A new method of determining the characteristic equation of a matrix was developed. This new metho... more A new method of determining the characteristic equation of a matrix was developed. This new method presents the coefficients of the characteristic equation as the sums of determinants of smaller (co-diagonal) sub matrices within the matrix. It identifies a connection between the coefficients (sum of determinant and sum of cofactors), and by extension of this connection provides a proof that the determinant of a null matrix is 1, the determinant of an identity matrix. Keywords: Characteristic equations, matrix and determinant, co-diagonal sub matrix, sum of determinant and joint-cofactors, null matrix, identity matrix.
Journal of Petroleum Exploration and Production Technology, 2015
The compressibility factor (z-factor) of gases is a thermodynamic property used to account for th... more The compressibility factor (z-factor) of gases is a thermodynamic property used to account for the deviation of real gas behavior from that of an ideal gas. Correlations based on the equation of state are often implicit, because they require iteration and are computationally expensive. A number of explicit correlations have been derived to enhance simplicity; however, no single explicit correlation has been developed for the full range of pseudoreduced temperatures 1:05 T pr 3 À Á and pseudo-reduced pressures 0:2 P pr 15 À Á , which represents a significant research gap. This work presents a new z-factor correlation that can be expressed in linear form. On the basis of Hall and Yarborough's implicit correlation, we developed the new correlation from 5346 experimental data points extracted from 5940 data points published in the SPE natural gas reservoir engineering textbook and created a linear z-factor chart for a full range of pseudo-reduced temperatures ð1:15 T pr 3Þ and pseudo-reduced pressures ð0:2 P pr 15Þ.
Proceedings of the West Virginia Academy of Science, Mar 20, 2019
An alternative approach to describe flame acceleration in micro-tubes due to wall friction. Among... more An alternative approach to describe flame acceleration in micro-tubes due to wall friction. Among various existing analytical models proposed to describe flame acceleration (FA) and deflagrationto-detonation transition (DDT), none accounts for all distinctive stages of the FA and DDT processes. To overcome such a gap, here we propose an alternative model, which is based on the first physical principles and agrees with the experimental finding that FA is subsequently replaced by steady flame propagation. Starting with the Navier-stokes equation for an axial flow in a cylindrical tube, we set the pressure gradient to be proportional to the radial component of a velocity function and then absorbed the driving force into the temporal component of the resulting velocity differential equation. This leads to a model with two unknown parameters (coming from the temporal and radial component of the velocity function). Since the chemistry of the combustion is not considered in the model, these two parameters were computed by nonlinear fitting of the model to the experimental measurement showing good agreement between the model and the experiments.
A horizontal well with a non-linear trajectory is fundamentally an intricate system, and determin... more A horizontal well with a non-linear trajectory is fundamentally an intricate system, and determination of its inflow productivity index using numerical simulation is computationally challenging. This work presents an approach that is more efficient than numerical simulation. The methodology involves dividing the reservoir into different sections, with each section treated as a closed-box model. A constant pressure is assumed for the two sides of the sections, which are parallel to the plane of the trajectory, and end flow is eliminated so that each section of the well is fully penetrating. A simplified isobaric geometry and a flow path were developed using the numerical simulation of flow in a fully penetrating well in a box model; an analytical index equation was then developed from the simplified geometry. The results of the numerical simulation were used to generate an empirical correlation for the shape factor to bring the result of the productivity index equation close to simul...
A horizontal well with a non-linear trajectory is fundamentally an intricate system, and determin... more A horizontal well with a non-linear trajectory is fundamentally an intricate system, and determination of its inflow productivity index using numerical simulation is computationally challenging. This work presents an approach that is more efficient than numerical simulation. The methodology involves dividing the reservoir into different sections, with each section treated as a closed-box model. A constant pressure is assumed for the two sides of the sections, which are parallel to the plane of the trajectory, and end flow is eliminated so that each section of the well is fully penetrating. A simplified isobaric geometry and a flow path were developed using the numerical simulation of flow in a fully penetrating well in a box model; an analytical index equation was then developed from the simplified geometry. The results of the numerical simulation were used to generate an empirical correlation for the shape factor to bring the result of the productivity index equation close to simul...
