Anomalous Diffusion and Kinetics Properties of Some Generalized Diffusion-Reaction Systems
PhDT, 1993
ABSTRACT For many years the topic of diffusion has motivated extensive studies on theoretical mod... more ABSTRACT For many years the topic of diffusion has motivated extensive studies on theoretical models, due to its fundamental importance and widespread applications in science and technology. In this thesis, a study of anomalous diffusion and the kinetic properties of some diffusion-reaction systems are presented. The term anomalous diffusion refers to stochastic processes in which the mean square displacement does not scale linearly with time, i.e., ~ t^alpha with alphane 1. Processes with alpha 1 are called superdiffusive. In the first part of this thesis, I present new models for anomalous diffusion that not only can help us to understand the origin of the anomalous behavior in physical systems, but also may have applications in a variety of fields such as groundwater hydrology and turbulent diffusion. In the second part of this thesis, I study the kinetics of chemical reactions controlled by diffusion, with emphasis on the role of fluctuations due to the diffusive motion of the reactants. Here, it is assumed that the particles that participate in the reaction do not interact while not in contact, and the attention is centered in the study of collective effects such as the spatial correlations that develop as the particles move. Two types of reactions are considered: A+Bto C and A+B to B. In addition to their simplicity these reactions are amenable to analytical and numerical treatment, and display all the characteristics of diffusion-controlled systems. In particular, the reaction A+Bto C with initially separated reactants is study extensively. Under this condition, a reaction front develops along the interface between the two reactants. The time evolution of the width and height of the front, and the local concentration in the front are evaluated for the cases in which both reactants diffuse and the case in which one reactant is static. Finally, I present a numerical study of the phenomenon of self-segregation of reactants in the trapping reaction A+Bto B for low dimensional systems.
Uncertainty quantification of production forecasts is crucially important for business planning o... more Uncertainty quantification of production forecasts is crucially important for business planning of hydrocarbon-field developments. This is still a very challenging task, especially when subsurface uncertainties must be conditioned to production data. Many different approaches have been proposed, each with their strengths and weaknesses. In this work, we develop a robust uncertainty-quantification work flow by seamless integration of a distributed-Gauss-Newton (GN) (DGN) optimization method with a Gaussian mixture model (GMM) and parallelized sampling algorithms. Results are compared with those obtained from other approaches. Multiple local maximum-a-posteriori (MAP) estimates are determined with the local-search DGN optimization method. A GMM is constructed to approximate the posterior probability-density function (PDF) by reusing simulation results generated during the DGN minimization process. The traditional acceptance/rejection (AR) algorithm is parallelized and applied to improve the quality of GMM samples by rejecting unqualified samples. AR-GMM samples are independent, identically distributed samples that can be directly used for uncertainty quantification of model parameters and production forecasts. The proposed method is first validated with 1D nonlinear synthetic problems with multiple MAP points. The AR-GMM samples are better than the original GMM samples. The method is then tested with a synthetic history-matching problem using the SPE01 reservoir model (Odeh 1981; Islam and Sepehrnoori 2013) with eight uncertain parameters. The proposed method generates conditional samples that are better than or equivalent to those generated by other methods, such as Markov-chain Monte Carlo (MCMC) and global-search DGN combined with the randomized-maximum-likelihood (RML) approach, but have a much lower computational cost (by a factor of five to 100). Finally, it is applied to a real-field reservoir model with synthetic data, with 235 uncertain parameters. A GMM with 27 Gaussian components is constructed to approximate the actual posterior PDF. There are 105 AR-GMM samples accepted from the 1,000 original GMM samples, and they are used to quantify the uncertainty of production forecasts. The proposed method is further validated by the fact that production forecasts for all AR-GMM samples are quite consistent with the production data observed after the history-matching period. The newly proposed approach for history matching and uncertainty quantification is quite efficient and robust. The DGN optimization method can efficiently identify multiple local MAP points in parallel. The GMM yields proposal candidates with sufficiently high acceptance ratios for the AR algorithm. Parallelization makes the AR algorithm much more efficient, which further enhances the efficiency of the integrated work flow.
