The oil production from well fractured carbonate reservoirs is a considerable part of the total oil production in the world. The petroleum resource base in naturally fractured reservoirs is estimated to be in the range of billions of barrels in the U.S and in addition, a multibillion- barrel international oil resource base exists in naturally fractured reservoirs. Gravity drainage is important in some of oil recovery processes, either acting as the driving force in processes using horizontal wells or altering the displacement patterns during water-flooding, chemical flooding, CO2 flooding and other EOR methods. The gravity drainage process has a major effect on oil recovery from oil reservoirs. Gravity drainage driven oil production in naturally fractured and other complex reservoirs falls into two regimes: the balk flow regime and the film flow regime. Oil recovery by gravity drainage in a fractured reservoir strongly depends on the capillary height of the porous medium. Capillarity and gravity forces are usually the major driving forces in fractured reservoirs. This PhD thesis consists of two main parts namely: 1) Experimental works on gravity drainage, and 2) Modeling and simulation of the gravity drainage processes using COMSOL® software. An appropriate design of experiment (DOE) method was selected to find the most important parameters contributing in gravity drainage and then conduct the experiments in a useful as well as economic manner. A two-dimensional experimental setup was employed to investigate free fall gravity drainage (FFGD) and controlled gravity drainage (CGD) using unconsolidated glass beads fractured porous media having various fractures configurations. Flow visualization measurements were carried out. Following the flow visualization experiments, parametric sensitivity analysis was performed considering the effects of different system parameters such as fracture aperture, matrix height, permeability, and fluid properties on the dependent variables including drainage rate, critical pumping rate, maximum drainage rate, recovery factor and so on. These experiments enabled us to capture some aspects of the recovery mechanism and the flow communication between matrix block and fracture during gravity drainage. After analyzing the experimental data for the FFGD test runs, it was found that the rate of liquid flowing from matrix to fracture is proportional to the difference of liquid levels in the matrix and in the fracture. In addition, the characteristic rate and the maximum liquid drainage rate from the fractured models were determined for such a stable gravity-dominated process. The experiments showed that the presence of fracture is more influential in lower matrix permeability systems. For a given fracture-matrix system with different initial liquid saturation conditions, it was seen that the production history can be correlated by plotting the fraction of recoverable liquid as a function of time. Furthermore, the recovery factor can be correlated using dimensionless numbers such as the Bond number and the dimensionless time. For the controlled gravity drainage (CGD) test runs conducted, the experimental results indicated that higher pumping rates cause a higher difference between the liquid levels in the fracture and in the matrix, thus the gas breakthrough happens sooner. Moreover, it was found that as long as the porous medium is drained with a constant liquid pumping rate but lower than critical rate, the height difference between the G-L interfaces in matrix and fracture remains constant. In this study, a new concept of “Critical Pumping Rate” (CPR) was defined at which each particular porous medium has recovery factor equal to the recovery factor for higher rates just before gas breakthrough. The difference between liquid levels in fracture and matrix remains unchanged at rates higher than CPR. Known this particular withdrawal rate, there are two main advantages, namely: 1) choosing a pumping rate lower than it to drain the reservoir without getting gas breakthrough; and 2) understanding the physics of pumping behaviour from fractured media and extending the concept to the real cases. In addition, the maximum liquid pumping rate from each physical model was studied and it was found that the rate depends strongly on the storage capacity of the fractures, petrophysical properties of each model as well as physical properties of test fluids. The critical rate, maximum rate, recovery factor at gas breakthrough and difference of gas liquid interface positions in matrix and fracture were correlated by dimensionless numbers such as Bond number, Capillary, and the ratio of permeabilities. Linear regression correlations presented in this study can predict production history and flow behaviour in the fractured porous media for a wide range of dimensionless numbers. The COMSOL® software was used to numerically simulate the gravity drainage processes in the two-dimensional flow experiments for fractured porous media. The parameters of the model were based on theory, as well as on the results of the two-dimensional gravity drainage experiments. The simulation results for the gravity drainage processes compared favourably with the experimental results, as a good match between the numerical solution and the experimental data was found. The simulation model developed provides a basis for further modeling of gravity drainage process in more complicated porous media.