Journal of Petroleum Exploration and Production Technology, 2015
The compressibility factor (z-factor) of gases is a thermodynamic property used to account for th... more The compressibility factor (z-factor) of gases is a thermodynamic property used to account for the deviation of real gas behavior from that of an ideal gas. Correlations based on the equation of state are often implicit, because they require iteration and are computationally expensive. A number of explicit correlations have been derived to enhance simplicity; however, no single explicit correlation has been developed for the full range of pseudoreduced temperatures 1:05 T pr 3 À Á and pseudo-reduced pressures 0:2 P pr 15 À Á , which represents a significant research gap. This work presents a new z-factor correlation that can be expressed in linear form. On the basis of Hall and Yarborough's implicit correlation, we developed the new correlation from 5346 experimental data points extracted from 5940 data points published in the SPE natural gas reservoir engineering textbook and created a linear z-factor chart for a full range of pseudo-reduced temperatures ð1:15 T pr 3Þ and pseudo-reduced pressures ð0:2 P pr 15Þ.
Nigeria Annual International Conference and Exhibition, 2010
... Kareem Lateef, A*; SPE, Omeke James, E.; SPE, Achumba G. I; SPE (Shell Chair, Federal Univers... more ... Kareem Lateef, A*; SPE, Omeke James, E.; SPE, Achumba G. I; SPE (Shell Chair, Federal University Of Technology, Owerri) ... For a huge offshore gas reservoir, Lawal and Eweje(1), using full factorial design (FFD) augmented with two centre points derived recovery factor (RF ...
Nigeria Annual International Conference and Exhibition, 2011
ABSTRACT This paper was prepared for presentation at the Nigeria Annual International Conference ... more ABSTRACT This paper was prepared for presentation at the Nigeria Annual International Conference and Exhibition held in Abuja, Nigeria, 30 July -3 August 2011. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper 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 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright. Abstract Natural gas engineering entails production, processing, storage and transportation of natural gas. A good handling of the gas requires a sophisticated understanding of how its density, compressibility, pseudo-pressure, and specific heat capacity varies with the gas condition. While petroleum & gas journals and a host of scholastic materials have presented varieties of means to evaluate other properties, they neglected or underscored the need for same for specific heat capacity of natural gas. The only available mathematical relation for this property only predicts its value at 1500F-not at other temperatures. Samples of natural gas collected from Bell field, Sabine field, Bacon lime and paradox formation were used as data source. The variation of the respective specific heat capacity of the components and the effect of the composition on the specific gravity and overall specific heat capacity of the gas was taken into consideration giving rise to a robust correlation that reads in the individual composition of the gas, its density and temperature to generate the specific heat capacity of the gas. The result yielded 98.3% accurate result compared to the method of isentropic coefficient at 150 0 F and an average error of 0.3% within a range of 491 0 R to 2740 0 R. The benefit of this work is that it provides a means of dealing with situation where the heat transferred into or out of a natural gas system is to be calculated over a wide range of temperature as it allows the specific heat to be expressed as an integratable function of temperature other than the isentropic coefficient method which only gives a constant value for a variable that is not constant.
Journal of Natural Gas Science and Engineering, 2014
ABSTRACT Natural gas engineering entails production, processing, storage and transportation of na... more ABSTRACT Natural gas engineering entails production, processing, storage and transportation of natural gas. A good handling of the gas requires a sophisticated understanding of how its density, compressibility, pseudo-pressure and specific heat capacity vary with the gas condition. A variety of methods have been presented in petroleum and gas journals and a host of scholastic materials to evaluate other properties over a wide range of temperatures, however, the available correlation for isobaric specific heat capacity is for only 150 °F. We generated 200 samples of natural gas mixture with methane component ranging from 0.74 to 0.9985 using normally distributed experimental design. The variations of the respective specific heat capacity of the components and the effect of composition on the specific gravity and overall specific heat capacity of the gas were taken into consideration. The developed correlation reads in the specific gravity and temperature to generate the ideal gas specific heat capacity of the sample. The result yielded 99.75% accuracy at 150 °F when compared to experimental data, as against the result from isentropic coefficient method which overestimated the ideal gas specific heat capacity by 25% at the same temperature. The ideal gas specific heat capacity developed compared to 6000 data points generated from mixing rule at different temperatures resulted in correlation regression coefficient of 0.9999. To account for the deviation from ideal gas behaviour, this work presents 99.7% R squared value for dimensionless residual specific heat capacity as a function of reduced temperature and pressure compared to that calculated from Starling Carnahan equation of state. This model is the first explicit correlation for the residual specific heat capacity of natural gas to be derived.
