Estudo da segregação gravitacional do processo de injeção de vapor em reservátórios heterogêneos

Due to reservoirs complexity and significantly large reserves, heavy oil recovery has become one of the major oil industry challenges. Thus, thermal methods have been widely used as a strategic method to improve heavy oil recovery. These methods improve oil displacement through viscosity reduction, enabling oil production in fields which are not considered commercial by conventional recovery methods. Among the thermal processes, steam flooding is the most used today. One consequence in this process is gravity segregation, given by difference between reservoir and injected fluids density. This phenomenon may be influenced by the presence of reservoir heterogeneities. Since most of the studies are carried out in homogeneous reservoirs, more detailed studies of heterogeneities effects in the reservoirs during steam flooding are necessary, since most oil reservoirs are heterogeneous. This paper presents a study of reservoir heterogeneities and their influence in gravity segregation during steam flooding process. In this study some heterogeneous reservoirs with physical characteristics similar those found in the Brazilian Northeast Basin were analyzed. To carry out the simulations, it was used the commercial simulator STARS by CMG (Computer Modeling Group) - version 2007.11. Heterogeneities were modeled with lower permeability layers. Results showed that the presence of low permeability barriers can improve the oil recovery, and reduce the effects of gravity segregation, depending on the location of heterogeneities. The presence of these barriers have also increased the recovered fraction even with the reduction of injected steam rate

Estudo do processo de combustão in-situ em reservatórios maduros de óleos médios e leves (high pressure air injection)

Nearly 3 x 1011 m3 of medium and light oils will remain in reservoirs worldwide after conventional recovery methods have been exhausted and much of this volume would be recovered by Enhanced Oil Recovery (EOR) methods. The in-situ combustion (ISC) is an EOR method in which an oxygen-containing gas is injected into a reservoir where it reacts with the crude oil to create a high-temperature combustion front that is propagated through the reservoir. The High Pressure Air Injection (HPAI) method is a particular denomination of the air injection process applied in light oil reservoirs, for which the combustion reactions are dominant between 150 and 300°C and the generation of flue gas is the main factor to the oil displacement. A simulation model of a homogeneous reservoir was built to study, which was initially undergone to primary production, for 3 years, next by a waterflooding process for 21 more years. At this point, with the mature condition established into the reservoir, three variations of this model were selected, according to the recovery factors (RF) reached, for study the in-situ combustion (HPAI) technique. Next to this, a sensitivity analysis on the RF of characteristic operational parameters of the method was carried out: air injection rate per well, oxygen concentration into the injected gas, patterns of air injection and wells perforations configuration. This analysis, for 10 more years of production time, was performed with assistance of the central composite design. The reservoir behavior and the impacts of chemical reactions parameters and of reservoir particularities on the RF were also evaluated. An economic analysis and a study to maximize the RF of the process were also carried out. The simulation runs were performed in the simulator of thermal processes in reservoirs STARS (Steam, Thermal, and Advanced Processes Reservoir Simulator) from CMG (Computer Modelling Group). The results showed the incremental RF were small and the net present value (NPV) is affected by high initial investments to compress the air. It was noticed that the adoption of high oxygen concentration into the injected gas and of the five spot pattern tends to improve the RF, and the wells perforations configuration has more influence with the increase of the oil thickness. Simulated cases relating to the reservoir particularities showed that smaller residual oil saturations to gas lead to greater RF and the presence of heterogeneities results in important variations on the RF and on the production curves

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

Análise sísmica usando transformada de Curvelet

Oil prospecting is one of most complex and important features of oil industry Direct prospecting methods like drilling well logs are very expensive, in consequence indirect methods are preferred. Among the indirect prospecting techniques the seismic imaging is a relevant method. Seismic method is based on artificial seismic waves that are generated, go through the geologic medium suffering diffraction and reflexion and return to the surface where they are recorded and analyzed to construct seismograms. However, the seismogram contains not only actual geologic information, but also noise, and one of the main components of the noise is the ground roll. Noise attenuation is essential for a good geologic interpretation of the seismogram. It is common to study seismograms by using time-frequency transformations that map the seismic signal into a frequency space where it is easier to remove or attenuate noise. After that, data is reconstructed in the original space in such a way that geologic structures are shown in more detail. In addition, the curvelet transform is a new and effective spectral transformation that have been used in the analysis of complex data. In this work, we employ the curvelet transform to represent geologic data using basis functions that are directional in space. This particular basis can represent more effectively two dimensional objects with contours and lines. The curvelet analysis maps real space into frequencies scales and angular sectors in such way that we can distinguish in detail the sub-spaces where is the noise and remove the coefficients corresponding to the undesired data. In this work we develop and apply the denoising analysis to remove the ground roll of seismograms. We apply this technique to a artificial seismogram and to a real one. In both cases we obtain a good noise attenuation

