Current methodologies for analytically determining the onset of buckling of drillstrings within c... more Current methodologies for analytically determining the onset of buckling of drillstrings within curved boreholes are limited. In this paper, the Hypergeometric Model is shown to be an effective model to determine drillstring buckling within curved boreholes. With the Hypergeometric Model, the analysis of drillstring buckling results in curves expressing the local buckling force versus the angle of inclination. The local buckling force alone, however, does not contain all the information required for a practical analysis. From the local buckling force curve, the positional buckling force is derived. The positional buckling force considers the distributed weight of the drillstring and the friction between the drillstring and the borehole wall. From this curve, the point of minimum resistance to buckling of the drillstring is determined. Using the local and positional buckling force curves, experimental results and simulations are presented. When multiple configurations exist (for exam...
Drill pipe fatigue occurs due to the cyclic loading that takes place at curved sections of the we... more Drill pipe fatigue occurs due to the cyclic loading that takes place at curved sections of the well originated by the rotation of the tubes. The failure caused by the fatigue crack nucleation and propagation is considered the major risk to the integrity of the tubes. The fatigue damage isinitially accumulated as surface plastic strain resulting in slip bands. This highlights the importance of studying the fatigue crack initiation to correctly analyze the fatigue behavior of a material or component and has motivated the project of an experimental system comprising the in situ differential interference contrast optical analysis of the surface fatigue cracks and damage accumulation. A fatigue test rig to perform full-scale fatigue tests under bending and tension combined loading to simulate the physical conditions found at the well was also designed and built. API S – 135 steel samples were machined out of drill pipes used by Petrobras at deep-water oil production. Tensile mechanical p...
Current methodologies for analytically determining the onset of buckling of drillstrings within c... more Current methodologies for analytically determining the onset of buckling of drillstrings within curved boreholes are limited. In this paper, the Hypergeometric Model is shown to be an effective model to determine drillstring buckling within curved boreholes. With the Hypergeometric Model, the analysis of drillstring buckling results in curves expressing the local buckling force versus the angle of inclination. The local buckling force alone, however, does not contain all the information required for a practical analysis. From the local buckling force curve, the positional buckling force is derived. The positional buckling force considers the distributed weight of the drillstring and the friction between the drillstring and the borehole wall. From this curve, the point of minimum resistance to buckling of the drillstring is determined. Using the local and positional buckling force curves, experimental results and simulations are presented. When multiple configurations exist (for exam...
A model for buckling within curved boreholes is important in the drilling of extended reach and h... more A model for buckling within curved boreholes is important in the drilling of extended reach and horizontal wells. It has been noted in drilling operations that a curved borehole increases the buckling resistance of the drillstring compared to a straight borehole. The effects of the curvature, however, cannot be correctly determined from the current buckling models developed for straight boreholes, from where the current models for curved boreholes in the literature borrow their fundamentals. A mathematical model for analyzing buckling of drillstring within curved boreholes has been developed. This model predicts the unloading buckling force of a drillstring. The results show that one can apply higher axial forces at the bit and obtain longer extended reach or horizontal sections without putting the drillstring under risk of helical buckling and the consequent lock-up of the column. The model presented here, called the Hypergeometric Model, uses an analytical method employing an incl...
An innovative theoretical model to quantify the risk of differential sticking is presented. The p... more An innovative theoretical model to quantify the risk of differential sticking is presented. The proposed risk assessment is based on the concept of likelihood versus consequence. The likelihood of the problem's occurrence in a given wellbore segment (case) is evaluated from a knowledge-based model and translated by a similarity measure of relevant operational conditions between the target case and historical cases with known outcomes. This standalone module performed satisfactorily and predicts the likelihood of occurrence by more than a chance probability, demonstrated by a rate of sixty eight percent (68%) correct predictions against field data from forty four wells drilled by different operators in several fields. The consequence assessment is performed through one-dimensional mechanistic model that predicts the downhole overpull (differential sticking force), which is not detailed in this article. Together, the models serve as a risk assessment tool able to correctly describe risky operational trends while designing or drilling wells, with critical situations being defined as high likelihood plus high potential overpulls. Both models utilize unique experimental data about mechanical properties of drilling fluids filtercakes (hardness, torque resistance and adhesion-cohesion strength) under simulated downhole conditions, raised through the HTHP Mudcake Characterization Equipment (HPHT MCCE) developed during the course of this research work.