Nigeria Annual International Conference and Exhibition, 2012
The problem of reservoir heterogeneity has made the continued use of Inflow Performance Relation ... more The problem of reservoir heterogeneity has made the continued use of Inflow Performance Relation (IPR) models developed on the assumption of homogeneity impractical. Furui in 2003 (and previously Butler in 1994) solved the problem using fully penetrating well idea so that the model can be applied to different sections of the reservoir. This paper corrects two errors in Furui's model. The first error is the use of arithmetic mean of radii to evaluate the elliptic surface area of the well when an anisotropic reservoir is converted into an isotropic equivalent. This was corrected using an equivalent cylindrical surface area. The second error is the use of a planar isobaric surface at the end of the radial flow region instead of a circular one. These corrections gave the model a better performance-average of 99% against 96% by the original version, when compared with line source solution obtained by using Green function. Equating the hydrostatic and viscous pressure differences betw...
SPE Nigeria Annual International Conference and Exhibition, 2013
ABSTRACT All natural gas processes, including production, sweetening, drying, transportation, sto... more ABSTRACT All natural gas processes, including production, sweetening, drying, transportation, storage, metering and selling requires that we possess ability to predict with great accuracy its volume, pressure, temperature, specific heat capacity etc. Unlike an ideal gas, a real gas does not expand and contract according the simple pressure-volume-temperature relation. This deviation from the ideal gas behavior is corrected with the use of z-factor. Z factor is simply the ratio of the volume of a real gas to that which equal mass of an ideal gas will occupy under the same condition. Several computational methods of obtaining this factor have been developed, but the implicit nature of these correlations called for an explicit method of evaluating the multivariate parameter. In this paper, we used over 6000 data points to develop coefficients of a 2D regression which is Fourier cosine in reduced pressure and polynomial in the reciprocal of the reduced temperature. The result was found to match the result to a very high accuracy without over fitting.
Compressibility factor (z-factor) of gasses is a thermodynamic property used to account for the d... more Compressibility factor (z-factor) of gasses is a thermodynamic property used to account for the deviation of real gas deviation from the ideal gas behavior. The best correlations for this factor given by Hall and Yarborough, Dranchuk & Abou-Kassem and Dranchuk, Purvis & Robinson are based on nonlinear equation of state requiring iterative solution. It is not uncommon for nonlinear equations to have multiple roots, hence, Newton-Raphson often fail to converge or converges on the undesired root of these equations. This unstable behavior of iterative procedure requires that the initial guess is set close to the desired root to ensure convergence. Here we examine the residual equations of the reduced densities of these correlations and set the criteria for the determination of the initial guess as function of the reduced temperature (1.05 ≤ Tpr ≤ 3) and pressure (0.2 ≤ Ppr ≤ 15), we retuned the coefficients using 5940 experimental data points from Handbook of Natural Gas Engineering and...
Natural gas engineering entails production, processing, storage and transportation of natural gas... more Natural gas engineering entails production, processing, storage and transportation of natural gas. A good handling of the gas requires a sophisticated understanding of how its density, compressibility, pseudo-pressure and specific heat capacity vary with the gas condition. A variety of methods have been presented in petroleum and gas journals and a host of scholastic materials to evaluate other properties over a wide range of temperatures, however, the available correlation for isobaric specific heat capacity is for only 150 °F. We generated 200 samples of natural gas mixture with methane component ranging from 0.74 to 0.9985 using normally distributed experimental design. The variations of the respective specific heat capacity of the components and the effect of composition on the specific gravity and overall specific heat capacity of the gas were taken into consideration. The developed correlation reads in the specific gravity and temperature to generate the ideal gas specific heat capacity of the sample. The result yielded 99.75% accuracy at 150 °F when compared to experimental data, as against the result from isentropic coefficient method which overestimated the ideal gas specific heat capacity by 25% at the same temperature. The ideal gas specific heat capacity developed compared to 6000 data points generated from mixing rule at different temperatures resulted in correlation regression coefficient of 0.9999. To account for the deviation from ideal gas behaviour, this work presents 99.7% R squared value for dimensionless residual specific heat capacity as a function of reduced temperature and pressure compared to that calculated from Starling Carnahan equation of state. This model is the first explicit correlation for the residual specific heat capacity of natural gas to be derived.
