Modeling Of Filtration Processes Research Articles

ON INFLUENCE OF PHYSICAL AND CHEMICAL MODIFICATION OF WETTABILITY OF FILTRATION SURFACE ON INTERCHANGEABILITY OF IMMISCIBLE FLUIDS IN RESERVOIR FORMATIONS

The article presents and discusses the results of experimental studies of the processes of mutual substitution (displacement) of immiscible fluids, proceeding by the mechanism of impregnation and drainage in layered-heterogeneous reservoirs with hydrodynamically connected and separated interlayers.
 Physical modeling of filtration processes, taking into account the similarity criteria, made it possible to establish that during the mutual substitution of immiscible fluids at the phase boundary and lithological differences, nonequilibrium capillary phenomena develop, which, through the action of capillary forces, significantly affect fluid filtration and saturation distribution in an inhomogeneous porous medium. In order to eliminate the influence of the viscous instability factor on the motion of the displacement front, the processes of displacement of a less viscous fluid by a more viscous one were studied.
 It has been established that non-equilibrium capillary phenomena manifest themselves most intensively in reservoirs with a heterophilic surface, where capillary forces can initiate or block fluid flows between differently permeable interlayers. It has been experimentally shown that in layered-heterogeneous reservoirs with a heterophilic filtration surface in the interlayers, capillary phenomena largely determine the nature of the movement of the fluid displacement front (from the almost complete suppression of the “run-up” of the displacement fronts in the interlayers to the formation of an advanced front in the low-permeability interlayer). In order to exclude the influence of errors of a systematic or random nature on the results of the experiments, their reproducibility and the significance of differences were assessed using the statistical criteria of Student and Cochran, which showed the reliability of the above conclusions.
 The results obtained indicate the dominant effect of crossflows between interlayers on the formation of the displacement front of immiscible fluids in layered-heterogeneous reservoirs, especially with a heterophilic wettability characteristic, as well as the possibility of controlling this process by means of physicochemical modification of the wettability conditions of the filtration surface, for example, using surface active substances (surfactants) of various nature and structure.

Approval of the combined reserve calculation method (Chervonozayarske Gas Field as an example)

The object of the study is the calculation of the producing reserves of the gas-bearing reservoir. Increasingly, published studies provide justification for the possibility of restoring reserves in old depleted gas fields by gas flow from deep horizons. Given the possibility of resuming producing gas reserves, the issue of clarifying their volume in the reservoirs of fields at a late stage of development is promising. In the course of the study, theoretical research methods were used: a system analysis of the inreservoir used, numerical modeling based on a combined finite element-difference method, methods for visualizing the inreservoir obtained, and analytical methods. The method proposed in the paper for refining gas reserves combines the volumetric method and modeling of filtration processes using a combined finite element-difference method. The latter makes it possible to take into account the reservoir structure that is heterogeneous in terms of permeability and adequately describe the distribution of non-stationary reservoir pressure around the production well on a quantitative level. By applying an analytical formula based on the values of average reservoir and bottomhole pressures, the radii of the well feed contour were calculated for different periods of reservoir development. Thus, the active area (and volume) of the reservoir is determined, according to which the calculations of the producing reserves of the field are carried out. The study was carried out on the example of the Chervonozayarske Gas Field (Ukraine) for the reservoir V-26-T-1a, discovered by one production well 468-B(D). The recoverable reserves of the V-26-T-1a reservoir calculated in this way are 597.69 million m3 of gas. At the same time, the error relative to the value indicated in the Atlas of Ukrainian Fields is 4.63 %. The method of calculating reserves proposed in this study is useful for refining the reserves of depleted fields. The combination of the volumetric method with the results of simulation of filtration processes is an operational method for calculating the reserves of a reservoir discovered by one production well. At the same time, the use of a combined finite element-difference method makes it possible to take into account the complex heterogeneous structure of the reservoir and predict the distribution of reservoir non-stationary pressures around the production well.

Modeling of filtration processes in periodic porous media

Modeling of dynamic processes of diffusion and filtration of liquids in porous media are discussed. The media are formed by a large number of blocks with low permeability, and separated by a connected system of faults with high permeability. The modeling is based on solving initial boundary value problems for parabolic equations of diffusion and filtration in porous media. The structure of the media leads to the dependence of the equations on a small parameter. Assertions on the solvability and regularity of such problems and the corresponding homogenized convolution problems are considered. The statements are actual for the numerical solution of this problem with guaranteed accuracy that is necessary to model the considered processes.

