Modelling In-situ Upgrading (ISU) of heavy oil using dimensionless analysis and operator splitting method

The In-Situ Upgrading (ISU) of bitumen and oil shale 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. 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. The behaviours of these systems are difficult to predict as relatively small changes in the material composition can significantly change the thermophysical properties. Accurate prediction is further complicated by the fact that many of the inputs needed to describe these processes are uncertain, e.g. the reaction constants and the temperature dependence of the material properties. The large number of components and chemical reactions involves a non-linear system that is often too large for full field simulation using the Fully Implicit Method (FIM). Operator splitting (OS) methods are one way of potentially improving computational performance. Each numerical operator in a process is modelled separately, allowing the best solution method to be used for the given numerical operator. A significant drawback to the approach is that decoupling the governing equations introduces an additional source of numerical error, known as splitting error. Obviously the best splitting method for modelling a given process is the one that minimises the splitting error whilst improving computational performance over that obtained from using a fully implicit approach. Although operator splitting has been widely used for the modelling of reactive-transport problems, it has not yet been applied to models that involve the coupling of mass transport, heat transfer and chemical reactions. One reason is that it is not clear which operator splitting technique to use. Numerous such techniques are described in the literature and each leads to a different splitting error, which depends significantly on the relative importance of the mechanisms involved in the system. While this error has been extensively analysed for linear operators for a wide range of methods, the results observed cannot be extended to general non-linear systems. It is therefore not clear which of these techniques is most appropriate for the modelling of ISU. Analysis using dimensionless numbers can provide a useful insight into the relative importance of different parameters and processes. 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. Combined with Design of Experiments (DOE), which allows quantification of the impact of the parameters with a minimal number of numerical experiments, dimensionless analysis enables experimental programmes to be focused on acquiring the relevant data with the appropriate accuracy by ranking the different parameters controlling the process. It can also help us design a better splitting method by identifying the couplings that need to be conserved and the ones that can be relaxed. This work has three main objectives: (1) to quantify the main interactions between the heat conduction, the heat and mass convection and the chemical reactions, (2) to identify the primary parameters for the efficiency of the process and (3) to design a numerical method that reduces the CPU time of the simulations with limited loss in accuracy. We first consider a simplified model of the ISU process in which a solid reactant decomposes into non-reactive gas. This model allows us to draw a parallel between the in-situ conversion of kerogen and the thermal decomposition of polymer composite when used as heat-shield. The model is later extended to include a liquid phase and several reactions. We demonstrate that a ISU model with nf fluid components, ns solid components and k chemical reactions depends on 9+k*(3+nf+ns-2)+8nf+2ns dimensionless numbers. The sensitivity analysis shows that (1) the heat conduction is the primary operator controlling the time scale of the process and (2) the chemical reactions control the efficiency of the process through the extended Damköhler numbers, which quantify the ratio of chemical rate to heat conduction rate at the heater temperature for each reaction in the model. In the absence of heat loss and gravity effects, we show that the ISU process is most efficient at a heater temperature for which the minimum of the extended Damköhler numbers of all reactions included in the model was between 10 and 20. For the numerical method, the standard Iterative Split Operator (ISO) does not perform well due to many convergence failures, whereas the standard Sequential Split Operator (SSO) and the Strang-Marchuk Split Operator (SMSO) give large discretization errors. We develop a new method, called SSO-CKA, which has smaller discretization error. This method simply applies SSO with three decoupled operators: the heat conduction (operator $C$), the chemical reactions (operator $K$) and the heat and mass convection (operator $A$), applied in this order. When we apply SSO-CKA with the second-order trapezoidal rule (TR) for solving the chemical reaction operator, we obtain a method which generally gives smaller discretization errors than FIM. We design an algorithm, called SSO-CKA-TR-AIM, which is faster and generally more accurate than FIM for simulations with a kinetic model including a large number of components that could be regrouped into a small number of chemical classes for the advection and heat conduction operator. SSO-CKA works best for ISU models with small reaction enthalpies and no other reaction than pyrolysis reactions, but can give a large discretization method for ISU models with non-equilibrium reactions.Open Acces