This work presents the mathematical method to design complex trajectories for threedimensional (3... more This work presents the mathematical method to design complex trajectories for threedimensional (3D) wells using spline in tension as coordinate functions. 3D spline-intension trajectories are obtained for various end conditions: free end, set end, free inclination/set azimuth, and set inclination/free azimuth. The resulting trajectories are smooth continuous functions which better suit the expected performance of modern rotary steerable deviation tools, in particular, point-the-bit and push-the-bit systems. A continuous and gradual change in path curvature and tool face results in the smoothest trajectory for 3D wells, which, in turn, results in lower torque, drag, and equipment wear. The degree of freedom and the associated parameters of the 3D curves express the commitment between the average curvature to the final length of the path that can be adjusted to fit the design requirements and to optimize the trajectory. Several numerical examples illustrate the various end conditions. This paper also presents the full mathematical expressions for the 3D path for four end conditions. The method is directly applicable to the well planning cycle as well as to automatic and manual hole steering's. Spline-intension functions differ from the cubic functions in the extent that an additional parameter, which represent the "tension" of the curve, can be controlled. A totally "relaxed" curve is identical to a cubic curve, and as the tension increases a shorter curve length is obtained with a consequent effect in the curvature profile along the curve. In the limit, as the tension increases to infinite, the spline-in-tension approaches to a straight line. The tension offers an additional degree of freedom, which can be used to further optimize the final trajectory. The 3D spline-in-tension model provides the most versatile model to plan a 3D well trajectory to date. Suitable manipulation of the curve parameters, namely, L 0 , L 1 , and the three tensions, allows to give to the planned trajectory any desired behavior.
This work presents a mathematical method to design complex trajectories for threedimensional (3D)... more This work presents a mathematical method to design complex trajectories for threedimensional (3D) wells. Three-dimensional cubic trajectories are obtained for various end conditions: free end, set end, free inclination/set azimuth, and set inclination/free azimuth. The resulting trajectories are smooth continuous functions, which better suit the expected performance of modern rotary steerable deviation tools, in particular point-thebit and push-the-bit systems. A continuous and gradual change in path curvature and tool face results in the smoothest trajectory for 3D wells, that in turn results in lower torque, drag, and equipment wear. The degree of freedom and the associated parameters of the 3D curves express the commitment between the average curvature to the final length of the path, which can be adjusted to fit the design requirements and to optimize the trajectory. Several numerical examples illustrate the various end conditions. The paper also presents the full mathematical results (expressions for the 3D path, actual curvature, and actual tool face). The method is directly applicable to the well planning cycle as well as to automatic and manual hole steering.
This work presents an iterative method to obtain the perpendicular offsets linear least squares r... more This work presents an iterative method to obtain the perpendicular offsets linear least squares regression of a set of points (x i , y i ) using a sequence of vertical offset linear least squares regressions. Using a similar approach, the method is then extended to set of points (x i , y i , z i ). The method can be further extended to arbitrary n-dimensional space.
The dierential equation that governs the buckling behavior of an inclined beam-column is obtained... more The dierential equation that governs the buckling behavior of an inclined beam-column is obtained using the energy method, and the use of a suitable change of variable reduces the various geometrical and physical parameters into a single dimensionless length parameter (X). An exact solution is presented via the use of some members of the family of generalized hypergeometric functions. One type of boundary condition (pinned-ends) is presented and analyzed, and others boundary conditions may be easily studied following the same process. The analysis shows the singular behavior of the inclined beam-column and demonstrates the procedure used to obtain the critical values of the axial force. An important application of this model is its usefulness in the analysis of buckling of drillstrings within curved boreholes. Ó 1998 Elsevier Science Inc. All rights reserved.
