables representing the error associated with recording the tool response and follow a Gaussian distribution N(μ, σ) where μ = 0 and σ = 0.05. There are totally 2 × N independent random variables representing the noise E = [u1 , v1 , u2 , v2 , … , uN , vN ]. Monte-Carlo simulation was used to study the effect of noise on the inverted petrophysical parameters using the two inversion methods described in previous sections. 10000 realization of the vector E were used. For each realization, the perturbed tool response is calculated and used to obtain the inverted petrophysical parameters σw and Sw representing water conductivity and water saturation, respectively. Figure 2 shows the relative magnitude and phase between receivers as the tool response in a homogenous medium with electromagnetic properties shown in Figure 1. The perturbed response from a realization of random vector representing noise is also shown. As discussed before and observable from the figure, the elements of the random vector representing noise are independent from each other. Figure 3 shows the distribution of petrophysical parameters obtained from two-step inversion method. The actual value for the petrophysical parameters is shown as a dotted line. As it can be seen, the inverted petrophysical parameters with the highest probability, correspond to values that are far from the actual ones. In the case of the inverted water saturation, Sw , although the value corresponding to the highest probability matches the actual water saturation, the probability of finding an inverted water saturation that is far from its actual value is not negligible. As it can be seen, the two-step inversion method results are not satisfactory as it is not tolerant to the noisy tool
Figure 1, Experimental dispersive permittivity and fitted MG mixing model for a sandstone core. Top, real part of permittivity. Bottom, imaginary part of permittivity.
5
SPWLA 58th Annual Logging Symposium, June 17-21, 2017
response used in this example.
Figure 3, Inversion with 2 steps; Top, probability distribution of the inverted water salinity, ssw. Bottom, probability distribution of the inverted water saturation, Sw. Dashed line shows the actual petrophysical parameters.
Figure 2, Relative magnitude and relative phase measured at discrete frequencies. Both actual response (solid line) and a realization of perturbed response (dashed line) are shown.
Also, the inverted petrophysical parameters using the one-step method is displayed in Figure 4 where the location of actual petrophysical parameters is also demonstrated by a dotted line. It can be seen that the inverted petrophysical parameters with highest probability correspond to the actual petrophysical parameters. Furthermore, the probability of finding inverted petrophysical parameters far from actual parameters is small, as shown in Figure 4. Hence, it can be concluded that the one-step inversion method is much more tolerant to the error in the recorded tool response than the two-step inversion method.
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SPWLA 58th Annual Logging Symposium, June 17-21, 2017
step. The inversion in the second step provides petrophysical parameters of the formation. In doing so, petrophysical models (mixing laws) that relate the petrophysical parameters and electromagnetic properties of formation need to be validated by experimental results on cores. Appropriate constraints for the petrophysical parameters are also used in the inversion problem for the second step. Additionally, regularization of the solution to the inversion problem of the second step can be implemented using the prior knowledge obtained either from past experience or from values obtained from adjacent zones in the borehole. It should be noted that application of the regularization on the solution of the inversion problem in the first step is not recommended. The reason for this is that the outputs from the first inversion at different frequencies form a dispersive behavior and it is exactly this dispersive relation that is the subject of the inversion in the second step. Any attempt for arbitrarily regularizing the solution that alters the dispersive behavior of permittivity and conductivity can add unnecessary noise to the process and deteriorate the overall noise tolerance of the method. The only plausible method of regularizing the permittivity and conductivity as the solution of the inverse problem in the first step is to use the same validated mixing model that relates dispersive behavior of permittivity and conductivity to the petrophysical parameters of the formation in the inversion problem of the second step. However, since the application of the mixing model requires having the petrophysical parameters as the independent variables and they are not available for the inversion problem of the first step, these models cannot be used for regularizing the solution of the inversion problem in the first step.
Figure 4, Inversion with one-step using mixing model as regularization; Top, probability distribution of the inverted water salinity, ssw. Bottom, probability distribution of the inverted water saturation, Sw. Dashed line shows the actual petrophysical parameters.