Investigation of the influence of the heterogeneous permeability distribution on the oil phase displacement processes

The object of research is the filtration processes of displacement of the oil phase under the influence of an injection well in a heterogeneous porous medium. It is possible to evaluate and take into account the effect of reservoir heterogeneity on the distribution of reservoir pressure (and, consequently, on the intensity of the filtration process) using numerical modeling of filtration processes based on the piezoelectric equation. To solve the non-stationary anisotropic problem of piezoconductivity, it is proposed to apply the combined finite-element-difference method of M. Lubkov, which makes it possible to take into account the inhomogeneous distribution of permeability inside the anisotropic oil-bearing formation and at its boundaries, and to adequately calculate the distribution of reservoir pressure. The use of the combined finite-element-difference method allows to combine the advantages of the finite-element method and the finite difference method: to model geometrically complex areas, to find the value at any point of the object under study. At the same time, the use of an implicit difference scheme when finding the nodal values of the grid provides high reliability and convergence of the results. The simulation results show that the distribution of the pressure field between the production and injection wells significantly depends on their location, both in the isotropic landslide and in the anisotropic oil-bearing reservoir. It is shown that the distance between the wells of more than 1 km levels out the effectiveness of the impact of the injection well on the oil filtration process. The influence of the permeability of the oil phase in the shear direction dominates the influence of the permeability in the axial directions (affects the pressure decrease by 4–9.5 %). In the case of a landslide-isotropic reservoir, the wells should be located in the shear (diagonal) direction, which will provide the lowest level of drop in the average reservoir pressure (by 4 %). Based on the information obtained, for the effective use of anisotropic low-permeability formations, it is necessary to place production and injection wells in areas with relatively low anisotropy of the formation permeability, especially to avoid places with the presence of landslide permeability of the formation. The location of the wells is important so that, on the one hand, there is no blockage of oil from the side of reduced permeability, and on the other hand, rapid depletion of the formation from the side of increased permeability does not occur. And also the mutual exchange between the production and injection wells did not stop. When placing a system of production and injection wells in anisotropic formations of an oil field, it is necessary to carry out a systematic analysis of the surrounding anisotropy of the formations in order to place them in such a way that would ensure effective dynamics of filtration processes around these wells. Using the method used, it is possible to predict the impact of an injection well on the distribution of reservoir pressure in the reservoir.

Mathematical modelling of filtration processes in drainage systems with different depths of drainage

Mathematical modelling of filtration processes in drainage systems with different depths of drainage

MODELING OF DISPLACEMENT PROCESSES IN HETEROGENEOUS ANISOTROPIC GAS RESERVOIRS

Nowadays there are important problems of increasing efficiency of development and exploitation of gas deposits. There are problems associated with the growth of gas production in heterogeneous anisotropic reservoirs, increasing gas recovery, achieving economic efficiency and so on. In this situation, there are popular methods of computer modeling of gas productive reservoirs, because they allow getting information of the structure and characteristics of the gas reservoir, the distribution parameters of permeability and other important factors in it. They also allow evaluating and calculating uncertainty arising from the lack of information about the gas reservoir properties outside the well. Currently there are many methods of computer modeling, allowing solving various practical problems. From another hand there are some problems related to the accuracy and adequacy of simulation of heterogeneous anisotropic permeable collector systems in real conditions of gas deposits exploitation. On the base of combined finite-element-difference method for solving the nonstationary anisotropic piezoconductivity Lebenson problem, with calculating of heterogeneous distribution of permeable characteristics of the gas reservoir, we carried out modeling of filtration processes between production and injection wells. The results of computer modeling show that intensity of the filtration process between production and injection wells depends essentially on their location both in a shifting-isotropic and anisotropic gas reservoir. Therefore, for the effective using of poorly permeable shifting-isotropic gas-bearing reservoirs, it is necessary to place production and injection wells along the main anisotropy axes of the gas-bearing layers. At the placing production and injection well systems in low-permeable anisotropic reservoirs of a gas field, the most effective exchange between them will take place when the direction of increased permeability of the reservoirs coincides with the direction of the location of the wells. Obviously, the best conditions for gas production processes in any practical case can be achieved due to optimal selection of all anisotropic filtration parameters of the gas reservoir. One can use obtained results for practical geophysical works with a purpose optimizing of gas production activity in low-permeable heterogeneous anisotropic reservoirs. Presented method for more detailed investigation of low-permeable heterogeneous anisotropic gas-bearing deposits can be used.