A horizontal well with a non-linear trajectory is fundamentally an intricate system, and determin... more A horizontal well with a non-linear trajectory is fundamentally an intricate system, and determination of its inflow productivity index using numerical simulation is computationally challenging. This work presents an approach that is more efficient than numerical simulation. The methodology involves dividing the reservoir into different sections, with each section treated as a closed-box model. A constant pressure is assumed for the two sides of the sections, which are parallel to the plane of the trajectory, and end flow is eliminated so that each section of the well is fully penetrating. A simplified isobaric geometry and a flow path were developed using the numerical simulation of flow in a fully penetrating well in a box model; an analytical index equation was then developed from the simplified geometry. The results of the numerical simulation were used to generate an empirical correlation for the shape factor to bring the result of the productivity index equation close to simulation and line source solutions, thus converting the analytical index equation into a semianalytical equation. The application of the semi-analytical equation to a horizontal well, undulating in a vertical plane, to predict its productivity was demonstrated using an example. This model is the first productivity index equation with the capability to handle a horizontal well with a non-linear trajectory.
The compressibility factor (z-factor) of gases is a thermodynamic property used to account for th... more The compressibility factor (z-factor) of gases is a thermodynamic property used to account for the deviation of real gas behavior from that of an ideal gas. Correlations based on the equation of state are often implicit, because they require iteration and are computationally expensive. A number of explicit correlations have been derived to enhance simplicity; however, no single explicit correlation has been developed for the full range of pseudoreduced temperatures 1.05 <Tpr <3 and pseudo-reduced pressures 0.2 <Ppr <15 , which represents a significant research gap. This work presents a new z-factor correlation that can be expressed in linear form. On the basis of Hall and Yarborough’s implicit correlation, we developed the new correlation from 5346 experimental data points extracted from 5940 data points published in the SPE natural gas reservoir engineering textbook and created a linear z-factor chart for a full range of pseudo-reduced temperatures 1:15 < Tpr<3 and pseudo-reduced pressures 0:2<Ppr <15.
Compressibility factor (z-factor) of gasses is a thermodynamic property used to account for the d... more Compressibility factor (z-factor) of gasses is a thermodynamic property used to account for the deviation of real gas deviation from the ideal gas behavior. The best correlations for this factor given by Hall and Yarborough, Dranchuk & Abou-Kassem and Dranchuk, Purvis & Robinson are based on nonlinear equation of state requiring iterative solution.
It is not uncommon for nonlinear equations to have multiple roots, hence, Newton-Raphson often fail to converge or converges on the undesired root of these equations. This unstable behavior of iterative procedure requires that the initial guess is set close to the desired root to ensure convergence.
Here we examine the residual equations of the reduced densities of these correlations and set the criteria for the determination of the initial guess as function of the reduced temp...
Natural gas engineering entails production, processing, storage and transportation of natural gas... more Natural gas engineering entails production, processing, storage and transportation of natural gas. A good handling of the gas requires a sophisticated understanding of how its density, compressibility, pseudo-pressure, and specific heat capacity varies with the gas condition. While petroleum & gas journals and a host of scholastic materials have presented varieties of means to evaluate other properties, they neglected or underscored the need for same for specific heat capacity of natural gas. The only available mathematical relation for this property only predicts its value at 1500F-not at other temperatures.
Recovery factor in recent years has been modelled empirically due to complexities that exist subs... more Recovery factor in recent years has been modelled empirically due to complexities that exist subsurface, and as a result most of the models lacked dimensional homogeneity and neglected the physics of reservoir driving forces that complementarily produce fluids from the reservoir. While these models (mostly Proxies) might satisfy statistical conditions and predict the recovery factors with some degree of accuracy, they fail to reflect well established relationship between physical parameters of the models.
A new method of determining the characteristic equation of a matrix was developed. This new metho... more A new method of determining the characteristic equation of a matrix was developed. This new method presents the coefficients of the characteristic equation as the sums of determinants of smaller (co-diagonal) sub matrices within the matrix. It identifies a connection between the coefficients (sum of determinant and sum of cofactors), and by extension of this connection provides a proof that the determinant of a null matrix is 1, the determinant of an identity matrix. Keywords: Characteristic equations, matrix and determinant, co-diagonal sub matrix, sum of determinant and joint-cofactors, null matrix, identity matrix.