DISCUSSION The goal of this paper is to increase the noise tolerance of the inversion method for dielectric logging. The existence of noise in the data can lead to an ill-posed inverse problem where the uniqueness of the solution cannot be guaranteed. In order to avoid this problem, regularization methods are usually incorporated into inversion. We have discussed two different inversion methods for dielectric logging. The first method divides the task of inversion into two steps. The first step uses the magnitude and phase of electromagnetic wave propagating in the formation to provide electromagnetic properties of formation at different frequencies through an inversion problem. The solution to inversion problems would be those values of permittivity and conductivity at each frequency that can reproduce the measured magnitude and phase of electromagnetic wave propagation in the formation. Appropriate constraints on the values of permittivity and conductivity are implemented to guarantee values for permittivity and conductivity that are physically plausible. The values obtained at the end of this step for permittivity and conductivity at different frequencies exhibit a variation with respect to frequency that is called dispersion. It is this dispersive behavior that would be the input to the inversion problem in the second
Drawbacks of the classical two-step inversion method for interpretation of dielectric log discussed in the previous section lead us to propose another approach for inversion problems. In the new method, only one inversion problem needs to be solved where the observable parameters in the inversion problem are the magnitude and phase of electromagnetic wave, and the solutions are the petrophysical parameters of inversion. The objective function is still the difference between measured and calculated magnitude and phase of electromagnetic wave, but 7
SPWLA 58th Annual Logging Symposium, June 17-21, 2017
the independent variables are the petrophysical parameters. In order to provide the relation between independent and observable variables, the forward model in this method is divided into two steps. The first step uses the validated mixing model to convert the petrophysical properties of formation to electromagnetic properties of formation, and the second step uses the electromagnetic properties of formation to calculate the magnitude and phase of electromagnetic wave. Since a mixing model is used to generate the permittivity and conductivity, at each frequency they follow the intended dispersive behavior. It should be noted that selecting the mixing model beforehand does not impose any drawback, as the classical two-step method of inversion also requires the selection of mixing model for the second step of inversion. In addition the fact that only one inversion problem needs to be solved rather than two, reduces the error associated with numerical convergence of the inverse problem, and requires less computational resources. The proposed method is also able to provide the dispersive conductivity and permittivity of the formation for the petrophysical parameters of inversion as they are calculated as part of the forward model used in the inversion. Finally, reducing the number of inversion problems to one imposes no drawbacks on the number of parameters used or the type of forward model implemented. For example, if properties of bore-hole fluid or geometric parameters of the formation are to be added as independent variables in the inversion, the process can be done seamlessly using the proposed method.
APPENDIX MAXWELL-GARNETT MODEL Maxwell-Garnett (MG) is based on how introduction of inclusions into a host material (background) would alter the distribution of electric field. The effective relative permittivity in Maxwell-Garnett model is calculated as below [Maxwell-Garnett, 1904, Sihvola et. al., 1989, Seleznev et. al., 2004]
ε̃f = ε̃b +
ε̃b 1 ∑ f (ε̃ −ε̃b ) ∑i=x,y,z 3 j j j ε̃b +Nij (ε̃j −ε̃b ) Nij 1 1− ∑j fj (ε̃j −ε̃b ) ∑i=x,y,z 3 ε̃b +Nij (ε̃j −ε̃b )
(A1)
Where index j is over the inclusion types, index i is for three principal axes, ε̃b is the permittivity of background, ε̃j is the permittivity of inclusions, f is volume fraction of inclusions and N is the depolarization factor that depends on the shape of the inclusions. It is assumed that the inclusions are dilute and they are homogenously distributed with random orientations. Assuming ellipsoidal shapes for the inclusions (with the main axes of a, b=c along local axes x, y and z respectively), the depolarization factors for inclusion j along principal axes can be written as
Naj =
Rab 2
∞
∫0 (s + R2ab )
−1.5
Nbj = Ncj = 0.5(1 − Naj )
CONCLUSION
(s + 1)−1 ds
(A2) (A3)
where R ab = a/b is aspect ratio of inclusion. The parameters for this mixing model are ε̃m , SW and σW , R ab .
Two different methods for inverting dielectric logging data are proposed. These methods take the relative magnitude and phase of an electromagnetic wave traveling in the formation and extract relevant petrophysical properties. The difference between methods is in their ability to include a petrophysically based regularization function in their search for the best parameters that could explain the observed response. The methods are applied to synthetic data perturbed by noise and the advantage of the method that includes the petrophysically based regularization (One-step method) is shown.