Análise de terrenos na porção setentrional da Província Borborema, NE do Brasil: integração de dados geológicos e gravimétricos

It is presently assumed that the Borborema Province resulted from a complex collisional process associated with the convergent movement of plates, possibly involving amalgamation and accretion of microplates. This process was consolidated at the end of the Brasiliano event. It is investigated the possible limits for the tectonostratigraphic terranes in the northern portion of the province based on an integrated study of geological and gravity data. The study area comprises the portion of the Borborema Province located north of the Patos Lineament, limited by longitudes 33º00 W and 43º29 44"W and latitudes 1º36 S and 8º00 S. A revision of the regional geology allowed to identify areas presenting contrasting geological attributes, possibly representing different terranes whose limits are always shear zones of Brasiliano-age. The Sobral-Pedro II shear zone is the only one undoubtedly presenting geological attributes of sutures zones. The other shear zones are very likely associated with a geodinymic context of accretion, involving oblique collisions (docking), transcurrent and/or transforming sutures, and deep intracrustal shear zones. The gravity data contributed as a tool to identify strong lateral contrasts of density inside the upper crust possibly associated with crustal blocks tectonically juxtaposed. The dominant long wavelength anomaly in the Bouguer anomaly map is an expressive gradient, grossly parallel to the continental margin, caused by density variation across the crust-mantle interface in the transition from the continental crust to the oceanic crust originated by the separation between South America and Africa. Medium to small wavelength anomalies are due to intracrustal heterogeneities such as different Precambrian crustal blocks, Brasiliano-age granites and Mesozoic sedimentary basins. A regional-residual separation of the Bouguer anomaly map was performed in order to enhance in the residual map the effect due to intracrustal heterogeneities. The methodology used for this separation was a robust polinomial fitting. The inversion of residual gravity field resulted in a density contrast map (Δρ), in an equivalent layer that provided more accurated anomalies contours and consolidated the model which the sources of residual anomalies are located in the upper part of the present crust. Based on the coincidence of gravity lineaments in the residual map and Brasiliano shear zones, and using additional geological information, the following shear zones are proposed as limits between terranes: Patos shear zone, Sobral-Pedro II shear zone, Picuí-João Câmara shear zone, Remígio-Pocinhos shear zone, Senador Pompeu shear zone, Tauá shear zone, and Portalegre shear zone. Based on the geological/geophysical information it is attributed a higher level of confidence to the first three proposed limits(Patos, Sobral Pedro II, and Picuí-João Câmara shear zones). From west to east, these shear zones individualize the following terranes: Northwest of Ceará terrane, Central Ceará terrane, Tauá terrane, Orós-Jaguaribe terrane, Seridó terrane, and São José de Campestre terrane. In our study, the Rio Piranhas and Patos terranes are questioned because their previously proposed limits do not present good geological and gravimetric evidences. On the other hand, the previously proposed Cearense terrane is now subdivided into Central Ceará and Tauá terranes. Two residual gravity profiles located in the Seridó belt were interpreted using 2 ½ D direct gravity modeling. The main result of the modeling process is that all anomalies, with the exception of one, can be explained by outcroppring bodies, therefore restricted to the upper part of the present crust

Proposta metodológica para o imageamento digital e modelagem virtual 3d de um bloco de rochas travertinas