The oil production from well fractured carbonate reservoirs is a considerable part of the total oil production in the world. The petroleum resource base in naturally fractured reservoirs is estimated to be in the range of billions of barrels in the U.S and in addition, a multibillion- barrel international oil resource base exists in naturally fractured reservoirs. Gravity drainage is important in some of oil recovery processes, either acting as the driving force in processes using horizontal wells or altering the displacement patterns during water-flooding, chemical flooding, CO2 flooding and other EOR methods. The gravity drainage process has a major effect on oil recovery from oil reservoirs. Gravity drainage driven oil production in naturally fractured and other complex reservoirs falls into two regimes: the balk flow regime and the film flow regime. Oil recovery by gravity drainage in a fractured reservoir strongly depends on the capillary height of the porous medium. Capillarity and gravity forces are usually the major driving forces in fractured reservoirs. This PhD thesis consists of two main parts namely: 1) Experimental works on gravity drainage, and 2) Modeling and simulation of the gravity drainage processes using COMSOL® software. An appropriate design of experiment (DOE) method was selected to find the most important parameters contributing in gravity drainage and then conduct the experiments in a useful as well as economic manner. A two-dimensional experimental setup was employed to investigate free fall gravity drainage (FFGD) and controlled gravity drainage (CGD) using unconsolidated glass beads fractured porous media having various fractures configurations. Flow visualization measurements were carried out. Following the flow visualization experiments, parametric sensitivity analysis was performed considering the effects of different system parameters such as fracture aperture, matrix height, permeability, and fluid properties on the dependent variables including drainage rate, critical pumping rate, maximum drainage rate, recovery factor and so on. These experiments enabled us to capture some aspects of the recovery mechanism and the flow communication between matrix block and fracture during gravity drainage. After analyzing the experimental data for the FFGD test runs, it was found that the rate of liquid flowing from matrix to fracture is proportional to the difference of liquid levels in the matrix and in the fracture. In addition, the characteristic rate and the maximum liquid drainage rate from the fractured models were determined for such a stable gravity-dominated process. The experiments showed that the presence of fracture is more influential in lower matrix permeability systems. For a given fracture-matrix system with different initial liquid saturation conditions, it was seen that the production history can be correlated by plotting the fraction of recoverable liquid as a function of time. Furthermore, the recovery factor can be correlated using dimensionless numbers such as the Bond number and the dimensionless time. For the controlled gravity drainage (CGD) test runs conducted, the experimental results indicated that higher pumping rates cause a higher difference between the liquid levels in the fracture and in the matrix, thus the gas breakthrough happens sooner. Moreover, it was found that as long as the porous medium is drained with a constant liquid pumping rate but lower than critical rate, the height difference between the G-L interfaces in matrix and fracture remains constant. In this study, a new concept of “Critical Pumping Rate” (CPR) was defined at which each particular porous medium has recovery factor equal to the recovery factor for higher rates just before gas breakthrough. The difference between liquid levels in fracture and matrix remains unchanged at rates higher than CPR. Known this particular withdrawal rate, there are two main advantages, namely: 1) choosing a pumping rate lower than it to drain the reservoir without getting gas breakthrough; and 2) understanding the physics of pumping behaviour from fractured media and extending the concept to the real cases. In addition, the maximum liquid pumping rate from each physical model was studied and it was found that the rate depends strongly on the storage capacity of the fractures, petrophysical properties of each model as well as physical properties of test fluids. The critical rate, maximum rate, recovery factor at gas breakthrough and difference of gas liquid interface positions in matrix and fracture were correlated by dimensionless numbers such as Bond number, Capillary, and the ratio of permeabilities. Linear regression correlations presented in this study can predict production history and flow behaviour in the fractured porous media for a wide range of dimensionless numbers. The COMSOL® software was used to numerically simulate the gravity drainage processes in the two-dimensional flow experiments for fractured porous media. The parameters of the model were based on theory, as well as on the results of the two-dimensional gravity drainage experiments. The simulation results for the gravity drainage processes compared favourably with the experimental results, as a good match between the numerical solution and the experimental data was found. The simulation model developed provides a basis for further modeling of gravity drainage process in more complicated porous media.

No description available.