REFERENCES Cox P.T., Warren W.F., “Development and testing of the Texaco dielectric log”, SPWLA 24th annual logging symposium, 1983 Golikov, NA, Elcov, T.I., Melkozerova, S.N., Novikov,I.V., “Measurement of complex dielectric permittivity of fluid-saturated rock samples“, Internal report from Trofimuk Institute of 8
SPWLA 58th Annual Logging Symposium, June 17-21, 2017
Petroleum Geology and Geophysics at Siberian Branch of the Russian Academy of Sciences, 2015
Evaluation in Baker Hughes, Inc. supporting Drilling Systems, Wireline Systems, and Drill Bit divisions. Currently, he has responsibility over areas of product research and development processes, technical standards, service and product technical compliance, performance, integrity and content, patent portfolio management, and product and technology roadmaps. During his career he has worked in innovation and state-of-the-art projects in multiple industries such as oilfield services, semiconductor, broadcast, printing, communication, and textile industries. Fanini has accumulated 35 years of engineering experience, over 50 patents issued, and over 60 technical publications. He holds a Master of Science degree in Electrical Engineering from Texas A&M University, an MBA degree from Houston Baptist University, and a Bachelor degree in Electrical Engineering from the Universidade Federal do Rio de Janeiro (UFRJ) in Rio de Janeiro, Brazil. Fanini is a member of IEEE, SPE, SPWLA, ASQ, and INCOSE.
Hizem, M., Budan H., Deville B., Faivre O., Mosse L., Simon M., ”Dielectric dispersion: A new wireline petrophysical measurement”, SPE annual Technical Conference and Exhibition, 2008 Kouchmeshky, B., Fanini, O., “Dielectric logging for heavy oil reservoirs”, World Heavy Oil Congress, WHOC16-400, 2016 Kouchmeshky, B., Fanini, O., Nikitenko, M., “Validating mixing models for dielectric logging”, SPE Russian petroleum technology conference, 182096, 2016 Maxwell-Garnett, J.D., "Colures in metal glasses and in metal films", Transactions of the Royal Society, CCIII, London, 385-420, 1904 Rau R., Davies R., Finke M., Manning M., “Advances in high frequency dielectric logging”, SPWLA 32nd Annual logging symposium, 1991
Alberto G. Mezzatesta is the Manager of Research NMR Science and Integrated Interpretation within the BHI Houston Technology Center. With more than 35 years in the Oil Industry, Alberto has been involved with E&P, Consulting, Technology Development, and the Academia. During his tenure of 24 years with BHI, Alberto has been involved with Formation Evaluation, Interpretation Development, Logging Tool Design and Development, Geoscience Applications, and Reservoir Engineering. Alberto received a Petroleum Engineering degree from the National University of Cuyo, Argentina, and a Ph.D. degree in Chemical Engineering from the University of Houston. He is an active member of the SPE and SPWLA and has authored and co-authored several publications and patents.
Seleznev, N., Boyd, A., Habashy, T, "Dielectric mixing laws for fully and partially saturated carbonate rocks", SPWLA 45th Annual logging symposium, 2004 Sihvola, A., and Kong, J.A., “Effective permittivity of dielectric mixture”, IEEE transaction on Geoscience and Remote sensing, 26(4), 420-429, 1989
ABOUT THE AUHTOR Babak Kouchmeshky received his PhD from Cornell University school of Engineering in 2009. Between 2009 and 2011 he was a post doc at the national center of hypersonic structures in UTA. He joined Baker Hughes in 2011 where he is currently an R&D engineer. He has worked on various aspects of sensor development including design, simulation, experimentation, and interpretation for acoustic and electromagnetic tools. His current focus is on the development of a dielectric logging tool. He is the author of several patent applications on the sensor design, inversion algorithms, and petrophysical interpretation for wireline tools.
Roberto Arro is a Geoscientist at the Houston Technology Center since June 2014. He received his Telecommunications Engineer grade from the La Plata National University, Argentina in 1980, then, he initiated his professional career in Baker Hughes (previously Dresser Atlas) in the same year, completing his Field Engineering progression in 1988 as General Field Engineer. He has acted as Operations Manager and District Manager at various locations in Argentina. During 2007-2008 he took a M.Sc course in Applied Statistics in the Universidad Nacional del Comahue, Argentina.
Otto Fanini currently holds the position of Global Principal Engineer (Electrical) for Drilling & 9