Journal of Petroleum Exploration and Production Technology, 2015
The compressibility factor (z-factor) of gases is a thermodynamic property used to account for th... more The compressibility factor (z-factor) of gases is a thermodynamic property used to account for the deviation of real gas behavior from that of an ideal gas. Correlations based on the equation of state are often implicit, because they require iteration and are computationally expensive. A number of explicit correlations have been derived to enhance simplicity; however, no single explicit correlation has been developed for the full range of pseudoreduced temperatures 1:05 T pr 3 À Á and pseudo-reduced pressures 0:2 P pr 15 À Á , which represents a significant research gap. This work presents a new z-factor correlation that can be expressed in linear form. On the basis of Hall and Yarborough's implicit correlation, we developed the new correlation from 5346 experimental data points extracted from 5940 data points published in the SPE natural gas reservoir engineering textbook and created a linear z-factor chart for a full range of pseudo-reduced temperatures ð1:15 T pr 3Þ and pseudo-reduced pressures ð0:2 P pr 15Þ.
Proceedings of the West Virginia Academy of Science, Mar 20, 2019
An alternative approach to describe flame acceleration in micro-tubes due to wall friction. Among... more An alternative approach to describe flame acceleration in micro-tubes due to wall friction. Among various existing analytical models proposed to describe flame acceleration (FA) and deflagrationto-detonation transition (DDT), none accounts for all distinctive stages of the FA and DDT processes. To overcome such a gap, here we propose an alternative model, which is based on the first physical principles and agrees with the experimental finding that FA is subsequently replaced by steady flame propagation. Starting with the Navier-stokes equation for an axial flow in a cylindrical tube, we set the pressure gradient to be proportional to the radial component of a velocity function and then absorbed the driving force into the temporal component of the resulting velocity differential equation. This leads to a model with two unknown parameters (coming from the temporal and radial component of the velocity function). Since the chemistry of the combustion is not considered in the model, these two parameters were computed by nonlinear fitting of the model to the experimental measurement showing good agreement between the model and the experiments.
A horizontal well with a non-linear trajectory is fundamentally an intricate system, and determin... more A horizontal well with a non-linear trajectory is fundamentally an intricate system, and determination of its inflow productivity index using numerical simulation is computationally challenging. This work presents an approach that is more efficient than numerical simulation. The methodology involves dividing the reservoir into different sections, with each section treated as a closed-box model. A constant pressure is assumed for the two sides of the sections, which are parallel to the plane of the trajectory, and end flow is eliminated so that each section of the well is fully penetrating. A simplified isobaric geometry and a flow path were developed using the numerical simulation of flow in a fully penetrating well in a box model; an analytical index equation was then developed from the simplified geometry. The results of the numerical simulation were used to generate an empirical correlation for the shape factor to bring the result of the productivity index equation close to simul...
A horizontal well with a non-linear trajectory is fundamentally an intricate system, and determin... more A horizontal well with a non-linear trajectory is fundamentally an intricate system, and determination of its inflow productivity index using numerical simulation is computationally challenging. This work presents an approach that is more efficient than numerical simulation. The methodology involves dividing the reservoir into different sections, with each section treated as a closed-box model. A constant pressure is assumed for the two sides of the sections, which are parallel to the plane of the trajectory, and end flow is eliminated so that each section of the well is fully penetrating. A simplified isobaric geometry and a flow path were developed using the numerical simulation of flow in a fully penetrating well in a box model; an analytical index equation was then developed from the simplified geometry. The results of the numerical simulation were used to generate an empirical correlation for the shape factor to bring the result of the productivity index equation close to simul...
Journal of Petroleum Exploration and Production Technology, 2015
The compressibility factor (z-factor) of gases is a thermodynamic property used to account for th... more The compressibility factor (z-factor) of gases is a thermodynamic property used to account for the deviation of real gas behavior from that of an ideal gas. Correlations based on the equation of state are often implicit, because they require iteration and are computationally expensive. A number of explicit correlations have been derived to enhance simplicity; however, no single explicit correlation has been developed for the full range of pseudoreduced temperatures 1:05 T pr 3 À Á and pseudo-reduced pressures 0:2 P pr 15 À Á , which represents a significant research gap. This work presents a new z-factor correlation that can be expressed in linear form. On the basis of Hall and Yarborough's implicit correlation, we developed the new correlation from 5346 experimental data points extracted from 5940 data points published in the SPE natural gas reservoir engineering textbook and created a linear z-factor chart for a full range of pseudo-reduced temperatures ð1:15 T pr 3Þ and pseudo-reduced pressures ð0:2 P pr 15Þ.
Nigeria Annual International Conference and Exhibition, 2010
... Kareem Lateef, A*; SPE, Omeke James, E.; SPE, Achumba G. I; SPE (Shell Chair, Federal Univers... more ... Kareem Lateef, A*; SPE, Omeke James, E.; SPE, Achumba G. I; SPE (Shell Chair, Federal University Of Technology, Owerri) ... For a huge offshore gas reservoir, Lawal and Eweje(1), using full factorial design (FFD) augmented with two centre points derived recovery factor (RF ...