An innovative mathematical model to describe the mechanical buckling of drillstrings within curve... more An innovative mathematical model to describe the mechanical buckling of drillstrings within curved boreholes was developed. The hypergeometric model congregates the curved borehole theory and the generalized beam-column theory, both developed and presented in this work. The curved borehole theory dictates the conditions a drillstring must satisfy to buckle within a curved borehole. The generalized beamcolumn theory describes the singular behavior of an inclined beam-column subjected to a distributed weight and axial forces applied on its ends. The differential equation of the inclined beam-column was derived using the energy method and the general solution was written in a closed form using generalized hypergeometric functions. The conditions required by the curved borehole theory are then imposed to the general solution of the differential equation. This results in a numerical procedure with which the buckling force can be calculated for any point along a curved borehole , called local buckling force. From this force derives the positional buckling force which accounts for the effects of the distributed weight and friction. Curves plotted using these two forces, called buckling graphs, permit a complete analysis of the buckling behavior of the drillstring for constant cross-sectional drillstrings, tapered drillstrings, tapered boreholes , and multi-curved boreholes. All this is possible using the P-curve shifting method developed and presented in this work. The buckling graph and the P-curve shifting method constitute a unique tool for designing optimal drillstrings to drill horizontal oil, gas, and geothermal wells. The model was experimentally validated using a medium-scale apparatus designed and constructed in the Colorado School of Mines. Predictions using the hypergeometric model and results of the experiments are presented.
This papsf was selected fbr presentation by an SPE Program Committee folIowing review of inform a... more This papsf was selected fbr presentation by an SPE Program Committee folIowing review of inform aticm contained in an abstract submitted by the author(s). Cwtents of the paper, as presented, hava not been reviewed by the Society of Petroleum Engineers and are subject to wrrsction by the authw(s), The material, as presented, does not necessarily reflect any position of the Society of Petrolaum Engineers, ifs officers, or members. Papers presented at SPE meetings are subject to publication reviaw by Editorial Committees of the Sociaty of Pafroleum Engineers. Electronic reproduction, distribution, or storage of any parl of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 3W words; illustrations may not be copied.
Proceedings of SPE/IADC Indian Drilling Technology Conference and Exhibition, 2006
Drilling operations have always been considered by environmental agencies because of generating l... more Drilling operations have always been considered by environmental agencies because of generating large volumes of wastes during operation include drilling fluid, cuttings, rig wash water, etc…. Discharge of these wastes in the environment is the main concern and requires waste management plan before starting the project in the drilling site.
Journal of Petroleum Science and Engineering, 2010
Keywords: z-factor gas compressibility factor artificial Neural Network DAK numerical reservoir s... more Keywords: z-factor gas compressibility factor artificial Neural Network DAK numerical reservoir simulator gas flow simulator Gas compressibility factor (z-factor) is an important parameter widely used in petroleum and chemical engineering. Accurate and fast calculation of this parameter is of crucial need and challenges a large number of simulators used in petroleum engineering. The Standing-Katz chart was published in 1942 and since then has been considered an industry standard. Several methods have been tried and developed to calculate z-factor by fitting models on the smoothed Standing-Katz data. Some of these models are the Dranchuk and Abou-Kassem (DAK), the Nishiumi-Saito, the Nishiumi, and the Brill-Beggs correlations. All models developed afterwards the Standing-Katz charts present some limitation like instability close to certain boundaries, convergence, and/or accuracy. In fact, different correlations tend to fit better to a particular area of the domain for P pr and T pr (pseudo-reduced pressure and temperature), but fail badly close and beyond to their limits. Also, most correlations require iterative procedures to obtain the corresponding z-factor, and may even present different results dependent on the initial guess for the initial iteration. The DAK correlation is one of the most widely used models. In this study we propose and develop a methodology to obtain z-factors for Natural Hydrocarbon Gases using Artificial Neural Networks (ANN). Data obtained directly from the Standing-Katz and Katz compressibility charts were used to train several topologies of ANN. The input parameters in the ANN are the pseudoreduced pressure and temperature and the output is the z-factor. Two of the successful networks have two hidden layers. The first ANN uses five neurons in each hidden layer and the second ANN uses ten neurons in each hidden layer (called 2-5-5-1 and 2-10-10-1 networks respectively). These topologies were trained with the data from the charts using a back-propagation training algorithm. The results are compared with the charts (with values not used during the training section), along with the results obtained using DAK correlation. In addition, performance comparisons were made between the ANN model and the DAK correlation. In both situations, the ANN models are superior to the DAK correlation. In addition, the ANN model covers a wider range of P pr and T pr , which surpasses the limits of all other correlations together. Typically, the time needed to obtain results for a 2-5-5-1 network corresponds to the time of one single iteration needed for the DAK correlation. The paper discusses these results, and provides the weight sets (values of synapses and biases) needed to reproduce the ANN, which can be easily implemented in an electronic spreadsheet.