Machine learning to reduce cycle time for time-lapse seismic data assimilation into reservoir management
Summary The proposed low cost 4D QI workflow using Machine Learning fills the gap between qualita... more Summary The proposed low cost 4D QI workflow using Machine Learning fills the gap between qualitative interpretation of 4D attribute maps and 4D probabilistic inversion of seismic wiggles, thus enabling the rapid quantification of reservoir property changes. This workflow has been applied in several deepwater fields with multiple 4D acquisitions. The estimated water saturation changes have been used to provide key geophysical input to analyze injection efficiency, support the water flood optimization and infill drilling, especially meeting the deadline of business decision making.
The understanding of contact line fluctuations in heterogeneous systems of controlled wettability... more The understanding of contact line fluctuations in heterogeneous systems of controlled wettability is relevant to many industrial processes. Despite its importance, it is poorly understood. Here, we present results on an experimental study of fluid displacement on modified Hele-Shaw cells with surface defects as heterogeneities. The system wettability is controlled by defect surface coverage. Three different surface coverage regimes were studied. For each one, the morphology and deformation energy of the displacement front is determined. The width front is described in terms of two exponents, the roughness exponent (α) and the one that describes its growth (β). In all cases, it is found that the width increases logarithmically in time up to a characteristic value, where a crossover to a saturation behavior is observed. The crossover time is a function of the surface coverage. For low coverage 0.51 ≤ β ≤ 0.59 and 0.65 ≤ α ≤ 0.67. For medium and high coverage the values obtained for the exponents are similar to those of directed percolation. The deformation energy associated with the displacement front morphology makes it possible to identify the individual pinning role of the surface defects.
The transport of a scalar by jump-type random advection and diffusion is described by a mean fiel... more The transport of a scalar by jump-type random advection and diffusion is described by a mean field formulation in terms of a Langevin equation for the fluctuations of the scalar. It is shown how the distribution of the scalar fluctuations is sensistive to the relative strength of advection versus diffusion, and the details of the advection process.
Maximizing VOI of Frequent Seismic Monitoring of Heavy Oil Fields: Case Study at Peace River Pad 31
SPE Heavy Oil Conference and Exhibition, 2016
In May 2014 a permanent seismic monitoring system was deployed in Peace River Pad 31 to monitor a... more In May 2014 a permanent seismic monitoring system was deployed in Peace River Pad 31 to monitor areal steam conformance during pad re-development in this heavy oil field in Alberta, Canada. The dataset comprises a two-year monitoring period and was used within the Well and Reservoir Management framework to optimize production performance and increase field recovery. With seismic snapshots available daily, one area of investigation was to determine the monitoring frequency that maximizes Value of Information (VOI). A lookback study with a panel of independent experts showed that for the particular case of Pad 31, with very limited control due to the existing well completions, quarterly monitoring would be sufficient. Additionally, guidelines were developed for defining an effective seismic monitoring program (e.g., align monitoring with major field interventions, allow enough time for changes to be actionable, etc.). Although based on observations from the Pad 31 trial, these guideli...
Effects of Disorder on Relaxation Processes on Regular and Fractal lattices
Relaxation processes on disordered lattices are studied by using random walks models. Two types o... more Relaxation processes on disordered lattices are studied by using random walks models. Two types of structures are considered: i) regular lattices in one and two dimensions, with a disorder variable attached to each lattice site, and ii) a fractal substrate which is a spanning percolation cluster on a square lattice. For regular lattices, the random variable that represents disorder can be quenched or annealed, and is taken from a power-law distribution of the form |mu| xi^mu-1, with mu in a range where the distribution is normalizable but has a divergent mean and variance. For the fractal substrate, disorder is structural. Different response functions such as the characteristic function and the complex susceptibility are calculated, and compared with the results for the relaxation on a non-disordered structure. We show that for the two cases, two types of anomalous relaxation are found as the disorder exponent mu is varied in the range 0
The problem of Andreev reflection between a normal metal and a multiband superconductor is addres... more The problem of Andreev reflection between a normal metal and a multiband superconductor is addressed. The appropriate matching conditions for the wave function at the interface are established on the basis of an extension of quantum waveguide theory to these systems. Interference effects between different bands of the superconductor manifest themselves in the conductance and the case of FeAs superconductors is specifically considered, in the framework of a recently proposed effective two-band model, in the sign-reversed s-wave pairing scenario. Resonant transmission through surface Andreev bound states is found as well as destructive interference effects that produce zeros in the conductance at normal incidence. Both these effects occur at nonzero bias voltage.