Nigeria Annual International Conference and Exhibition, 2011
ABSTRACT This paper was prepared for presentation at the Nigeria Annual International Conference ... more ABSTRACT This paper was prepared for presentation at the Nigeria Annual International Conference and Exhibition held in Abuja, Nigeria, 30 July -3 August 2011. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper 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 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright. Abstract Natural gas engineering entails production, processing, storage and transportation of natural gas. A good handling of the gas requires a sophisticated understanding of how its density, compressibility, pseudo-pressure, and specific heat capacity varies with the gas condition. While petroleum &amp; gas journals and a host of scholastic materials have presented varieties of means to evaluate other properties, they neglected or underscored the need for same for specific heat capacity of natural gas. The only available mathematical relation for this property only predicts its value at 1500F-not at other temperatures. Samples of natural gas collected from Bell field, Sabine field, Bacon lime and paradox formation were used as data source. The variation of the respective specific heat capacity of the components and the effect of the composition on the specific gravity and overall specific heat capacity of the gas was taken into consideration giving rise to a robust correlation that reads in the individual composition of the gas, its density and temperature to generate the specific heat capacity of the gas. The result yielded 98.3% accurate result compared to the method of isentropic coefficient at 150 0 F and an average error of 0.3% within a range of 491 0 R to 2740 0 R. The benefit of this work is that it provides a means of dealing with situation where the heat transferred into or out of a natural gas system is to be calculated over a wide range of temperature as it allows the specific heat to be expressed as an integratable function of temperature other than the isentropic coefficient method which only gives a constant value for a variable that is not constant.
Journal of Natural Gas Science and Engineering, 2014
ABSTRACT Natural gas engineering entails production, processing, storage and transportation of na... more ABSTRACT Natural gas engineering entails production, processing, storage and transportation of natural gas. A good handling of the gas requires a sophisticated understanding of how its density, compressibility, pseudo-pressure and specific heat capacity vary with the gas condition. A variety of methods have been presented in petroleum and gas journals and a host of scholastic materials to evaluate other properties over a wide range of temperatures, however, the available correlation for isobaric specific heat capacity is for only 150 °F. We generated 200 samples of natural gas mixture with methane component ranging from 0.74 to 0.9985 using normally distributed experimental design. The variations of the respective specific heat capacity of the components and the effect of composition on the specific gravity and overall specific heat capacity of the gas were taken into consideration. The developed correlation reads in the specific gravity and temperature to generate the ideal gas specific heat capacity of the sample. The result yielded 99.75% accuracy at 150 °F when compared to experimental data, as against the result from isentropic coefficient method which overestimated the ideal gas specific heat capacity by 25% at the same temperature. The ideal gas specific heat capacity developed compared to 6000 data points generated from mixing rule at different temperatures resulted in correlation regression coefficient of 0.9999. To account for the deviation from ideal gas behaviour, this work presents 99.7% R squared value for dimensionless residual specific heat capacity as a function of reduced temperature and pressure compared to that calculated from Starling Carnahan equation of state. This model is the first explicit correlation for the residual specific heat capacity of natural gas to be derived.
Nigeria Annual International Conference and Exhibition, 2012
The problem of reservoir heterogeneity has made the continued use of Inflow Performance Relation ... more The problem of reservoir heterogeneity has made the continued use of Inflow Performance Relation (IPR) models developed on the assumption of homogeneity impractical. Furui in 2003 (and previously Butler in 1994) solved the problem using fully penetrating well idea so that the model can be applied to different sections of the reservoir. This paper corrects two errors in Furui's model. The first error is the use of arithmetic mean of radii to evaluate the elliptic surface area of the well when an anisotropic reservoir is converted into an isotropic equivalent. This was corrected using an equivalent cylindrical surface area. The second error is the use of a planar isobaric surface at the end of the radial flow region instead of a circular one. These corrections gave the model a better performance-average of 99% against 96% by the original version, when compared with line source solution obtained by using Green function. Equating the hydrostatic and viscous pressure differences betw...