Current methodologies for analytically determining the onset of buckling of drillstrings within c... more Current methodologies for analytically determining the onset of buckling of drillstrings within curved boreholes are limited. In this paper, the Hypergeometric Model is shown to be an effective model to determine drillstring buckling within curved boreholes. With the Hypergeometric Model, the analysis of drillstring buckling results in curves expressing the local buckling force versus the angle of inclination. The local buckling force alone, however, does not contain all the information required for a practical analysis. From the local buckling force curve, the positional buckling force is derived. The positional buckling force considers the distributed weight of the drillstring and the friction between the drillstring and the borehole wall. From this curve, the point of minimum resistance to buckling of the drillstring is determined. Using the local and positional buckling force curves, experimental results and simulations are presented. When multiple configurations exist (for exam...
Drill pipe fatigue occurs due to the cyclic loading that takes place at curved sections of the we... more Drill pipe fatigue occurs due to the cyclic loading that takes place at curved sections of the well originated by the rotation of the tubes. The failure caused by the fatigue crack nucleation and propagation is considered the major risk to the integrity of the tubes. The fatigue damage isinitially accumulated as surface plastic strain resulting in slip bands. This highlights the importance of studying the fatigue crack initiation to correctly analyze the fatigue behavior of a material or component and has motivated the project of an experimental system comprising the in situ differential interference contrast optical analysis of the surface fatigue cracks and damage accumulation. A fatigue test rig to perform full-scale fatigue tests under bending and tension combined loading to simulate the physical conditions found at the well was also designed and built. API S – 135 steel samples were machined out of drill pipes used by Petrobras at deep-water oil production. Tensile mechanical p...
Current methodologies for analytically determining the onset of buckling of drillstrings within c... more Current methodologies for analytically determining the onset of buckling of drillstrings within curved boreholes are limited. In this paper, the Hypergeometric Model is shown to be an effective model to determine drillstring buckling within curved boreholes. With the Hypergeometric Model, the analysis of drillstring buckling results in curves expressing the local buckling force versus the angle of inclination. The local buckling force alone, however, does not contain all the information required for a practical analysis. From the local buckling force curve, the positional buckling force is derived. The positional buckling force considers the distributed weight of the drillstring and the friction between the drillstring and the borehole wall. From this curve, the point of minimum resistance to buckling of the drillstring is determined. Using the local and positional buckling force curves, experimental results and simulations are presented. When multiple configurations exist (for exam...
A model for buckling within curved boreholes is important in the drilling of extended reach and h... more A model for buckling within curved boreholes is important in the drilling of extended reach and horizontal wells. It has been noted in drilling operations that a curved borehole increases the buckling resistance of the drillstring compared to a straight borehole. The effects of the curvature, however, cannot be correctly determined from the current buckling models developed for straight boreholes, from where the current models for curved boreholes in the literature borrow their fundamentals. A mathematical model for analyzing buckling of drillstring within curved boreholes has been developed. This model predicts the unloading buckling force of a drillstring. The results show that one can apply higher axial forces at the bit and obtain longer extended reach or horizontal sections without putting the drillstring under risk of helical buckling and the consequent lock-up of the column. The model presented here, called the Hypergeometric Model, uses an analytical method employing an incl...
An innovative theoretical model to quantify the risk of differential sticking is presented. The p... more An innovative theoretical model to quantify the risk of differential sticking is presented. The proposed risk assessment is based on the concept of likelihood versus consequence. The likelihood of the problem's occurrence in a given wellbore segment (case) is evaluated from a knowledge-based model and translated by a similarity measure of relevant operational conditions between the target case and historical cases with known outcomes. This standalone module performed satisfactorily and predicts the likelihood of occurrence by more than a chance probability, demonstrated by a rate of sixty eight percent (68%) correct predictions against field data from forty four wells drilled by different operators in several fields. The consequence assessment is performed through one-dimensional mechanistic model that predicts the downhole overpull (differential sticking force), which is not detailed in this article. Together, the models serve as a risk assessment tool able to correctly describe risky operational trends while designing or drilling wells, with critical situations being defined as high likelihood plus high potential overpulls. Both models utilize unique experimental data about mechanical properties of drilling fluids filtercakes (hardness, torque resistance and adhesion-cohesion strength) under simulated downhole conditions, raised through the HTHP Mudcake Characterization Equipment (HPHT MCCE) developed during the course of this research work.