Concept of technology for determining the permeability and porosity properties of terrigenous reservoirs on a digital rock sample model

The aim of the article is to form the concept of technology for determining the permeability and porosity properties of terrigenous reservoirs using mathematical modeling methods on a digital rock sample model.
 Digital rock sample modeling is used to assess geological oil reserves. The article presents the concept of digital rock sample modeling technology, which allows carrying out qualitative investigations to determine the permeability and porosity characteristics of the formation, including modeling the pore space and filtration processes. The essence of the concept is that the simulation model of the microstructure for the digital model is formed on the basis of a large number of parameters obtained during lithological and petrographic investigations of thin sections, a study of the sludge and geophysical investigations of wells.
 The acquired model can be used as a basis for subsequent modeling of filtration processes. Conductivity of single channels of the formed model can be calculated using molecular dynamics methods, models of Boltzmann's lattice equations, and other mathematical models and methods.
 Based on the results of the study carried out, the application of stochastic packing methods for modeling the structure of the pore space in the digital rock sample model of terrigenous reservoirs is substantiated.
 In connection with the development of computer and nanotechnologies and their use in the oil and gas industry, solutions that allow obtaining adequate results of digital rock sample models are of high importance and relevance for the production sector. It is especially important to use digital rock sample models in the study of reservoir rocks of shelf fields in the western part of the Russian Arctic, oil shales, rocks represented by loose weakly cemented reservoirs, and others, which are complex for physical experiments.

Physical modeling of filtration processes of heat-resistant nickel alloys during casting in a vacuum induction installation

The article considers issues related to the efficiency of metal melts’ filtration depending on the size of non-metallic inclusions, parameters of ceramic foam filters and their location options. Studies of influence of the main structural elements on the filtration processes of nickel melts during casting in a vacuum induction installation were carried out on low-temperature physical models. Modeling of melt filtration processes is based on the hydrodynamic similarity of the processes of motion of melt flows and nonmetallic inclusions in casting tanks. A modeling technique has been developed, the scale has been determined and a model installation has been made. Influence of the arrangement of filtration and dividing walls on the dynamics of metal flows, non-metallic inclusions and filtration efficiency is considered. The efficiency of nickel melts filtration is described depending on the technical parameters both on the filter itself (effective filtration surface, filter thickness, channel dimensions, number of channels per unit area), as well as on the type and size of non-metallic inclusions, design features of the casting device and filter layouts. It was found that the overall filtration efficiency is influenced by the rate and uniformity of the melt flows’ distribution in front of the filter. To ensure uniform distribution of the melt flow rates, a dividing wall with bypass holes is installed in front of the filter, the location of which and their number was also the subject of research. As a result of the studies, the relationships were established between the filtration efficiency, the size and type of non-metallic inclusions when using vertical and horizontal foam ceramic filters during the casting of nickel melts in an intermediate casting tank of a vacuum induction installation. It was found that with a vertical arrangement of the filter, its efficiency is higher than with a horizontal one. An additional means of increasing efficiency of the filtration system is the use of a dividing wall. The optimal number of holes and the location of the baffle in the casting tank were determined, ensuring a uniform distribution of melt flows along the height in front of the filter and an increase in its operation time.

Experimental study of the flux Law of flat ceramic membranes under different pressures

Abstract The flux performance of ceramic membranes is the basis for their efficient use. To study ceramic membrane flux variation, different filtration operating conditions were tested and the functional relationship between the membrane's clean water flux and the operating pressure within a given range obtained. The membrane's critical pressure and flux were determined by using pressure increments, and the flux variation law under different pressures determined experimentally. Analysis of the flux law and the membrane parameters enabled establishment of the flux model of filtration process and a model of flux stabilization after the deposition layer formed. The applicability of the model was proved by comparing and verifying the experimental data.

Modeling of submerged membrane filtration processes using recurrent artificial neural networks

<span lang="EN-US">The modeling of membrane filtration processes is a challenging task because it involves many interactions from both biological and physical operational behavior. Membrane fouling behaviour in filtration processes is complex and hard to understand, and to derive a robust model is almost not possible. Therefore, it is the aim of this paper to study the potential of time series neural network based dynamic model for a submerged membrane filtration process. The developed model that represent the dynamic behavior of filtration process is later used in control design of the membrane filtration processes. In order to obtain the dynamic behaviour of permeate flux and transmembrane pressure (TMP), a random step was applied to the suction pump. A recurrent neural network (RNN) structure was employed to perform as the dynamic models of a filtration process, based on nonlinear auto-regressive with exogenous input (NARX) model structure. These models are compared with the linear auto-regressive with exogenous input (ARX) model. The performance of the models were evaluated in terms of %<em>R<sup>2</sup></em>, mean square error (MSE,) and a mean absolute deviation (MAD). For filtration control performance, a proportional integral derivative (PID) controller was implemented. The results showed that the RNN-NARX structure able to model the dynamic behavior of the filtration process under normal conditions in short range of the filtration process. The developed model can also be a reliable assistant for two different control strategies development in filtration processes.</span>