In this paper we present the methodological procedures involved in the digital imaging in mesoscale of a block of travertines rock of quaternary age, originating from the city of Acquasanta, located in the Apennines, Italy. This rocky block, called T-Block, was stored in the courtyard of the Laboratório Experimental Petróleo "Kelsen Valente" (LabPetro), of Universidade Estadual de Campinas (UNICAMP), so that from it were performed Scientific studies, mainly for research groups universities and research centers working in brazilian areas of reservoir characterization and 3D digital imaging. The purpose of this work is the development of a Model Solid Digital, from the use of non-invasive techniques of digital 3D imaging of internal and external surfaces of the T-Block. For the imaging of the external surfaces technology has been used LIDAR (Light Detection and Range) and the imaging surface Interior was done using Ground Penetrating Radar (GPR), moreover, profiles were obtained with a Gamma Ray Gamae-spectômetro laptop. The goal of 3D digital imaging involved the identification and parameterization of surface geological and sedimentary facies that could represent heterogeneities depositional mesoscale, based on study of a block rocky with dimensions of approximately 1.60 m x 1.60 m x 2.70 m. The data acquired by means of terrestrial laser scanner made available georeferenced spatial information of the surface of the block (X, Y, Z), and varying the intensity values of the return laser beam and high resolution RGB data (3 mm x 3 mm), total points acquired 28,505,106. This information was used as an aid in the interpretation of radargrams and are ready to be displayed in rooms virtual reality. With the GPR was obtained 15 profiles of 2.3 m and 2 3D grids, each with 24 sections horizontal of 1.3 and 14 m vertical sections of 2.3 m, both the Antenna 900 MHz to about 2600 MHz antenna. Finally, the use of GPR associated with Laser Scanner enabled the identification and 3D mapping of 3 different radarfácies which were correlated with three sedimentary facies as had been defined at the outset. The 6 profiles showed gamma a low amplitude variation in the values of radioactivity. This is likely due to the fact of the sedimentary layers profiled have the same mineralogical composition, being composed by carbonate sediments, with no clay in siliciclastic pellitic layers or other mineral carrier elements radioactive

Caracterização de reservatórios siliciclásticos neoaptianos: um estudo do membro carmópolis no campo de Camorim, sub-bacia de Sergipe, Brasil

The Camorim Oilfield, discovered in 1970 in the shallow water domain of the Sergipe Sub-basin, produces hydrocarbons from the Carmópolis Member of the Muribeca Formation, the main reservoir interval, interpreted as siliciclastics deposited in an alluvial-fluvial-deltaic context during a late rifting phase of Neoaptian age, in the Sergipe-Alagoas Basin. The structural setting of the field defines different production blocks, being associated to the evolution of the Atalaia High during the rift stage and subsequent reactivations, encompassing NE-SW trending major normal faults and NWEW trending secondary faults. The complexity of this field is related to the strong facies variation due to the interaction between continental and coastal depositional environments, coupled with strata juxtaposition along fault blocks. This study aims to geologically characterize its reservoirs, to provide new insights to well drilling locations in order to increase the recovery factor of the field. Facies analysis based on drill cores and geophysical logs and the 3D interpretation of a seismic volume, provide a high resolution stratigraphic analysis approach to be applied in this geodynamic transitional context between the rift and drift evolutionary stages of the basin. The objective was to define spatial and time relations between production zones and the preferential directions of fluid flow, using isochore maps that represent the external geometry of the deposits and facies distribution maps to characterize the internal heterogeneities of these intervals, identified in a 4th order stratigraphic zoning. This work methodology, integrated in a 3D geological modelling process, will help to optimize well drilling and hydrocarbons production. This methodology may be applied in other reservoirs in tectonic and depositional contexts similar to the one observed at Camorim, for example, the oil fields in the Aracaju High, Sergipe Sub-basin, which together represent the largest volume of oil in place in onshore Brazilian basins

Análise computacional de imagens de lâminas delgadas na predição dos parâmetros hidráulicos porosidade e condutividade hidráulica do aquífero Barreiras-RN

The understanding of the occurrence and flow of groundwater in the subsurface is of fundamental importance in the exploitation of water, just like knowledge of all associated hydrogeological context. These factors are primarily controlled by geometry of a certain pore system, given the nature of sedimentary aquifers. Thus, the microstructural characterization, as the interconnectivity of the system, it is essential to know the macro properties porosity and permeability of reservoir rock, in which can be done on a statistical characterization by twodimensional analysis. The latter is being held on a computing platform, using image thin sections of reservoir rock, allowing the prediction of the properties effective porosity and hydraulic conductivity. For Barreiras Aquifer to obtain such parameters derived primarily from the interpretation of tests of aquifers, a practice that usually involves a fairly complex logistics in terms of equipment and personnel required in addition to high cost of operation. Thus, the analysis and digital image processing is presented as an alternative tool for the characterization of hydraulic parameters, showing up as a practical and inexpensive method. This methodology is based on a flowchart work involving sampling, preparation of thin sections and their respective images, segmentation and geometric characterization, three-dimensional reconstruction and flow simulation. In this research, computational image analysis of thin sections of rocks has shown that aquifer storage coefficients ranging from 0,035 to 0,12 with an average of 0,076, while its hydrogeological substrate (associated with the top of the carbonate sequence outcropping not region) presents effective porosities of the order of 2%. For the transport regime, it is evidenced that the methodology presents results below of those found in the bibliographic data relating to hydraulic conductivity, mean values of 1,04 x10-6 m/s, with fluctuations between 2,94 x10-6 m/s and 3,61x10-8 m/s, probably due to the larger scale study and the heterogeneity of the medium studied.