Pore scale interaction between matrix and fracture during miscible and immiscible CO2 injection was studied experimentally using visual models. Initially, visualization experiments were conducted on 2-D glass bead packed models by injecting n-heptane (solvent) displacing different kinds of processed oil. The focus was on the displacement patterns and solvent breakthrough controlled by matrix-fracture interaction and the pore scale behaviour of solvent-oil interaction for different fracture and injection conditions (rate, vertical vs. horizontal injection) as well as oil viscosity. Besides the visual investigation, effluent was also analyzed to calculate the solvent cut and oil recovery. Next, the process was modeled numerically using a commercial compositional simulator and the saturation distribution in the matrix was matched to the experimental data. The key parameters in the matching process were the effective diffusion coefficients and the longitudinal and transverse dispersivities. The diffusion coefficients were specified for each fluid and dispersivities were assigned into grid blocks separately for the fracture and the matrix. Finally, glass etched microfluidic models were used to investigate pore scale interaction between the matrix and the fracture. The models were prepared by etching homogeneous and heterogeneous micro scale pore patterns on glass sheets bonded together and then saturated with colored n-decane as the oleic phase. CO2 was injected at miscible and immiscible conditions. The focus was on visual pore scale analysis of miscibility, breakthrough of CO2 and oil/CO2 transfer between the matrix and the fracture under different miscibility, injection rate and wettability conditions. / Petroleum Engineering

[pt] Esse trabalho apresenta um modelo numérico para a análise de processos acoplados de efeitos mecânicos e escoamento bifásico em meios porosos fraturados, com a utilização de diferentes métodos numéricos combinados (Elementos finitos contínuos e descontínuos), e utilizando uma mesma malha de elementos finitos para representar uma célula de modelo de simulação de reservatório. As descontinuidades são inseridas na malha como elementos de nós duplicados colapsados. Empregam-se procedimentos numéricos desenvolvidos em dois grupos distintos. Um primeiro grupo de simulações trata de um procedimento numérico de escoamento bifásico, com ênfase à obtenção de um balanço de volumes verdadeiramente conservativo. Nesta fase, avalia-se uma formulação numérica que emprega um processo em três etapas: o método dos elementos finitos (EF), para a aproximação da equação da pressão; intermediariamente, utiliza-se o método de Raviart-Thomas de mais baixa ordem para aproximação da velocidade; e a aproximação da equação da saturação pelo método dos elementos finitos descontínuos (MEFD), que utiliza um limitador de inclinação multidimensional de modo a evitar oscilações na reconstrução dos dados de saturação. Para fins de validação da formulação desenvolvida, comparam-se os resultados obtidos com simulações utilizando o Método do Volumes Finitos (VF). O segundo grupo de simulações trata de acoplar o módulo mecânico (em EF) ao simulador de escoamento bifásico, de modo que a variação do estado de tensões, decorrente da explotação, seja considerada nas simulações. Essa análise permite uma melhor representação do fenômeno estudado além de proporcionar melhores resultados quanto à chegada da água nos poços produtores, afetando a produtividade do modelo. / [en] This work presents a numerical model for the analysis of coupled processes of mechanical effects and two-phase flow in fractured porous media using different numerical methods (continuous and discontinuous finite elements), and using the same finite element mesh to represent a cell of reservoir simulation model. The discontinuities are inserted into the mesh as elements of collapsed duplicate nodes. Numerical procedures developed in two distinct groups are used. A first group of simulations deals with a numerical two-phase flow procedure, with special emphasis on obtaining a truly conservative volume balance. At this stage, a numerical formulation using a three-step process is evaluated: The Finite Element Method (EF), for the approximation of the pressure equation; the lower order of Raviart-Thomas method is used to velocity approximation; and the approximation of the saturation equation by the discontinuous finite element method (MEFD), using a multidimensional slope limiter in order to avoid oscillations in the reconstruction of the saturation data. For the validation of the developed formulation, the results obtained are compared with simulations using the Finite Volume Method (VF), with focus on the analysis of the conservation of volumes. The second group of simulations couple the mechanical module (in EF) to twophase flow computer program, so the variation of the stress state, due to exploitation, is considered in the simulations. This analysis allows a better representation of the phenomenon. In addition to providing better results regarding the arrival of water in the producing wells, affecting the productivity of the model.

