Modelling Heat and Mass Transfer in Porous Material during Pyrolysis using Operator Splitting and Dimensionless Analysis

Dimensionless analysis isused to improve the computational performance when using operator splitting methods to model the heat and mass transfer during pyrolysis. The specific examples investigated are thermal decomposition of polymer composite when used as heat shields during space-craft re-entry or for rocket nozzle’s protection, and the In-Situ Upgrading (ISU) of solid oil shale by subsurface pyrolysis to form liquid oil and gas. ISU is a very challenging process to model numerically because a large number of components need to be modelled using a system of equations that are both highly non-linear and strongly coupled. Inspectional Analysis is used to determine the minimum number of dimensionless groups that can be used to describe the process. This set of dimensionless numbers is then reduced to those that are key to describing the system behaviour. This is achieved byperforming a sensitivity study using Experimental Design torank the numbers in terms of their impact on system behaviour. The numbers are then sub-divided into those of primary importance, secondary importance and those which are insignificant based on the t-value of their effect, which is compared to the Bonferroni corrected t-limit and Lenth’s margin of error. Finally we use the sub-set of the most significant numbers to improve the stability and performance when numerically modelling this process. A range of operator splitting techniques is evaluated including the Sequential Split Operator (SSO), the Iterative Split Operator (ISO) and theAlternating Split Operator (ASO

Scaling heat and mass flow through porous media during pyrolysis.

The modelling of heat and mass flow through porous media in the presence of pyrolysis is complex because various physical and chemical phenomena need to be represented. In addition to the transport of heat by conduction and convection, and the change of properties with varying pressure and temperature, these processes involve transport of mass by convection, evaporation, condensation and pyrolysis chemical reactions. Examples of such processes include pyrolysis of wood, thermal decomposition of polymer composite and in situ upgrading of heavy oil and oil shale. The behaviours of these systems are difficult to predict as relatively small changes in the material composition can significantly change the thermophysical properties. Scaling reduces the number of parameters in the problem statement and quantifies the relative importance of the various dimensional parameters such as permeability, thermal conduction and reaction constants. This paper uses inspectional analysis to determine the minimum number of dimensionless scaling groups that describe the decomposition of a solid porous material into a gas in one dimension. Experimental design is then used to rank these scaling groups in terms of their importance in describing the outcome of two example processes: the thermal decomposition of heat shields formed from polymer composites and the in situ upgrading of heavy oils and oil shales. A sensitivity analysis is used to divide these groups into three sets (primary, secondary and insignificant), thus identifying the combinations of solid and fluid properties that have the most impact on the performance of the different processes

Modelling In-situ Upgrading of Heavy Oil Using Operator Splitting Methods

Heavy oil and oil sands are important hydrocarbon resources that account for over 10 trillion barrels (Meyer et al., 2007), nearly three times the conventional oil in place in the world. There are huge, wellknown resources of heavy oil, extra-heavy oil, and bitumen in Canada, Venezuela, Russia, the USA and many other countries. The oil sands of Alberta alone contain over two trillion barrels of oil. In Canada, approximately 20% of oil production is from heavy oil and oil sand resources

Scaling heat and mass flow through porous media in the presence of pyrolysis

The modelling of heat and mass flow through porous media in the presence of pyrolysis is complex as various physical and chemical phenomena needs to be represented. In addition to the transport of heat by conduction and convection and the change of properties with varying pressure and temperature, these processes involve transport of mass by convection, evaporation, condensation and pyrolysis chemical reactions. Examples of such process includes pyrolysis of wood, thermal decomposition of polymer composite and in-situ upgrading of heavy oil and oil shale. The behaviour of these systems are complex as relatively small changes in the material composition can significantly change the thermophysical properties. Scaling reduces the number of parameters in the problem statement and quantifies the relative importance of the various dimensional parameters (permeability, thermal conduction, reaction constants...) This paper presents the scaling by Inspectional Analysis (IA) method of a one-dimensional problem where a solid phase decomposes into non-reactive gas. The IA method is based on the underlying physical laws, expressed in the form of partial differential equations and boundary conditions. We find a minimum set of dimension less groups required to describe the problem. The analysis is validated considering the example of thermal decomposition of polymer composite. Then, we study the variability of the heat and mass flow with the scaling groups by performing a sensitivity analysis using experimental design

Scaling analysis of the In-Situ Upgrading of heavy oil and oil shale

International audienceThe In-Situ Upgrading (ISU) of heavy oil and oil shale is investigated. We develop a mathematical model for the process and identify the full set of dimensionless numbers describing the model. We demonstrate that for a model with nf fluid components (gas and oil), ns solid components and k chemical reactions, the model was represented by 9 + k x (3 + nf + ns - 2) + 8nf + 2ns dimensionless numbers. We calculated a range of values for each dimensionless numbers from a literature study. Then, we perform a sensitivity analysis using Design of Experiments (DOE) and Response Surface Methodology (RSM) to identify the primary parameters controlling the production time and energy efficiency of the process. The Damköhler numbers, quantifying the ratio of chemical reaction rate to heat conduction rate for each reaction, are found to be the most important parameters of the study. They depend mostly on the activation energy of the reactions and of the heaters temperature. The reduced reaction enthalpies are also important parameters and should be evaluated accurately. We show that for the two test cases considered in this paper, the Damköhler numbers needed to be at least 10 for the process to be efficient. We demonstrate the existence of an optimal heater temperature for the process and obtain a correlation that can be used to estimate it using the minimum of the Damköhler numbers of all reactions