Development of fuzzy-based autoregressive integrated moving average exogenous input model for filtration process

Development of black-box model for filtration process has been carried out in this work. Data needed for the model development was obtained through experimental study on filtration unit using aqueous calcium carbonate (CaCO3) slurry. The input and output data generated from the experiment consisted of one manipulated variable (feed pressure, Pr), one disturbance variable (concentration of the solute in the feed, CA0) and one controlled variable (suspension concentration, CA). The data were used to develop a fuzzy-based autoregressive integrated moving average exogenous input (FARIMAX) model structure. Model order selection was carried out based on trial and error while optimal model order was determined using factorial technique. The performance of the developed model was determined using root mean square error (RMSE), coefficient of determination (R2) and model fit. The model gave optimal order [33 3 3 1], RMSE (1.855 × 10−6), R2 (1.000) and fit (99.9980%). These results revealed that the model can be used to represent dynamic behaviours of the system and the model can be subsequently used for model base control design and dynamic optimisation of the

Нелинейность законов фильтрации в низкопроницаемых коллекторах

Filtration processes in low-permeability oil and gas reservoirs are characterized by non-linearity of filtration laws, which determines the features of mathematical modeling of these processes. Based on the concept of the formation of adsorption-solvate layers of a filtering liquid near the pore surface, which narrow the effective flow section of the pore channels, nonlinear dependences of the filtration rate on the applied pressure gradient are obtained. The obtained dependencies are in good agreement with the available experimental data and can be recommended for use in mathematical modeling of filtration processes in low-permeability rocks.

Computer modeling of filtration processes with piston extrusion

In this work, computer simulation of filtration processes based on the laws of hydrodynamics is considered. The adequacy of the developed models was verified by conducting a series of computational experiments. Created mathematical and software serves the purpose of research, forecasting and decision-making in the development and design of oil and gas fields.

Development of fuzzy-based autoregressive integrated moving average exogenous input model for filtration process

Development of fuzzy-based autoregressive integrated moving average exogenous input model for filtration process

Novel adsorption model of filtration process in polycarbonate track-etched membrane: Comparative study

Current assumptions are used in the formulation of pseudo-first (PFO) and second-order (PSO) models to describe the kinetic data of filtration based on ideal operating conditions. This paper presents a new model developed with pseudo <i>n<sup>th</sup></i> order and based on real assumption. A comparison was performed between PFO, PSO and the new model to highlight their performance and the optimisation of the pseudo-order equation, using MATLAB software. Adsorption characteristic of bovine serum albumin adsorption on the track-etched membrane are used as a medium based on protein filtration data were extracted from the literature for different concentrations to demonstrate the comparison between PFO/PSO and the new model. The pseudo first and second-order kinetic models were applied to test the experimental data and they did not provide reasonable values. The results show that the predicted values are consistent with experimental values giving a good correlation coefficient <i>R</i><sup>2</sup> = 0.997 and a minimum root mean squared error RMSE = 0.0171. Indeed, the experimental results follow the new model and the optimal pseudo equation order <i>n</i> = 1.115, the most suitable curves for the new model. As a result, we used different experimental adsorption data from the literature to examine and check the applicability and validity of the model.

Mathematical modelling of filtration processes in drainage systems using conformal mapping

AbstractThe situation when groundwater considerably rises above the “normal” level, water intake, lowering of groundwater levels and other relevant practical tasks require the drainage facilities. The most effective techniques of numerical studies of the corresponding boundary problems at present time are methods of dealing with inverse boundary value problems (conformal and quasi-conformal mappings). As basis of this research we used the case of combining the fictitious domain methods with quasi-conformal mappings of the solution of nonlinear boundary value problems for the calculation of filtration regimes in environments with free boundary areas (depression curves) and zones of “mountainous” areas.This paper reviews the stationary issue of flat-vertical stationary non-pressure liquid filtration to horizontal symmetric drainage. In the paper a practical methodology for solving boundary value problems on conformal mappings is suggested for the calculation of the filtration process in the horizontal symmetrical drainage.The idea of block iterative methods was used during the creation of the corresponding algorithm which is based on the alternating “freeze” of the anticipated conformance parameter, the internal and boundary connections of the curvilinear area.The results of the conducted numerical calculations confirmed the effectiveness of the suggested problem formulations and algorithms of their numerical solution and the possibility of their use in the modelling of nonlinear filtration processes occurring in horizontal drainage systems, as well as in the design of drainage facilities and optimizing other hydrosystems. Therefore these results are of great importance.

