scholarly journals A general real-time formulation for multi-rate mass transfer problems

2009 ◽  
Vol 13 (8) ◽  
pp. 1399-1411 ◽  
Author(s):  
O. Silva ◽  
J. Carrera ◽  
M. Dentz ◽  
S. Kumar ◽  
A. Alcolea ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Reactive Transport ◽  
River Flow ◽  
Breakthrough Curves ◽  
Published Data ◽  
Flow And Transport ◽  
Slow Kinetics ◽  
Multiple Processes ◽  
Transfer Problems ◽  
Non Equilibrium

Abstract. Many flow and transport phenomena, ranging from delayed storage in pumping tests to tailing in river or aquifer tracer breakthrough curves or slow kinetics in reactive transport, display non-equilibrium (NE) behavior. These phenomena are usually modeled by non-local in time formulations, such as multi-porosity, multiple processes non equilibrium, continuous time random walk, memory functions, integro-differential equations, fractional derivatives or multi-rate mass transfer (MRMT), among others. We present a MRMT formulation that can be used to represent all these models of non equilibrium. The formulation can be extended to non-linear phenomena. Here, we develop an algorithm for linear mass transfer, which is accurate, computationally inexpensive and easy to implement in existing groundwater or river flow and transport codes. We illustrate this approach by application to published data involving NE groundwater flow and solute transport in rivers and aquifers.

scholarly journals A general real-time formulation for multi-rate mass transfer problems

2009 ◽  
Vol 6 (2) ◽  
pp. 2415-2449 ◽  
Author(s):  
O. Silva ◽  
J. Carrera ◽  
S. Kumar ◽  
M. Dentz ◽  
A. Alcolea ◽  
...  
Keyword(s):  
Mass Transfer ◽  
River Flow ◽  
Breakthrough Curves ◽  
Flow And Transport ◽  
Multiple Processes ◽  
Programming Effort ◽  
Non Local ◽  
Time Formulation ◽  
Transfer Problems ◽  
Non Equilibrium

Abstract. Many flow and transport phenomena, ranging from delayed storage observed in pumping tests to tailing in river or aquifer tracer breakthrough curves, display non-equilibrium behavior. Usually, they are modeled by non-local in time formulations, such as multi-porosity, multiple processes non equilibrium, continuous time random walk, memory functions, integro-differential equations, fractional derivatives or multi-rate mass transfer (MRMT), among others. We develop a MRMT algorithm that can be used to represent all these formulations. The method is accurate, computationally inexpensive and easy to implement in groundwater or river flow and transport codes. In fact, we present a module that can be linked to existing programs with minimal programming effort. Its accuracy is verified by comparison with existing solutions.

A Novel Pore-Scale Thermal-Fracture-Acidizing Model With Heterogeneous Rock Properties

SPE Journal ◽  
2016 ◽  
Vol 21 (01) ◽  
pp. 280-292 ◽  
Author(s):  
John Lyons ◽  
Hadi Nasrabadi ◽  
Hisham A. Nasr-El-Din
Keyword(s):  
Mass Transfer ◽  
Reactive Transport ◽  
Reaction Rate ◽  
Oil And Gas ◽  
Injection Rate ◽  
Rock Properties ◽  
Thermal Fracture ◽  
Pore Scale ◽  
Heterogeneous Rock ◽  
Acid Reaction

Summary Fracture acidizing is a well-stimulation technique used to improve the productivity of low-permeability reservoirs and to bypass deep formation damage. The reaction of injected acid with the rock matrix forms etched channels through which oil and gas can then flow upon production. The properties of these etched channels depend on the acid-injection rate, temperature, reaction chemistry, mass-transport properties, and formation mineralogy. As the acid enters the formation, it increases in temperature by heat exchange with the formation and the heat generated by acid reaction with the rock. Thus, the reaction rate, viscosity, and mass transfer of acid inside the fracture also increase. In this study, a new thermal-fracture-acidizing model is presented that uses the lattice Boltzmann method to simulate reactive transport. This method incorporates both accurate hydrodynamics and reaction kinetics at the solid/liquid interface. The temperature update is performed by use of a finite-difference technique. Furthermore, heterogeneity in rock properties (e.g., porosity, permeability, and reaction rate) is included. The result is a model that can accurately simulate realistic fracture geometries and rock properties at the pore scale and that can predict the geometry of the fracture after acidizing. Three thermal-fracture-acidizing simulations are presented here, involving injection of 15 and 28 wt% of hydrochloric acid into a calcite fracture. The results clearly show an increase in the overall fracture dissolution because of the addition of temperature effects (increasing the acid-reaction and mass-transfer rates). It has also been found that by introducing mineral heterogeneity, preferential dissolution leads to the creation of uneven etching across the fracture surfaces, indicating channel formation.

scholarly journals Modelling of a hybrid culture system with a stationary layer of liquid perfluorochemical applied as oxygen carrier

2016 ◽  
Vol 37 (1) ◽  
pp. 149-158
Author(s):  
Maciej Pilarek ◽  
Katarzyna Dąbkowska
Keyword(s):  
Mass Transfer ◽  
Aqueous Phase ◽  
Culture System ◽  
Oxygen Carrier ◽  
Published Data ◽  
Monod Kinetics ◽  
Batch Cultures ◽  
Whole Process ◽  
Hybrid Culture ◽  
Stationary Layer

Abstract A mathematical model of a hybrid culture system supported with a stationary layer of liquid perfluorochemical (PFC) as a source of O2 for cells which grow in the aqueous phase of culture medium has been developed and discussed. The two-substrate Monod kinetics without inhibition effects, i.e. the Tsao-Hanson equation, has been assumed to characterise the biomass growth. The Damköhler number which relates the growth rate to the mass transfer effects has been used to appraise the regime (i.e. diffusion-limited or kinetics) of the whole process. The proposed model predicted accurately previously published data on the submerged batch cultures of Nicotiana tabacum BY-2 heterotrophic cells performed in a culture system supported with a stationary layer of hydrophobic perfluorodecalin as a liquid O2 carrier. Estimated values of the parameters of the model showed that the process proceeded in the kinetics regime and the growth kinetics, not the effects of the mass transfer between aqueous phase and liquid PFC, had essential influence on the growth of biomass.

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