Deep bed filtration and formation damage by particles with distributed properties
Nastaran Khazali A * , Gabriel Malgaresi B , Yuri Osipov C , Ludmila Kuzmina D and Pavel Bedrikovetsky AA
B
C
D
Nastaran Khazali is currently a PhD student at the University of Adelaide. She holds a Master’s degree in reservoir engineering and two Bachelor’s degrees in petroleum and industrial engineering, all from Amirkabir University of Technology (Tehran Polytechnic). She was awarded the privilege of a dual degree, studying as an exceptional talent student when she was an undergraduate student at Amirkabir University. A coupled background in petroleum and industrial engineering was the main motivation for the pursuit of her Bachelors’ and Master’s theses in the field of datamining/machine-learning and artificial intelligence and their applications in reservoir engineering. For her PhD thesis, she is working on size-distributed suspension/colloidal flow in porous media. Contact email: nastaran.khazali@adelaide.edu.au. |
Dr Gabriel Malgaresi is a Chemical Engineer with a Master’s degree in Reservoir Engineering from the State University of Northern Rio de Janeiro and a PhD in the same field from the University of Adelaide. Throughout his career, Gabriel has conducted research on diverse topics, such as formation damage, multi-component suspension particles, multi-phase flow in porous media, wettability alteration, and carbon dioxide (CO2) storage. Presently, he is employed at Predico Software, where he is engaged in the development of analyses and models for CO2 storage. Additionally, he is actively involved in expanding pressure, volume and temperature; tank; and wellbore models. Contact email: gabriel.malgaresi@predico.com.au. |
Professor Yuri Osipov teaches pure and applied mathematics at the Department of Informatics and Applied Mathematics, Moscow State University of Civil Engineering. His research interests include exact, asymptotic, and numerical solutions of non-linear filtration problems in porous media. He has published several papers on analytical modelling in deep bed filtration and formation damage in leading academic journals. Contact email: yuri-osipov@mail.ru. |
Professor Ludmila Kuzmina teaches differential and integral calculus and differential equations in the Department of Applied Mathematics of the Higher School of Economics (Moscow). Her research interests include mathematical models of deep bed filtration in porous media and non-linear problems of underground fluid mechanics. She has published several papers on exact and asymptotic solutions for non-linear transport of colloidal and nano-fluids. Contact email: l.kuzmina@mail.ru. |
Professor Pavel Bedrikovetsky is a Professor of Petroleum Engineering at the University of Adelaide. He authored a seminal book on reservoir engineering and 290 papers in international journals and SPE. His research covers CO2 and hydrogen storage, well injectivity and productivity, formation damage and enhanced oil recovery. He holds an MSc in Applied Mathematics, a PhD in Fluid Mechanics, and DSc in Reservoir Engineering, all from Moscow Gubkin Oil-Gas University. Pavel boasts 40 years of industrial experience in Europe, USA, Brazil, Ukraine, Russia, and Australia. Pavel was a 2008–2009 and 2016–2017 Society of Petroleum Engineers (SPE) Distinguished Lecturer. He is an SPE Distinguished Member. Pavel was ranked among the world’s top 2% of scientists by Stanford University (2020). Contact email: pavel.bedrikovetski@adelaide.edu.au. |
Abstract
Current models for deep bed filtration describe particles with uniform properties. Yet, the sizes, densities, and mineral composition of particles vary significantly in the same injection well. The aim of this work is to provide an effective mathematical model for water injection of particles with distributed properties and formation damage prediction. We average the set of traditional population balance equations for single-property particles and obtain one upscaled equation. The upscaled equation for particle retention rate contains a non-linear function of suspended concentration, which we call the 'suspension function'. We derive analytical solutions for the upscaled equation for linear (coreflood) and radial (well injectivity) flows. Then we treat lab coreflood data to determine the model suspension function and provide a model for well injectivity prediction. The retention profile for the flow of uniform particles has an exponential form. Frequently reported in the literature, hyper-exponential forms have been hypothetically explained by multiple particle properties. The inverse solution allows revealing the individual filtration coefficients for binary mixtures from total breakthrough concentrations during coreflood. Treatment of the data from lab experiments reveals individual filtration coefficients that belong to common intervals. For the first time, deep bed filtration of particles with distributed properties is upscaled and presented using a single equation that reflects the particle property distribution. This equation provides an effective mathematical model for tuning lab coreflood data, determines the model function, and uses it for injectivity decline prediction.
Keywords: deep bed filtration, filtration function, hyper-exponential retention, particle property distribution, size-distributed colloids, suspension function, suspension/colloidal flow, upscaling.
Nastaran Khazali is currently a PhD student at the University of Adelaide. She holds a Master’s degree in reservoir engineering and two Bachelor’s degrees in petroleum and industrial engineering, all from Amirkabir University of Technology (Tehran Polytechnic). She was awarded the privilege of a dual degree, studying as an exceptional talent student when she was an undergraduate student at Amirkabir University. A coupled background in petroleum and industrial engineering was the main motivation for the pursuit of her Bachelors’ and Master’s theses in the field of datamining/machine-learning and artificial intelligence and their applications in reservoir engineering. For her PhD thesis, she is working on size-distributed suspension/colloidal flow in porous media. Contact email: nastaran.khazali@adelaide.edu.au. |
Dr Gabriel Malgaresi is a Chemical Engineer with a Master’s degree in Reservoir Engineering from the State University of Northern Rio de Janeiro and a PhD in the same field from the University of Adelaide. Throughout his career, Gabriel has conducted research on diverse topics, such as formation damage, multi-component suspension particles, multi-phase flow in porous media, wettability alteration, and carbon dioxide (CO2) storage. Presently, he is employed at Predico Software, where he is engaged in the development of analyses and models for CO2 storage. Additionally, he is actively involved in expanding pressure, volume and temperature; tank; and wellbore models. Contact email: gabriel.malgaresi@predico.com.au. |
Professor Yuri Osipov teaches pure and applied mathematics at the Department of Informatics and Applied Mathematics, Moscow State University of Civil Engineering. His research interests include exact, asymptotic, and numerical solutions of non-linear filtration problems in porous media. He has published several papers on analytical modelling in deep bed filtration and formation damage in leading academic journals. Contact email: yuri-osipov@mail.ru. |
Professor Ludmila Kuzmina teaches differential and integral calculus and differential equations in the Department of Applied Mathematics of the Higher School of Economics (Moscow). Her research interests include mathematical models of deep bed filtration in porous media and non-linear problems of underground fluid mechanics. She has published several papers on exact and asymptotic solutions for non-linear transport of colloidal and nano-fluids. Contact email: l.kuzmina@mail.ru. |
Professor Pavel Bedrikovetsky is a Professor of Petroleum Engineering at the University of Adelaide. He authored a seminal book on reservoir engineering and 290 papers in international journals and SPE. His research covers CO2 and hydrogen storage, well injectivity and productivity, formation damage and enhanced oil recovery. He holds an MSc in Applied Mathematics, a PhD in Fluid Mechanics, and DSc in Reservoir Engineering, all from Moscow Gubkin Oil-Gas University. Pavel boasts 40 years of industrial experience in Europe, USA, Brazil, Ukraine, Russia, and Australia. Pavel was a 2008–2009 and 2016–2017 Society of Petroleum Engineers (SPE) Distinguished Lecturer. He is an SPE Distinguished Member. Pavel was ranked among the world’s top 2% of scientists by Stanford University (2020). Contact email: pavel.bedrikovetski@adelaide.edu.au. |
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