Le but de cette thèse est de développer et d’analyser les méthodes Hybrides d’Ordre Élevé (HHO: Hybrid High-Order, en anglais) pour des problèmes d’interfaces. Nous nous intéressons à deux types d’interfaces (i) les interfaces diffuses, et (ii) les interfaces traitées comme frontières internes du domaine computationnel. La première moitié de ce manuscrit est consacrée aux interfaces diffuses, et plus précisément aux célèbres équations de Cahn–Hilliard qui modélisent le processus de séparation de phase par lequel les deux composants d’un fluide binaire se séparent pour former des domaines purs en chaque composant. Dans la deuxième moitié, nous considérons des modèles à dimension hybride pour la simulation d’écoulements de Darcy et de transports passifs en milieu poreux fracturé, dans lequel la fracture est considérée comme un hyperplan (d’où le terme hybride) qui traverse le domaine computationnel. / The purpose of this Ph.D. thesis is to design and analyse Hybrid High-Order (HHO) methods on some interface problems. By interface, we mean (i) diffuse interface, and (ii) interface as an immersed boundary. The first half of this manuscrit is dedicated to diffuse interface, more precisely we consider the so called Cahn–Hilliard problem that models the process of phase separation, by which the two components of a binary fluid spontaneously separate and form domains pure in each component. In the second half, we deal with the interface as an immersed boundary and consider a hybrid dimensional model for the simulation of Darcy flows and passive transport in fractured porous media, in which the fracture is considered as an hyperplane that crosses our domain of interest.

Cette thèse est consacrée à l'étude mathématique d'un problème inverse en hydrogéologie : le but est d'identifier des fractures en milieu poreux, connaissant des mesures de l'écoulement dans le sous-sol. Le nombre, la localisation et les paramètres physiques des fractures sont recherchés. Ce problème est formulé comme la minimisation au sens des moindres carrés d'une fonctionnelle évaluant l'écart entre les mesures et les résultats du modèle direct. L'écoulement est celui d'un fluide monophasique incompressible (loi de Darcy). Un modèle traitant les fractures comme des interfaces est utilisé. Le problème direct est le modèle de fracture discrétisé par la méthode des éléments finis mixtes hybrides.Pour résoudre ce problème inverse, un nouvel algorithme itératif a été développé, basé sur l’utilisation d’indicateurs de fractures mis au point pendant la thèse. Ces indicateurs donnent une information au premier ordre concernant l'effet de l'ajout d'une nouvelle fracture. Comme ces indicateurs sont peu coûteux, un grand nombre de configurations de fractures sont testées à chaque itération. L’algorithme a été programmé, validé puis testé numériquement dans des situations variées, en utilisant des mesures synthétiques. Il donne des résultats très satisfaisants, bien que ce problème soit réputé difficile.Enfin, l’étude de l’identifiabilité du problème inverse a été amorcée. Pour un modèle simplifié de fractures (failles très perméables, cas le plus courant dans le sous-sol), on a montré que le problème. / This PhD is dedicated to the mathematical study of an inverse problem in hydrogeology: the goal is to identify fractures in porous medium, knowing measurements of the underground flow. The number, the location and the physical parameters of the fracture are looked for. This problem is formulated as the least squares minimization of a function evaluating the misfit between measurements and the result of the direct model. We used a model describing the flow of a monophasic incompressible fluid (Darcy's law), in a porous medium containing some fractures represented by interfaces. The direct problem is the fracture model discretized by the mixed hybrid finite element method. To solve this inverse problem, we developed an iterative algorithm, which is based on the use of fracture indicators that have been developed durig the thesis. These indicators give a first order information concerning the effect of the addition of a new fracture. As these indicators are inexpensive, a large number of configurations of new fractures is tested at each iteration. The algorithm was programmed, validated and tested numerically in various situations, using synthetic measurements. It gives very satisfactory results, although this problem is considered difficult. Finally, an early study of identifiability of the inverse problem of fractures in porous medium has been achieved. It allowed to prove the identifiability for a simplified model (very permeable faults, which is common in the underground). The question of identifiability for the full fracture model remains open.