This work presents the mathematical method to design complex trajectories for threedimensional (3... more This work presents the mathematical method to design complex trajectories for threedimensional (3D) wells using spline in tension as coordinate functions. 3D spline-intension trajectories are obtained for various end conditions: free end, set end, free inclination/set azimuth, and set inclination/free azimuth. The resulting trajectories are smooth continuous functions which better suit the expected performance of modern rotary steerable deviation tools, in particular, point-the-bit and push-the-bit systems. A continuous and gradual change in path curvature and tool face results in the smoothest trajectory for 3D wells, which, in turn, results in lower torque, drag, and equipment wear. The degree of freedom and the associated parameters of the 3D curves express the commitment between the average curvature to the final length of the path that can be adjusted to fit the design requirements and to optimize the trajectory. Several numerical examples illustrate the various end conditions. This paper also presents the full mathematical expressions for the 3D path for four end conditions. The method is directly applicable to the well planning cycle as well as to automatic and manual hole steering's. Spline-intension functions differ from the cubic functions in the extent that an additional parameter, which represent the "tension" of the curve, can be controlled. A totally "relaxed" curve is identical to a cubic curve, and as the tension increases a shorter curve length is obtained with a consequent effect in the curvature profile along the curve. In the limit, as the tension increases to infinite, the spline-in-tension approaches to a straight line. The tension offers an additional degree of freedom, which can be used to further optimize the final trajectory. The 3D spline-in-tension model provides the most versatile model to plan a 3D well trajectory to date. Suitable manipulation of the curve parameters, namely, L 0 , L 1 , and the three tensions, allows to give to the planned trajectory any desired behavior.
This work presents a mathematical method to design complex trajectories for threedimensional (3D)... more This work presents a mathematical method to design complex trajectories for threedimensional (3D) wells. Three-dimensional cubic trajectories are obtained for various end conditions: free end, set end, free inclination/set azimuth, and set inclination/free azimuth. The resulting trajectories are smooth continuous functions, which better suit the expected performance of modern rotary steerable deviation tools, in particular point-thebit and push-the-bit systems. A continuous and gradual change in path curvature and tool face results in the smoothest trajectory for 3D wells, that in turn results in lower torque, drag, and equipment wear. The degree of freedom and the associated parameters of the 3D curves express the commitment between the average curvature to the final length of the path, which can be adjusted to fit the design requirements and to optimize the trajectory. Several numerical examples illustrate the various end conditions. The paper also presents the full mathematical results (expressions for the 3D path, actual curvature, and actual tool face). The method is directly applicable to the well planning cycle as well as to automatic and manual hole steering.
This work presents an iterative method to obtain the perpendicular offsets linear least squares r... more This work presents an iterative method to obtain the perpendicular offsets linear least squares regression of a set of points (x i , y i ) using a sequence of vertical offset linear least squares regressions. Using a similar approach, the method is then extended to set of points (x i , y i , z i ). The method can be further extended to arbitrary n-dimensional space.
The dierential equation that governs the buckling behavior of an inclined beam-column is obtained... more The dierential equation that governs the buckling behavior of an inclined beam-column is obtained using the energy method, and the use of a suitable change of variable reduces the various geometrical and physical parameters into a single dimensionless length parameter (X). An exact solution is presented via the use of some members of the family of generalized hypergeometric functions. One type of boundary condition (pinned-ends) is presented and analyzed, and others boundary conditions may be easily studied following the same process. The analysis shows the singular behavior of the inclined beam-column and demonstrates the procedure used to obtain the critical values of the axial force. An important application of this model is its usefulness in the analysis of buckling of drillstrings within curved boreholes. Ó 1998 Elsevier Science Inc. All rights reserved.