Scaling of Reaction Fronts in the Presence of Disorder
MRS Proceedings, 1994
ABSTRACTA study of the dynamics of the reaction front that appears in diffusion-reaction systems ... more ABSTRACTA study of the dynamics of the reaction front that appears in diffusion-reaction systems of the form A + B → C with initially separated reactants in the presence of quenched disorder is presented. The scaling of the width of the front w is analyzed as a function of the “disorder strength” and the dimensionality of the system. It is shown that disorder strongly affects the width exponent α, ω tα even for d ≥ 2, where the mean field approximation is known to be valid. The scaling of the nearest neighbor distance, midpoint fluctuations and concentration profiles near the center of the front, are also studied.
We study the reaction front for the diffusion-reaction system A + B + C with initially separated ... more We study the reaction front for the diffusion-reaction system A + B + C with initially separated reactants. We present analytical results for the form of the front and the exponents that characterize its width and height asymptotically, which appear to hold in d Z = 2. We also present analytical and numerical results for the form of the reaction front for the 1D case in which one of the reactants is static, and find the width exponent (Y = l/4, which is larger than the mean field exponent (CI = 116) but smaller than the value for the case in which both species diffuse (a = 0.3). Recently there has been considerable interest in the study of the irreversible reaction A + B+ C (inert) in which the reactants are transported by diffusion and are initially separated in space [l-9]. Under these conditions the system is characterized by a “reaction front ” that develops at the interface between the two reactants, and that is marked by the presence of the inert C particles. The time evolutio...
Anomalous Diffusion and Kinetics Properties of Some Generalized Diffusion-Reaction Systems
PhDT, 1993
ABSTRACT For many years the topic of diffusion has motivated extensive studies on theoretical mod... more ABSTRACT For many years the topic of diffusion has motivated extensive studies on theoretical models, due to its fundamental importance and widespread applications in science and technology. In this thesis, a study of anomalous diffusion and the kinetic properties of some diffusion-reaction systems are presented. The term anomalous diffusion refers to stochastic processes in which the mean square displacement does not scale linearly with time, i.e., ~ t^alpha with alphane 1. Processes with alpha 1 are called superdiffusive. In the first part of this thesis, I present new models for anomalous diffusion that not only can help us to understand the origin of the anomalous behavior in physical systems, but also may have applications in a variety of fields such as groundwater hydrology and turbulent diffusion. In the second part of this thesis, I study the kinetics of chemical reactions controlled by diffusion, with emphasis on the role of fluctuations due to the diffusive motion of the reactants. Here, it is assumed that the particles that participate in the reaction do not interact while not in contact, and the attention is centered in the study of collective effects such as the spatial correlations that develop as the particles move. Two types of reactions are considered: A+Bto C and A+B to B. In addition to their simplicity these reactions are amenable to analytical and numerical treatment, and display all the characteristics of diffusion-controlled systems. In particular, the reaction A+Bto C with initially separated reactants is study extensively. Under this condition, a reaction front develops along the interface between the two reactants. The time evolution of the width and height of the front, and the local concentration in the front are evaluated for the cases in which both reactants diffuse and the case in which one reactant is static. Finally, I present a numerical study of the phenomenon of self-segregation of reactants in the trapping reaction A+Bto B for low dimensional systems.
