Physics-informed Neural Network (PINN) is a promising tool that has been applied in a variety of ... more Physics-informed Neural Network (PINN) is a promising tool that has been applied in a variety of physical phenomena described by partial differential equations (PDE). However, it has been observed that PINNs are difficult to train in certain “stiff” problems, which include various nonlinear hyperbolic PDEs that display shocks in their solutions. Recent studies added a diffusion term to the PDE, and an artificial viscosity (AV) value was manually tuned to allow PINNs to solve these problems. In this paper, we propose three approaches to address this problem, none of which rely on an a priori definition of the artificial viscosity value. The first method learns a global AV value, whereas the other two learn localized AV values around the shocks, by means of a parametrized AV map or a residual-based AV map. We applied the proposed methods to the inviscid Burgers equation and the Buckley-Leverett equation, the latter being a classical problem in Petroleum Engineering. The results show t...
SPE Annual Technical Conference and Exhibition, 2010
ABSTRACT Reservoir models utilize highly heterogenous permeability and porosity fields embedded i... more ABSTRACT Reservoir models utilize highly heterogenous permeability and porosity fields embedded in a structural model derived from geophysical and geological data. It is not uncommon for permeabilities in the initial model derived from static data to differ significantly from values obtained from the interpretation of well-test data. This paper presents the application of the ensemble Kalman Filter (EnKF) to assimilate pressure transient and production-logging data to update permeabilities, estimate layer skin factors and effective" well skin factor in multilayered reservoir models. The methodology is applied to two synthetic cases and a field case. For the eld case application, we consider two approaches. In the rst approach we simply use multipliers to adjust the heterogeneous permeability field in each layer. In the second approach, we adjust the prior mean of each layer log-permeability field together with individual gridblock log-permeabilities.
Physics-aware machine learning (ML) techniques have been used to endow data-driven proxy models w... more Physics-aware machine learning (ML) techniques have been used to endow data-driven proxy models with features closely related to the ones encountered in nature. Examples span from material balance and conservation laws. Physics-based and data-driven reduced-order models or a combination thereof (hybrid-based models) can lead to fast, reliable, and interpretable simulations used in many reservoir management workflows. We built on a recently developed deep-learning-based reduced-order modeling framework by adding a new step related to information of the input-output behavior (e.g., well rates) of the reservoir and not only the states (e.g., pressure and saturation) matching. A Combination of data-driven model reduction strategies and machine learning (deep- neural networks – NN) will be used here to achieve state and input-output matching simultaneously. In Jin, Liu and Durlofsky (2020), the authors use a NN architecture where it is possible to predict the state variables evolution af...
O agronegócio da mamona é de grande valia para o crescimento do semi-árido nordestino, pois a cad... more O agronegócio da mamona é de grande valia para o crescimento do semi-árido nordestino, pois a cadeia produtiva da mamona gera múltiplos produtos e subprodutos, dentre os quais podemos destacar o biodiesel, a glicerina, a ração para animais e o adubo vegetal. A produção de mamona como insumo para a produção de biodiesel pode contribuir decisivamente para o desenvolvimento econômico e social da região Nordeste, no entanto, problemas estruturais verificados em todo o setor de transportes implicam na perda de competitividade para vários tipos de agronegócios. Para os produtos agrícolas, (CAIXETA e MARTINS, 2000) estimam que a participação dos custos de transporte no preço final desses produtos no atacado seja mais que duas vezes aquela encontrada para os produtos manufaturados. Sendo assim, a localização de Plantas de Produção de Biodiesel da Mamona - PPBDM deve ser implementada buscando a configuração que minimize o custo total de implantação e distribuição. Este trabalho aplicou o Pro...
ABSTRACT Reservoir models utilize highly heterogenous permeability and porosity fields embedded i... more ABSTRACT Reservoir models utilize highly heterogenous permeability and porosity fields embedded in a structural model derived from geophysical and geological data. It is not uncommon for permeabilities in the initial model derived from static data to differ significantly from values obtained from the interpretation of well-test data. This paper presents the application of the ensemble Kalman Filter (EnKF) to assimilate pressure transient and production-logging data to update permeabilities, estimate layer skin factors and effective" well skin factor in multilayered reservoir models. The methodology is applied to two synthetic cases and a field case. For the eld case application, we consider two approaches. In the rst approach we simply use multipliers to adjust the heterogeneous permeability field in each layer. In the second approach, we adjust the prior mean of each layer log-permeability field together with individual gridblock log-permeabilities.