An innovative mathematical model to describe the mechanical buckling of drillstrings within curve... more An innovative mathematical model to describe the mechanical buckling of drillstrings within curved boreholes was developed. The hypergeometric model congregates the curved borehole theory and the generalized beam-column theory, both developed and presented in this work. The curved borehole theory dictates the conditions a drillstring must satisfy to buckle within a curved borehole. The generalized beamcolumn theory describes the singular behavior of an inclined beam-column subjected to a distributed weight and axial forces applied on its ends. The differential equation of the inclined beam-column was derived using the energy method and the general solution was written in a closed form using generalized hypergeometric functions. The conditions required by the curved borehole theory are then imposed to the general solution of the differential equation. This results in a numerical procedure with which the buckling force can be calculated for any point along a curved borehole , called local buckling force. From this force derives the positional buckling force which accounts for the effects of the distributed weight and friction. Curves plotted using these two forces, called buckling graphs, permit a complete analysis of the buckling behavior of the drillstring for constant cross-sectional drillstrings, tapered drillstrings, tapered boreholes , and multi-curved boreholes. All this is possible using the P-curve shifting method developed and presented in this work. The buckling graph and the P-curve shifting method constitute a unique tool for designing optimal drillstrings to drill horizontal oil, gas, and geothermal wells. The model was experimentally validated using a medium-scale apparatus designed and constructed in the Colorado School of Mines. Predictions using the hypergeometric model and results of the experiments are presented.
This papsf was selected fbr presentation by an SPE Program Committee folIowing review of inform a... more This papsf was selected fbr presentation by an SPE Program Committee folIowing review of inform aticm contained in an abstract submitted by the author(s). Cwtents of the paper, as presented, hava not been reviewed by the Society of Petroleum Engineers and are subject to wrrsction by the authw(s), The material, as presented, does not necessarily reflect any position of the Society of Petrolaum Engineers, ifs officers, or members. Papers presented at SPE meetings are subject to publication reviaw by Editorial Committees of the Sociaty of Pafroleum Engineers. Electronic reproduction, distribution, or storage of any parl of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 3W words; illustrations may not be copied.
Proceedings of SPE/IADC Indian Drilling Technology Conference and Exhibition, 2006
Drilling operations have always been considered by environmental agencies because of generating l... more Drilling operations have always been considered by environmental agencies because of generating large volumes of wastes during operation include drilling fluid, cuttings, rig wash water, etc…. Discharge of these wastes in the environment is the main concern and requires waste management plan before starting the project in the drilling site.
Journal of Petroleum Science and Engineering, 2010
Keywords: z-factor gas compressibility factor artificial Neural Network DAK numerical reservoir s... more Keywords: z-factor gas compressibility factor artificial Neural Network DAK numerical reservoir simulator gas flow simulator Gas compressibility factor (z-factor) is an important parameter widely used in petroleum and chemical engineering. Accurate and fast calculation of this parameter is of crucial need and challenges a large number of simulators used in petroleum engineering. The Standing-Katz chart was published in 1942 and since then has been considered an industry standard. Several methods have been tried and developed to calculate z-factor by fitting models on the smoothed Standing-Katz data. Some of these models are the Dranchuk and Abou-Kassem (DAK), the Nishiumi-Saito, the Nishiumi, and the Brill-Beggs correlations. All models developed afterwards the Standing-Katz charts present some limitation like instability close to certain boundaries, convergence, and/or accuracy. In fact, different correlations tend to fit better to a particular area of the domain for P pr and T pr (pseudo-reduced pressure and temperature), but fail badly close and beyond to their limits. Also, most correlations require iterative procedures to obtain the corresponding z-factor, and may even present different results dependent on the initial guess for the initial iteration. The DAK correlation is one of the most widely used models. In this study we propose and develop a methodology to obtain z-factors for Natural Hydrocarbon Gases using Artificial Neural Networks (ANN). Data obtained directly from the Standing-Katz and Katz compressibility charts were used to train several topologies of ANN. The input parameters in the ANN are the pseudoreduced pressure and temperature and the output is the z-factor. Two of the successful networks have two hidden layers. The first ANN uses five neurons in each hidden layer and the second ANN uses ten neurons in each hidden layer (called 2-5-5-1 and 2-10-10-1 networks respectively). These topologies were trained with the data from the charts using a back-propagation training algorithm. The results are compared with the charts (with values not used during the training section), along with the results obtained using DAK correlation. In addition, performance comparisons were made between the ANN model and the DAK correlation. In both situations, the ANN models are superior to the DAK correlation. In addition, the ANN model covers a wider range of P pr and T pr , which surpasses the limits of all other correlations together. Typically, the time needed to obtain results for a 2-5-5-1 network corresponds to the time of one single iteration needed for the DAK correlation. The paper discusses these results, and provides the weight sets (values of synapses and biases) needed to reproduce the ANN, which can be easily implemented in an electronic spreadsheet.
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