[pt] Meios porosos fraturados estão presentes em diferentes tipos de formações geológicas, como os maciços rochosos e os reservatórios de petróleo e gás. A modelagem adequada dos sistemas de fraturas presentes nesses meios é de grande relevância para o desenvolvimento de estratégias de exploração e produção dessas formações. Isso porque os processos de fluxo de fluido são fortemente influenciados pelas características dos sistemas de fraturas. Nesse contexto, diversas abordagens têm sido desenvolvidas para a modelagem desses problemas utilizando representações explícitas e implícitas para as fraturas. A representação explícita usando modelos de fraturas discretas fornece resultados precisos, mas possui um custo computacional elevado e apresenta dificuldades na construção de modelos mais complexos. Por outro lado, modelos de representação implícita, como o de dupla porosidade/dupla permeabilidade, são muito atrativos por incorporarem o efeito das fraturas nas simulações sem a necessidade de representá-las no modelo. No entanto, esses modelos são adequados para problemas envolvendo fraturas pequenas e conectadas, possuindo aplicabilidade limitada para representar fraturas principais de maior escala que podem dominar o fluxo. Assim, este trabalho apresenta algumas das abordagens disponíveis para a representação de formações porosas fraturadas. Diferentes cenários foram estudados para avaliar pontos fortes e limitações de cada método em diferentes aplicações. Além disso, uma nova formulação foi proposta para representar o efeito de fraturas isoladas, que se demonstrou eficiente em modelos com considerável número de fraturas. / [en] Fractured porous media are present in different types of geological formations as rock masses and oil and gas reservoirs. The proper modelling of the fractured systems present in these media is of high relevance to the development of production and exploitation strategies of these formations. This is because the fluid flow processes are strongly influenced by the fractured systems characteristics. In this context, several approaches have been developed to model these problems using explicit and implicit representations to fractures. The explicit representation using discrete fracture models provides accurate results, but has a high computational cost and exhibits difficulties to construct more complex models. On the other hand, implicit representation models, as the dual porosity/dual permeability, are very attractive because they incorporate the effect of fractures to simulations without the need to represent them explicitly in the models. However, these models are suitable to problems with small and connected fractures, and have limited capability to represent major fractures of larger scale that can dominate the flow. Therefore, this work shows some of the available approaches to represent fractured porous formations. Moreover, a new formulation was proposed to represent the effect of isolated fractures, which proved to be efficient in models with considerable number of fractures.

La caractérisation des circulations thermo-convectives dans les milieux naturels est particulièrement étudiée pour ses applications industrielles, notamment en géothermie. Cette caractérisation correspond à deux enjeux liés à (i) la détection des remontées hydrothermales et (ii) la quantification de l'énergie évacuée par le système actif. La méthodologie proposée par cette thèse comporte ainsi deux volets. Le premier volet vise la localisation des systèmes actifs par caractérisation géophysique de sub-surface. Les techniques de prospection mises en œuvre sont la tomographie de résistivité électrique (TRE), la mesure in situ de température et la mesure de polarisation spontanée (PS). L'objet étudié dans cette thèse est la remontée hydrothermale située au niveau de la limite supérieure de l'effondrement de Rina Grande, au sommet du volcan Stromboli. L'approche géophysique de sub-surface comprend une cartographie spatiale (à l’échelle métrique) en TRE, PS et température et un suivi temporel des signaux PS et thermique. La cartographie spatiale nous renseigne sur l'extension spatiale du système hydrothermal (TRE) et le caractère actif des circulations (PS et température). Le modèle de résistivité électrique a été amélioré en tenant compte de la topographie, issue d'un Modèle Numérique de Terrain généré par photogrammétrie. Le traitement des données de surveillance montre qu'une relation linéaire lie le signal thermique et le signal PS, une relation qui ne peut être purement thermo-électrique. Le jeu de données temporel met l'accent sur la dynamique du système convectif et notamment la probable dépendance de la vigueur du système convectif avec les variations saisonnières de température atmosphérique. Le second volet vise à quantifier l'énergie évacuée par des systèmes thermo-convectifs à l'aide d'une approche numérique. L'approche géophysique met en évidence le fait que les zones endommagées telles que des limites structurales favorisent la circulation des fluides hydrothermaux. Ceci s'explique par le fait que fractures, failles ouvertes, zones d'altération etc. changent à petite échelle la perméabilité du milieu. L'approche numérique est donc vouée à la simulation 3D de l'écoulement et du transfert de chaleur dans des milieux poreux fracturés. Le travail s'est basé sur un code d'écoulement en milieux poreux fracturé pré-existant. Ce code a été adapté afin de résoudre le problème thermique. L'étude théorique vise à quantifier l'influence des paramètres du réseau