SPE Nigeria Annual International Conference and Exhibition, 2013
ABSTRACT All natural gas processes, including production, sweetening, drying, transportation, sto... more ABSTRACT All natural gas processes, including production, sweetening, drying, transportation, storage, metering and selling requires that we possess ability to predict with great accuracy its volume, pressure, temperature, specific heat capacity etc. Unlike an ideal gas, a real gas does not expand and contract according the simple pressure-volume-temperature relation. This deviation from the ideal gas behavior is corrected with the use of z-factor. Z factor is simply the ratio of the volume of a real gas to that which equal mass of an ideal gas will occupy under the same condition. Several computational methods of obtaining this factor have been developed, but the implicit nature of these correlations called for an explicit method of evaluating the multivariate parameter. In this paper, we used over 6000 data points to develop coefficients of a 2D regression which is Fourier cosine in reduced pressure and polynomial in the reciprocal of the reduced temperature. The result was found to match the result to a very high accuracy without over fitting.
Compressibility factor (z-factor) of gasses is a thermodynamic property used to account for the d... more Compressibility factor (z-factor) of gasses is a thermodynamic property used to account for the deviation of real gas deviation from the ideal gas behavior. The best correlations for this factor given by Hall and Yarborough, Dranchuk & Abou-Kassem and Dranchuk, Purvis & Robinson are based on nonlinear equation of state requiring iterative solution. It is not uncommon for nonlinear equations to have multiple roots, hence, Newton-Raphson often fail to converge or converges on the undesired root of these equations. This unstable behavior of iterative procedure requires that the initial guess is set close to the desired root to ensure convergence. Here we examine the residual equations of the reduced densities of these correlations and set the criteria for the determination of the initial guess as function of the reduced temperature (1.05 ≤ Tpr ≤ 3) and pressure (0.2 ≤ Ppr ≤ 15), we retuned the coefficients using 5940 experimental data points from Handbook of Natural Gas Engineering and...
Natural gas engineering entails production, processing, storage and transportation of natural gas... more Natural gas engineering entails production, processing, storage and transportation of natural gas. A good handling of the gas requires a sophisticated understanding of how its density, compressibility, pseudo-pressure and specific heat capacity vary with the gas condition. A variety of methods have been presented in petroleum and gas journals and a host of scholastic materials to evaluate other properties over a wide range of temperatures, however, the available correlation for isobaric specific heat capacity is for only 150 °F. We generated 200 samples of natural gas mixture with methane component ranging from 0.74 to 0.9985 using normally distributed experimental design. The variations of the respective specific heat capacity of the components and the effect of composition on the specific gravity and overall specific heat capacity of the gas were taken into consideration. The developed correlation reads in the specific gravity and temperature to generate the ideal gas specific heat capacity of the sample. The result yielded 99.75% accuracy at 150 °F when compared to experimental data, as against the result from isentropic coefficient method which overestimated the ideal gas specific heat capacity by 25% at the same temperature. The ideal gas specific heat capacity developed compared to 6000 data points generated from mixing rule at different temperatures resulted in correlation regression coefficient of 0.9999. To account for the deviation from ideal gas behaviour, this work presents 99.7% R squared value for dimensionless residual specific heat capacity as a function of reduced temperature and pressure compared to that calculated from Starling Carnahan equation of state. This model is the first explicit correlation for the residual specific heat capacity of natural gas to be derived.
A horizontal well with a non-linear trajectory is fundamentally an intricate system, and determin... more A horizontal well with a non-linear trajectory is fundamentally an intricate system, and determination of its inflow productivity index using numerical simulation is computationally challenging. This work presents an approach that is more efficient than numerical simulation. The methodology involves dividing the reservoir into different sections, with each section treated as a closed-box model. A constant pressure is assumed for the two sides of the sections, which are parallel to the plane of the trajectory, and end flow is eliminated so that each section of the well is fully penetrating. A simplified isobaric geometry and a flow path were developed using the numerical simulation of flow in a fully penetrating well in a box model; an analytical index equation was then developed from the simplified geometry. The results of the numerical simulation were used to generate an empirical correlation for the shape factor to bring the result of the productivity index equation close to simulation and line source solutions, thus converting the analytical index equation into a semianalytical equation. The application of the semi-analytical equation to a horizontal well, undulating in a vertical plane, to predict its productivity was demonstrated using an example. This model is the first productivity index equation with the capability to handle a horizontal well with a non-linear trajectory.