GROUNDWATER FLOW MODELlING USING the FINITE DIFFERENCES METHOD AND the FINITE ELEMENTS METHOD – COMPARATIVE MODEL STUDIES

The filtration of groundwater is a complicated process, which is determined by natural environmental factors (hydrogeological conditions) and anthropogenic impacts. Reliable predictions of the impact of the established extortions on the groundwater environment require the use of an appropriate research method that will allow for a precise representation of groundwater circulation. Such methods include numerical modelling of filtration processes, using a mathematical description of groundwater flow, based on assumed parameters and boundary conditions. For groundwater flow modelling, software based on the finite differences method FDM, using Modflow simulators, is most commonly used. Due to the numerous advantages, mainly in terms of greater precision in the representation of the complex geometry of the aquifers and objects affecting the water circulation, the alternative FEM finite elements method is becoming increasingly important. The article presents characteristic features of modelling using both methods. Based on the established imaginary research site, representing typical valley hydrogeological conditions, the paper presents the methodology of model implementation and numerical calculations of water flow using FDM and FEM methods, each in two variants of grid density. Obtained results are presented, with an attempt to compare the advantages and disadvantages of both methods.

Performance of a depth fibrous filter at particulate loading conditions. Description of temporary and local phenomena with structure development

Optimization of a depth filter structure requires information about the filter's performance during its loading with particles. In this paper a macroscopic model of filtration process was proposed. It was based on the description of the loading process of three different gradient fibrous filters produced in the melt-blown technology process. Due to the contamination deposition on fibers, a new method of determination of the filter porosity transition, was suggested. It was based on growth of the deposit mass accumulated in individual filter layers, which was defined upon the scanning electron microscope images, the clearance of layer samples, and the overall increase of the filter mass. Local phenomena, i.e. the agglomerate structure, its spatial distribution and resuspension, were exposed through a two-stage character of the process. The empirical correlations obtained for deposition kinetics and pressure drop development are helpful in filter design. By knowing the desired contamination removal, fiber diameter and porosity can be verified mathematically, so that the filter will work the most efficiently. The proposed description of the structural loading of the multilayer filter is simple and reliable. Further research on biotic and abiotic particle transport mechanisms should be performed.

Modeling of the filtration processes in a rectangular area soils using the Darcy

In the framework of the research described in this paper we implemented the numerical algorithm and the program for the implementation of the algorithm, which makes it possible to calculate pressure field in the examined region and established convergence of the iterative process at optimal selection of the relaxation parameter. The obtained results enable carrying out estimation of the ground water level and propagation patterns under conditions of appropriate environmental characteristics of flow in the presence of varying geometrical configuration of outflow zones through the examined surface. The modelling of filtration processes in a rectangular plot of soil using the Darcy equations might also be used in the problems on estimating water quality, in the tasks on preventing flood waters, floods or mudflows. Such a simulation also makes it possible to explore the phenomena of fluid propagation in soils given the prospects of development of shale gas deposits in the regions of Lviv, Ternopil, Ivano-Frankivsk oblasts (Ukraine). Thus, the applied aspect of the use of the obtained scientific result is the possibility to improve the developed mathematical model of filtration processes through the inclusion of morphological characteristics of river and the river system. This is a prerequisite for obtaining operational data on a change in the level of soil and flood waters at a specified point in time in order to ensure ecological safety of the environment

Mathematical modeling of the process of fluid filtration through a multi-layer filtering element

The paper presents a mathematical model of the fluid filtration process in a porous medium. The mathematical model of fluid filtration in a porous medium is based on the equation of continuity and the Darcy law for a hollow porous cylinder. The porous cylinder consists of three materials having different mechanical and filtration properties, made of polypropylene fibers by extrusion, consisting of seven layers. Filtration is described by different types of research laws that establish the relationship between a velocity vector of the fluid filtration and the field of pressure. There are several ways to describe mathematically the process of filter colmatation. Present work considers a single-component model of the flow of suspension through a porous medium. An analysis of this model revealed that it can be implemented in the presence of empirical coefficients that take into account porosity of the sediment deposited on the walls of a porous space, linear functions that describe adsorption and desorption of precipitation on the pore walls, as well as functional dependences for the permeability of filter and the viscosity of suspension. An efficient technique to calculate complex models is to apply parallel programming methods, which make it possible to split calculations into streams performed on the basis of supercomputers, clusters, and other high-performance computing systems. The proposed method for organizing distributed calculations for a finite-element filter model could be used to construct a hydrodynamic model of the filtration process, as well as its program implementation, which is planned in the future.