Expressão geofísica-estrutural do lineamento transbrasiliano na porção central da Bacia do Parnaíba (Maranhão-Piauí)

The objective of this study was to characterize the structural-geophysical expression of the Transbrasiliano Lineament (TBL) in the east-central portion of the Parnaíba Basin. The TBL corresponds to a major Neoproterozoic NE-trending shear zone related to the Brasiliano orogenic cycle, with dextral strike-slip kinematics, underlying (but also laterally exposed in the NE and SW basin edges) the sedimentary section of the Parnaíba Basin. In this study, the interpretation of gravity and magnetic anomaly maps is consistent with the TBL kinematics, the signature of the geophysical anomalies corresponding to the high (plastic behaviour) and subsequent declining temperature (ductile to brittle behaviour) stages during Brasiliano and late Brasiliano times. The pattern of residual gravity anomalies is compatible with an S-C dextral pair shaping the geological bodies of an heterogeneous basement, such as slices of gneisses and granulites (positive anomalies), granitic and low-medium grade metasedimentary rocks (negative anomalies). Such anomalies curvilinear trends, ranging from NNE (interpreted as S surfaces) to NE (C surfaces), correspond to flattening surfaces (S), while the NE rectilinear trend must represent a C band. The narrower magnetic anomalies also display NNE to NE (S surfaces) trends and should correspond to similar (although narrower and more discontinuous) sources in the equivalent anomaly patterns. Pre-Silurian pull-apart style grabens may contribute to the NE negative gravimetric anomalies, although this interpretation demands control by seismic data analysis. On the other hand, the curvilinear anomalies associated to contractional trends are incompatible with their interpretation as pre-Silurian graben, in both maps. In the (reduced to the pole) magnetic anomalies map, most of these are again associated to low-temperature shear zones (C planes) and faults, juxtaposing distinct blocks in terms of magnetic properties, or eventually filled with basic bodies. It is also possible that some isolated magnetic anomalies correspond to igneous bodies of late-Brasiliano or Mesozoic age. The basement late discontinuities pattern can be interpreted in analogy to the Riedel fractures model, with steep dipping surfaces and a sub-horizontal movement section. This study also explored 2D gravity modeling controlled by the interpretation of a dip seismic line as regards to the Transbrasiliano Lineament. The rock section equivalent to the Jaibaras Group occupying a graben structure (as identified in the seismic line) corresponds to a discrete negative anomaly superimposed to a gravimetric high, once again indicating a stronger influence of older crystalline basement rocks as gravimetric sources, mainly reflecting the heterogeneities and anisotropies generated at high temperature conditions and their subsequent cooling along the TBL, during the Brasiliano cycle.

Expressão geofísica-estrutural do lineamento transbrasiliano na porção central da Bacia do Parnaíba (Maranhão-Piauí)

The objective of this study was to characterize the structural-geophysical expression of the Transbrasiliano Lineament (TBL) in the east-central portion of the Parnaíba Basin. The TBL corresponds to a major Neoproterozoic NE-trending shear zone related to the Brasiliano orogenic cycle, with dextral strike-slip kinematics, underlying (but also laterally exposed in the NE and SW basin edges) the sedimentary section of the Parnaíba Basin. In this study, the interpretation of gravity and magnetic anomaly maps is consistent with the TBL kinematics, the signature of the geophysical anomalies corresponding to the high (plastic behaviour) and subsequent declining temperature (ductile to brittle behaviour) stages during Brasiliano and late Brasiliano times. The pattern of residual gravity anomalies is compatible with an S-C dextral pair shaping the geological bodies of an heterogeneous basement, such as slices of gneisses and granulites (positive anomalies), granitic and low-medium grade metasedimentary rocks (negative anomalies). Such anomalies curvilinear trends, ranging from NNE (interpreted as S surfaces) to NE (C surfaces), correspond to flattening surfaces (S), while the NE rectilinear trend must represent a C band. The narrower magnetic anomalies also display NNE to NE (S surfaces) trends and should correspond to similar (although narrower and more discontinuous) sources in the equivalent anomaly patterns. Pre-Silurian pull-apart style grabens may contribute to the NE negative gravimetric anomalies, although this interpretation demands control by seismic data analysis. On the other hand, the curvilinear anomalies associated to contractional trends are incompatible with their interpretation as pre-Silurian graben, in both maps. In the (reduced to the pole) magnetic anomalies map, most of these are again associated to low-temperature shear zones (C planes) and faults, juxtaposing distinct blocks in terms of magnetic properties, or eventually filled with basic bodies. It is also possible that some isolated magnetic anomalies correspond to igneous bodies of late-Brasiliano or Mesozoic age. The basement late discontinuities pattern can be interpreted in analogy to the Riedel fractures model, with steep dipping surfaces and a sub-horizontal movement section. This study also explored 2D gravity modeling controlled by the interpretation of a dip seismic line as regards to the Transbrasiliano Lineament. The rock section equivalent to the Jaibaras Group occupying a graben structure (as identified in the seismic line) corresponds to a discrete negative anomaly superimposed to a gravimetric high, once again indicating a stronger influence of older crystalline basement rocks as gravimetric sources, mainly reflecting the heterogeneities and anisotropies generated at high temperature conditions and their subsequent cooling along the TBL, during the Brasiliano cycle.