de fractures sur l'énergie dissipée. L'influence de la densité de fractures, de la transmissivité de fractures et l'anisotropie du réseau de fractures sont évaluées. L'étude compare également les flux de chaleur dégagés par des modèles où les fractures sont insérées de manière discrète avec des modèles homogènes et de même propriétés macroscopiques (approche effective). Les résultats montrent que la validité de l'approche effective est fortement dépendante des paramètres du réseau de fracture. / The characterization of thermo-convective circulations in natural environments is particularly studied especially for geothermal applications. This characterization corresponds to two issues related to (i) the detection of the hydrothermal flows(ii) the quantification of the energy discharged by the active system. The methodology proposed by this thesis thus comprises two parts. The first component aims at locating active systems with geophysical methods. The prospecting techniques used are electrical resistivity tomography (ERT), in situ temperature measurement and self potential (SP) measurements. The object studied in this thesis is the hydrothermal system located at the upper limit of the Rina Grande sector collapse, at the top of the Stromboli volcano. The sub-surface geophysical approach includes spatial (metric) mapping in ERT, SP and temperature, and monitoring of SP and thermal signals. Spatial mapping informs us about the spatial extension of the hydrothermal system (ERT) and the active character of the circulations (SP and temperature). The model of electrical resistivity has been improved taking into account the topography, resulting from a Digital Elevation Model generated by photogrammetry. The treatment of the monitoring data shows that a linear relationship links the thermal and the PS signals, a relationship that can not be entirely due to thermoelectric effect. The temporal dataset focuses on the dynamics of the convective system and in particular the probable dependence of the vigor of the convective system on seasonal variations in atmospheric temperature.The second part aims at quantifying the energy released by thermo-convective systemsusing a numerical approach. The geophysical approach highlights the fact that damaged areas such as structural boundaries favor the circulation of hydrothermal fluids. This is due to the fact that fractures, open faults, alteration zones, etc. change the permeability of the medium on a small scale. The numerical approach is therefore dedicated to the 3D simulation of the flow and heat transfer in fractured porous media. The work is based on a pre-existing code in fracturing porous media, able to solve the flow problem. This code has been adapted to solve the thermal problem also. The theoretical study aims to quantify the influence of fracture network parameters on the released energy. The influence of fracture density, fracture transmissivity and fracture network anisotropy are evaluated. The study also compares the heat fluxes generated by models where the fractures are discretely inserted with homogeneous models with the same macroscopic properties (effective approach). The results show that the validity of the effective approach is highly dependent on the parameters of the fracture network.

Doctor of Philosophy / Department of Mechanical and Nuclear Engineering / Daniel V. Swenson / The objective of the thesis is to provide a fully coupled thermo-hydro-mechanical (THM) tool, T2STR, which enables quantitative understanding and prediction of thermal as well as mechanical effects on flow in the porous media under multiphase conditions. This is achieved by incorporating a finite element based hydro-thermo-mechanical stress capability into the well-established IFDM (Integrated Finite Difference Method) based flow simulation code TOUGH2. TOUGH2 is a program for calculation of multi-phase, multi-component, non-isothermal flow in porous media. It implements several equation of state modules to represent different fluid mixtures. The dual mesh technique is natural for combining both discretization methods and is used innovatively and effectively. A generalized approach is developed to accommodate the switching of variables implemented in TOUGH2 to adapt the phase changes. The forward coupling is achieved by using the thermal, hydrostatic, and poroelastic effects in the stress calculations. The backward coupling includes the effect of strain on the fluid flow. T2STR also allows the user to study the variation in porosity, permeability and capillary pressure as function of mean effective stress in the porous media. Multiple materials can be used to model the reservoir in T2STR, parallel to the implementation in TOUGH2. T2STR is implemented to carry out as a fully coupled, one way coupled (only deformation as function of hydro-thermal effects), or original TOUGH2 implementation. It provides the ability to switch on and off the thermal and/or poroelastic effects. T2STR is developed to model the fractured porous media using discrete fractures. The modeling of fractured porous media is limited to a staggered coupling approach. The fluid parameters like permeability, porosity are modified based on the stresses and/or aperture changes due to deformation. A set of verification problems, used to validate the code and display the capabilities of the code, are discussed. A graphical user interface is designed to pre-process the necessary data. Macros are developed for excel and Tecplot to post-process the results for easy visualization.