The compressibility factor (z-factor) of gases is a thermodynamic property used to account for th... more The compressibility factor (z-factor) of gases is a thermodynamic property used to account for the deviation of real gas behavior from that of an ideal gas. Correlations based on the equation of state are often implicit, because they require iteration and are computationally expensive. A number of explicit correlations have been derived to enhance simplicity; however, no single explicit correlation has been developed for the full range of pseudoreduced temperatures 1.05 <Tpr <3 and pseudo-reduced pressures 0.2 <Ppr <15 , which represents a significant research gap. This work presents a new z-factor correlation that can be expressed in linear form. On the basis of Hall and Yarborough’s implicit correlation, we developed the new correlation from 5346 experimental data points extracted from 5940 data points published in the SPE natural gas reservoir engineering textbook and created a linear z-factor chart for a full range of pseudo-reduced temperatures 1:15 < Tpr<3 and pseudo-reduced pressures 0:2<Ppr <15.
Compressibility factor (z-factor) of gasses is a thermodynamic property used to account for the d... more Compressibility factor (z-factor) of gasses is a thermodynamic property used to account for the deviation of real gas deviation from the ideal gas behavior. The best correlations for this factor given by Hall and Yarborough, Dranchuk & Abou-Kassem and Dranchuk, Purvis & Robinson are based on nonlinear equation of state requiring iterative solution.
It is not uncommon for nonlinear equations to have multiple roots, hence, Newton-Raphson often fail to converge or converges on the undesired root of these equations. This unstable behavior of iterative procedure requires that the initial guess is set close to the desired root to ensure convergence.
Here we examine the residual equations of the reduced densities of these correlations and set the criteria for the determination of the initial guess as function of the reduced temp...
Natural gas engineering entails production, processing, storage and transportation of natural gas... more Natural gas engineering entails production, processing, storage and transportation of natural gas. A good handling of the gas requires a sophisticated understanding of how its density, compressibility, pseudo-pressure, and specific heat capacity varies with the gas condition. While petroleum & gas journals and a host of scholastic materials have presented varieties of means to evaluate other properties, they neglected or underscored the need for same for specific heat capacity of natural gas. The only available mathematical relation for this property only predicts its value at 1500F-not at other temperatures.
Recovery factor in recent years has been modelled empirically due to complexities that exist subs... more Recovery factor in recent years has been modelled empirically due to complexities that exist subsurface, and as a result most of the models lacked dimensional homogeneity and neglected the physics of reservoir driving forces that complementarily produce fluids from the reservoir. While these models (mostly Proxies) might satisfy statistical conditions and predict the recovery factors with some degree of accuracy, they fail to reflect well established relationship between physical parameters of the models.
function best_variables = PartSwamOpt(fun, funCInEq, funCEq, lb, ub, penalty, popsize, maxiter, m... more function best_variables = PartSwamOpt(fun, funCInEq, funCEq, lb, ub, penalty, popsize, maxiter, maxrun) % fun = function handle for the function to be minimized % funCInEq = function handle for the inequality condition (set to % empty matrix when there is no inequality condition) % funCEq = function handle for the equality condition (set to % empty matrix when there is no equality condition) % lb = vector of lower bounds % ub = vector of upper bounds % penalty = scale violation of constrain conditions (usually between 10 % and 1000) % popsize = population size (usually 30 to 50) % maxiter = maximum iteration(less than 500) % maxrun = maximum number of runs(10 or less) %% %%%%%%%%%%%%%%%% Examples %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 1. % Roosenbrook = @(x) (1-x(1))^2 + 100*(x(2)-x(1)^2)^2; % 2. % Adjiman = @(x) cos(x(1))*sin(x(2)) – x(1)/(x(2)^2 + 1); % 3. % Beale = @(x) (1.5-x(1) + x(1)*x(2))^2 + (2.25-x(1) + x(1)*x(2)^2)^2 + (2.625-x(1) % + x(1)*x(2)^3)^2; %% %%%%%%%%%%%%%%%%%%%%%%%%%
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Papers by Adewale Kareem
It is not uncommon for nonlinear equations to have multiple roots, hence, Newton-Raphson often fail to converge or converges on the undesired root of these equations. This unstable behavior of iterative procedure requires that the initial guess is set close to the desired root to ensure convergence.
Here we examine the residual equations of the reduced densities of these correlations and set the criteria for the determination of the initial guess as function of the reduced temp...
It is not uncommon for nonlinear equations to have multiple roots, hence, Newton-Raphson often fail to converge or converges on the undesired root of these equations. This unstable behavior of iterative procedure requires that the initial guess is set close to the desired root to ensure convergence.
Here we examine the residual equations of the reduced densities of these correlations and set the criteria for the determination of the initial guess as function of the reduced temp...