Estudo da segregação gravitacional do processo de injeção de vapor em reservátórios heterogêneos

Due to reservoirs complexity and significantly large reserves, heavy oil recovery has become one of the major oil industry challenges. Thus, thermal methods have been widely used as a strategic method to improve heavy oil recovery. These methods improve oil displacement through viscosity reduction, enabling oil production in fields which are not considered commercial by conventional recovery methods. Among the thermal processes, steam flooding is the most used today. One consequence in this process is gravity segregation, given by difference between reservoir and injected fluids density. This phenomenon may be influenced by the presence of reservoir heterogeneities. Since most of the studies are carried out in homogeneous reservoirs, more detailed studies of heterogeneities effects in the reservoirs during steam flooding are necessary, since most oil reservoirs are heterogeneous. This paper presents a study of reservoir heterogeneities and their influence in gravity segregation during steam flooding process. In this study some heterogeneous reservoirs with physical characteristics similar those found in the Brazilian Northeast Basin were analyzed. To carry out the simulations, it was used the commercial simulator STARS by CMG (Computer Modeling Group) - version 2007.11. Heterogeneities were modeled with lower permeability layers. Results showed that the presence of low permeability barriers can improve the oil recovery, and reduce the effects of gravity segregation, depending on the location of heterogeneities. The presence of these barriers have also increased the recovered fraction even with the reduction of injected steam rate

Estudo do processo de combustão in-situ em reservatórios maduros de óleos médios e leves (high pressure air injection)

Nearly 3 x 1011 m3 of medium and light oils will remain in reservoirs worldwide after conventional recovery methods have been exhausted and much of this volume would be recovered by Enhanced Oil Recovery (EOR) methods. The in-situ combustion (ISC) is an EOR method in which an oxygen-containing gas is injected into a reservoir where it reacts with the crude oil to create a high-temperature combustion front that is propagated through the reservoir. The High Pressure Air Injection (HPAI) method is a particular denomination of the air injection process applied in light oil reservoirs, for which the combustion reactions are dominant between 150 and 300°C and the generation of flue gas is the main factor to the oil displacement. A simulation model of a homogeneous reservoir was built to study, which was initially undergone to primary production, for 3 years, next by a waterflooding process for 21 more years. At this point, with the mature condition established into the reservoir, three variations of this model were selected, according to the recovery factors (RF) reached, for study the in-situ combustion (HPAI) technique. Next to this, a sensitivity analysis on the RF of characteristic operational parameters of the method was carried out: air injection rate per well, oxygen concentration into the injected gas, patterns of air injection and wells perforations configuration. This analysis, for 10 more years of production time, was performed with assistance of the central composite design. The reservoir behavior and the impacts of chemical reactions parameters and of reservoir particularities on the RF were also evaluated. An economic analysis and a study to maximize the RF of the process were also carried out. The simulation runs were performed in the simulator of thermal processes in reservoirs STARS (Steam, Thermal, and Advanced Processes Reservoir Simulator) from CMG (Computer Modelling Group). The results showed the incremental RF were small and the net present value (NPV) is affected by high initial investments to compress the air. It was noticed that the adoption of high oxygen concentration into the injected gas and of the five spot pattern tends to improve the RF, and the wells perforations configuration has more influence with the increase of the oil thickness. Simulated cases relating to the reservoir particularities showed that smaller residual oil saturations to gas lead to greater RF and the presence of heterogeneities results in important variations on the RF and on the production curves

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.