Uncertainty quantification of production forecasts is crucially important for business planning o... more Uncertainty quantification of production forecasts is crucially important for business planning of hydrocarbon-field developments. This is still a very challenging task, especially when subsurface uncertainties must be conditioned to production data. Many different approaches have been proposed, each with their strengths and weaknesses. In this work, we develop a robust uncertainty-quantification work flow by seamless integration of a distributed-Gauss-Newton (GN) (DGN) optimization method with a Gaussian mixture model (GMM) and parallelized sampling algorithms. Results are compared with those obtained from other approaches. Multiple local maximum-a-posteriori (MAP) estimates are determined with the local-search DGN optimization method. A GMM is constructed to approximate the posterior probability-density function (PDF) by reusing simulation results generated during the DGN minimization process. The traditional acceptance/rejection (AR) algorithm is parallelized and applied to improve the quality of GMM samples by rejecting unqualified samples. AR-GMM samples are independent, identically distributed samples that can be directly used for uncertainty quantification of model parameters and production forecasts. The proposed method is first validated with 1D nonlinear synthetic problems with multiple MAP points. The AR-GMM samples are better than the original GMM samples. The method is then tested with a synthetic history-matching problem using the SPE01 reservoir model (Odeh 1981; Islam and Sepehrnoori 2013) with eight uncertain parameters. The proposed method generates conditional samples that are better than or equivalent to those generated by other methods, such as Markov-chain Monte Carlo (MCMC) and global-search DGN combined with the randomized-maximum-likelihood (RML) approach, but have a much lower computational cost (by a factor of five to 100). Finally, it is applied to a real-field reservoir model with synthetic data, with 235 uncertain parameters. A GMM with 27 Gaussian components is constructed to approximate the actual posterior PDF. There are 105 AR-GMM samples accepted from the 1,000 original GMM samples, and they are used to quantify the uncertainty of production forecasts. The proposed method is further validated by the fact that production forecasts for all AR-GMM samples are quite consistent with the production data observed after the history-matching period. The newly proposed approach for history matching and uncertainty quantification is quite efficient and robust. The DGN optimization method can efficiently identify multiple local MAP points in parallel. The GMM yields proposal candidates with sufficiently high acceptance ratios for the AR algorithm. Parallelization makes the AR algorithm much more efficient, which further enhances the efficiency of the integrated work flow.
Machine learning to reduce cycle time for time-lapse seismic data assimilation into reservoir management
Summary The proposed low cost 4D QI workflow using Machine Learning fills the gap between qualita... more Summary The proposed low cost 4D QI workflow using Machine Learning fills the gap between qualitative interpretation of 4D attribute maps and 4D probabilistic inversion of seismic wiggles, thus enabling the rapid quantification of reservoir property changes. This workflow has been applied in several deepwater fields with multiple 4D acquisitions. The estimated water saturation changes have been used to provide key geophysical input to analyze injection efficiency, support the water flood optimization and infill drilling, especially meeting the deadline of business decision making.
The understanding of contact line fluctuations in heterogeneous systems of controlled wettability... more The understanding of contact line fluctuations in heterogeneous systems of controlled wettability is relevant to many industrial processes. Despite its importance, it is poorly understood. Here, we present results on an experimental study of fluid displacement on modified Hele-Shaw cells with surface defects as heterogeneities. The system wettability is controlled by defect surface coverage. Three different surface coverage regimes were studied. For each one, the morphology and deformation energy of the displacement front is determined. The width front is described in terms of two exponents, the roughness exponent (α) and the one that describes its growth (β). In all cases, it is found that the width increases logarithmically in time up to a characteristic value, where a crossover to a saturation behavior is observed. The crossover time is a function of the surface coverage. For low coverage 0.51 ≤ β ≤ 0.59 and 0.65 ≤ α ≤ 0.67. For medium and high coverage the values obtained for the exponents are similar to those of directed percolation. The deformation energy associated with the displacement front morphology makes it possible to identify the individual pinning role of the surface defects.
The transport of a scalar by jump-type random advection and diffusion is described by a mean fiel... more The transport of a scalar by jump-type random advection and diffusion is described by a mean field formulation in terms of a Langevin equation for the fluctuations of the scalar. It is shown how the distribution of the scalar fluctuations is sensistive to the relative strength of advection versus diffusion, and the details of the advection process.