Channeling: a new class of dissolution in complex porous media

The current conceptual model of mineral dissolution in porous media is comprised of three dissolution patterns (wormhole, compact, and uniform) - or regimes - that develop depending on the relative dominance of flow, diffusion, and reaction rate. Here, we examine the evolution of pore structure during acid injection using numerical simulations on two porous media structures of increasing complexity. We examine the boundaries between regimes and characterise the existence of a forth regime called channeling, where already existing fast flow pathways are preferentially widened by dissolution. Channeling occurs in cases where the distribution in pore throat size results in orders of magnitude differences in flow rate for different flow pathways. This focusing of dissolution along only dominant flow paths induces an immediate, large change in permeability with a comparatively small change in porosity, resulting in a porosity-permeability relationship unlike any that has been previously seen. This work demonstrates that our current conceptual model of dissolution regimes must be modified to include channeling for accurate predictions of dissolution in applications such as geologic carbon storage and geothermal energy production

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

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 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

Experimental investigation of solubility trapping in 3D printed micromodels

Understanding interfacial mass transfer during dissolution of gas in a liquid is vital for optimising large-scale carbon capture and storage operations. While the dissolution of CO2 bubbles in reservoir brine is a crucial mechanism towards safe CO2 storage, it is a process that occurs at the pore-scale and is not yet fully understood. Direct numerical simulation (DNS) models describing this type of dissolution exist and have been validated with semi-analytical models on simple cases like a rising bubble in a liquid column. However, DNS models have not been experimentally validated for more complicated scenarios such as dissolution of trapped CO2 bubbles in pore geometries where there are few experimental datasets. In this work we present an experimental and numerical study of trapping and dissolution of CO2 bubbles in 3D printed micromodel geometries. We use 3D printing technology to generate three different geometries, a single cavity geometry, a triple cavity geometry and a multiple channel geometry. In order to investigate the repeatability of the trapping and dissolution experimental results, each geometry is printed three times and three identical experiments are performed for each geometry. The experiments are performed at low capillary number representative of flow during CO2 storage applications. DNS simulations are then performed and compared with the experimental results. Our results show experimental reproducibility and consistency in terms of CO2 trapping and the CO2 dissolution process. At such low capillary number, our numerical simulator cannot model the process accurately due to parasitic currents and the strong time step constraints associated with capillary waves. However, we show that, for the single and triple cavity geometry

Comparison of Flow and Transport Experiments on 3D Printed Micromodels with Direct Numerical Simulations

International audienceUnderstanding pore-scale flow and transport processes is important for understanding flow and transport within rocks on a larger scale. Flow experiments on small-scale micromodels can be used to experimentally investigate pore-scale flow. Current manufacturing methods of micromodels are costly and time consuming. 3D printing is an alternative method for the production of micromodels. We have been able to visualise small-scale, single-phase flow and transport processes within a 3D printed micromodel using a custom-built visualisation cell. Results have been compared with the same experiments run on a micromodel with the same geometry made from polymethyl methacrylate (PMMA, also known as Perspex). Numerical simulations of the experiments indicate that differences in experimental results between the 3D printed micromodel and the Perspex micromodel may be due to variability in print geometry and surface properties between the samples. 3D printing technology looks promising as a micromodel manufacturing method; however, further work is needed to improve the accuracy and quality of 3D printed models in terms of geometry and surface roughness

Comparison of Flow and Transport Experiments on 3D Printed Micromodels with Direct Numerical Simulations

Understanding pore-scale flow and transport processes is important for understanding flow and transport within rocks on a larger scale. Flow experiments on small-scale micromodels can be used to experimentally investigate pore-scale flow. Current manufacturing methods of micromodels are costly and time consuming. 3D printing is an alternative method for the production of micromodels. We have been able to visualise small-scale, single-phase flow and transport processes within a 3D printed micromodel using a custom-built visualisation cell. Results have been compared with the same experiments run on a micromodel with the same geometry made from polymethyl methacrylate (PMMA, also known as Perspex). Numerical simulations of the experiments indicate that differences in experimental results between the 3D printed micromodel and the Perspex micromodel may be due to variability in print geometry and surface properties between the samples. 3D printing technology looks promising as a micromodel manufacturing method; however, further work is needed to improve the accuracy and quality of 3D printed models in terms of geometry and surface roughness