Physics-informed Neural Network (PINN) is a promising tool that has been applied in a variety of ... more Physics-informed Neural Network (PINN) is a promising tool that has been applied in a variety of physical phenomena described by partial differential equations (PDE). However, it has been observed that PINNs are difficult to train in certain “stiff” problems, which include various nonlinear hyperbolic PDEs that display shocks in their solutions. Recent studies added a diffusion term to the PDE, and an artificial viscosity (AV) value was manually tuned to allow PINNs to solve these problems. In this paper, we propose three approaches to address this problem, none of which rely on an a priori definition of the artificial viscosity value. The first method learns a global AV value, whereas the other two learn localized AV values around the shocks, by means of a parametrized AV map or a residual-based AV map. We applied the proposed methods to the inviscid Burgers equation and the Buckley-Leverett equation, the latter being a classical problem in Petroleum Engineering. The results show t...
SPE Annual Technical Conference and Exhibition, 2010
ABSTRACT Reservoir models utilize highly heterogenous permeability and porosity fields embedded i... more ABSTRACT Reservoir models utilize highly heterogenous permeability and porosity fields embedded in a structural model derived from geophysical and geological data. It is not uncommon for permeabilities in the initial model derived from static data to differ significantly from values obtained from the interpretation of well-test data. This paper presents the application of the ensemble Kalman Filter (EnKF) to assimilate pressure transient and production-logging data to update permeabilities, estimate layer skin factors and effective" well skin factor in multilayered reservoir models. The methodology is applied to two synthetic cases and a field case. For the eld case application, we consider two approaches. In the rst approach we simply use multipliers to adjust the heterogeneous permeability field in each layer. In the second approach, we adjust the prior mean of each layer log-permeability field together with individual gridblock log-permeabilities.
Physics-aware machine learning (ML) techniques have been used to endow data-driven proxy models w... more Physics-aware machine learning (ML) techniques have been used to endow data-driven proxy models with features closely related to the ones encountered in nature. Examples span from material balance and conservation laws. Physics-based and data-driven reduced-order models or a combination thereof (hybrid-based models) can lead to fast, reliable, and interpretable simulations used in many reservoir management workflows. We built on a recently developed deep-learning-based reduced-order modeling framework by adding a new step related to information of the input-output behavior (e.g., well rates) of the reservoir and not only the states (e.g., pressure and saturation) matching. A Combination of data-driven model reduction strategies and machine learning (deep- neural networks – NN) will be used here to achieve state and input-output matching simultaneously. In Jin, Liu and Durlofsky (2020), the authors use a NN architecture where it is possible to predict the state variables evolution af...
O agronegócio da mamona é de grande valia para o crescimento do semi-árido nordestino, pois a cad... more O agronegócio da mamona é de grande valia para o crescimento do semi-árido nordestino, pois a cadeia produtiva da mamona gera múltiplos produtos e subprodutos, dentre os quais podemos destacar o biodiesel, a glicerina, a ração para animais e o adubo vegetal. A produção de mamona como insumo para a produção de biodiesel pode contribuir decisivamente para o desenvolvimento econômico e social da região Nordeste, no entanto, problemas estruturais verificados em todo o setor de transportes implicam na perda de competitividade para vários tipos de agronegócios. Para os produtos agrícolas, (CAIXETA e MARTINS, 2000) estimam que a participação dos custos de transporte no preço final desses produtos no atacado seja mais que duas vezes aquela encontrada para os produtos manufaturados. Sendo assim, a localização de Plantas de Produção de Biodiesel da Mamona - PPBDM deve ser implementada buscando a configuração que minimize o custo total de implantação e distribuição. Este trabalho aplicou o Pro...
ABSTRACT Reservoir models utilize highly heterogenous permeability and porosity fields embedded i... more ABSTRACT Reservoir models utilize highly heterogenous permeability and porosity fields embedded in a structural model derived from geophysical and geological data. It is not uncommon for permeabilities in the initial model derived from static data to differ significantly from values obtained from the interpretation of well-test data. This paper presents the application of the ensemble Kalman Filter (EnKF) to assimilate pressure transient and production-logging data to update permeabilities, estimate layer skin factors and effective" well skin factor in multilayered reservoir models. The methodology is applied to two synthetic cases and a field case. For the eld case application, we consider two approaches. In the rst approach we simply use multipliers to adjust the heterogeneous permeability field in each layer. In the second approach, we adjust the prior mean of each layer log-permeability field together with individual gridblock log-permeabilities.
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Papers by Emilio Coutinho