Maximizing VOI of Frequent Seismic Monitoring of Heavy Oil Fields: Case Study at Peace River Pad 31
SPE Heavy Oil Conference and Exhibition, 2016
In May 2014 a permanent seismic monitoring system was deployed in Peace River Pad 31 to monitor a... more In May 2014 a permanent seismic monitoring system was deployed in Peace River Pad 31 to monitor areal steam conformance during pad re-development in this heavy oil field in Alberta, Canada. The dataset comprises a two-year monitoring period and was used within the Well and Reservoir Management framework to optimize production performance and increase field recovery. With seismic snapshots available daily, one area of investigation was to determine the monitoring frequency that maximizes Value of Information (VOI). A lookback study with a panel of independent experts showed that for the particular case of Pad 31, with very limited control due to the existing well completions, quarterly monitoring would be sufficient. Additionally, guidelines were developed for defining an effective seismic monitoring program (e.g., align monitoring with major field interventions, allow enough time for changes to be actionable, etc.). Although based on observations from the Pad 31 trial, these guideli...
Effects of Disorder on Relaxation Processes on Regular and Fractal lattices
Relaxation processes on disordered lattices are studied by using random walks models. Two types o... more Relaxation processes on disordered lattices are studied by using random walks models. Two types of structures are considered: i) regular lattices in one and two dimensions, with a disorder variable attached to each lattice site, and ii) a fractal substrate which is a spanning percolation cluster on a square lattice. For regular lattices, the random variable that represents disorder can be quenched or annealed, and is taken from a power-law distribution of the form |mu| xi^mu-1, with mu in a range where the distribution is normalizable but has a divergent mean and variance. For the fractal substrate, disorder is structural. Different response functions such as the characteristic function and the complex susceptibility are calculated, and compared with the results for the relaxation on a non-disordered structure. We show that for the two cases, two types of anomalous relaxation are found as the disorder exponent mu is varied in the range 0
The problem of Andreev reflection between a normal metal and a multiband superconductor is addres... more The problem of Andreev reflection between a normal metal and a multiband superconductor is addressed. The appropriate matching conditions for the wave function at the interface are established on the basis of an extension of quantum waveguide theory to these systems. Interference effects between different bands of the superconductor manifest themselves in the conductance and the case of FeAs superconductors is specifically considered, in the framework of a recently proposed effective two-band model, in the sign-reversed s-wave pairing scenario. Resonant transmission through surface Andreev bound states is found as well as destructive interference effects that produce zeros in the conductance at normal incidence. Both these effects occur at nonzero bias voltage.
Scaling of Reaction Fronts in the Presence of Disorder
MRS Proceedings, 1994
ABSTRACTA study of the dynamics of the reaction front that appears in diffusion-reaction systems ... more ABSTRACTA study of the dynamics of the reaction front that appears in diffusion-reaction systems of the form A + B → C with initially separated reactants in the presence of quenched disorder is presented. The scaling of the width of the front w is analyzed as a function of the “disorder strength” and the dimensionality of the system. It is shown that disorder strongly affects the width exponent α, ω tα even for d ≥ 2, where the mean field approximation is known to be valid. The scaling of the nearest neighbor distance, midpoint fluctuations and concentration profiles near the center of the front, are also studied.
We study the reaction front for the diffusion-reaction system A + B + C with initially separated ... more We study the reaction front for the diffusion-reaction system A + B + C with initially separated reactants. We present analytical results for the form of the front and the exponents that characterize its width and height asymptotically, which appear to hold in d Z = 2. We also present analytical and numerical results for the form of the reaction front for the 1D case in which one of the reactants is static, and find the width exponent (Y = l/4, which is larger than the mean field exponent (CI = 116) but smaller than the value for the case in which both species diffuse (a = 0.3). Recently there has been considerable interest in the study of the irreversible reaction A + B+ C (inert) in which the reactants are transported by diffusion and are initially separated in space [l-9]. Under these conditions the system is characterized by a “reaction front ” that develops at the interface between the two reactants, and that is marked by the presence of the inert C particles. The time evolutio...
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Papers by Mariela Araujo