Splitting technique for analytical modelling of two-phase multicomponent flow in porous media

In this paper we discuss one-dimensional models for two-phase Enhanced Oil Recovery (EOR) floods (oil displacement by gases, polymers, carbonized water, hot water, etc.). The main result presented here is the splitting of the EOR mathematical model into thermodynamical and hydrodynamical parts. The introduction of a potential associated with one of the conservation laws and its use as a new independent coordinate reduces the number of equations by one. The (n) × (n) conservation law model for two-phase n-component EOR flows in new coordinates is transformed into a reduced (n − 1) × (n − 1) auxiliary system containing just thermodynamical variables (equilibrium fractions of components, sorption isotherms) and one lifting equation containing just hydrodynamical parameters (phase relative permeabilities and viscosities). The algorithm to solve analytically the problem includes solution of the reduced auxiliary problem, solution of one lifting hyperbolic equation and inversion of the coordinate transformation. The splitting allows proving the independence of phase transitions occurring during displacement of phase relative permeabilities and viscosities. For example, the minimum miscibility pressure (MMP) and transitional tie lines are independent of relative permeabilities and phases viscosities. Relative motion of polymer, surfactant and fresh water slugs depends on sorption isotherms only. Therefore, MMP for gasflood or minimum fresh water slug size providing isolation of polymer/surfactant from incompatible formation water for chemical flooding can be calculated from the reduced auxiliary system. Reduction of the number of equations allows the generation of new analytical models for EOR. The analytical model for displacement of oil by a polymer slug with water drive is presented.Adolfo P. Pires, Pavel G. Bedrikovetsky, Alexander A. Shapir

Correction of Basic Equations for Deep Bed Filtration with Dispersion

Copyright © 2006 Elsevier B.V. All rights reserved.Deep bed filtration of particle suspensions in porous media occurs during water injection into oil reservoirs, drilling fluid invasion into reservoir productive zones, fines migration in oil fields, bacteria, virus or contaminant transport in groundwater, industrial filtering, etc. The basic features of the process are advective and dispersive particle transport and particle capture by the porous medium. Particle transport in porous media is determined by advective flow of carrier water and by hydrodynamic dispersion in micro-heterogeneous media. Thus, the particle flux is the sum of advective and dispersive fluxes. Transport of particles in porous media is described by an advection–diffusion equation and by a kinetic equation of particle capture. Conventional models for deep bed filtration take into account hydrodynamic particle dispersion in the mass balance equation but do not consider the effect of dispersive flux on retention kinetics. In the present study, a model for deep bed filtration with particle size exclusion taking into account particle hydrodynamic dispersion in both mass balance and retention kinetics equations is proposed. Analytical solutions are obtained for flows in infinite and semi-infinite reservoirs and in finite porous columns. The physical interpretation of the steady-state flow regimes described by the proposed and the traditional models favours the former.Altoe, J. E., Bedrikovetski, P.G., Siqueira, A. G., de Souza, A. L., Shecaira, F.http://www.elsevier.com/wps/find/journaldescription.cws_home/503345/description#descriptio

Exact Solution for Long-Term Size Exclusion Suspension-Colloidal Transport in Porous Media

Long-term deep bed filtration in porous media with size exclusion particle capture mechanism is studied. For monodispersed suspension and transport in porous media with distributed pore sizes, the microstochastic model allows for upscaling and the exact solution is derived for the obtained macroscale equation system. Results show that transient pore size distribution and nonlinear relation between the filtration coefficient and captured particle concentration during suspension filtration and retention are the main features of long-term deep bed filtration, which generalises the classical deep bed filtration model and its latter modifications. Furthermore, the exact solution demonstrates earlier breakthrough and lower breakthrough concentration for larger particles. Among all the pores with different sizes, the ones with intermediate sizes (between the minimum pore size and the particle size) vanish first. Total concentration of all the pores smaller than the particles turns to zero asymptotically when time tends to infinity, which corresponds to complete plugging of smaller pores

In-situ fines migration and grains redistribution induced by mineral reactions – Implications for clogging during water injection in carbonate aquifers

Water injection into an aquifer is generally motivated by one of three objectives: disposal, managed aquifer recharge (MAR), or aquifer storage and recovery (ASR). Any of these would be undermined if an injection well were to become clogged. This paper investigates whether mineral reactions can cause mobilization of fines and rock grains, and if so, how this would affect clogging. Injection experiments are performed on Edwards Brown (dolomite) and Indiana limestone core samples. X-ray Powder Diffraction analysis of the rocks shows that no clays are present. Filtered-deaired deionized water and pure salts are used to prepare the injection fluids. The core samples are subjected to four sequential injections of fluids: at salinities 44,580 mg/L (referred to as “seawater”), 14,860 mg/L, 7,430 mg/L, and 0 mg/L (deionized water). These salinities are selected to represent disposal, and less saline fluids to represent MAR and ASR projects. Pressure difference is recorded across the core sample at each stage and is used to calculate permeability. The effluent samples are collected to characterize produced fines and elements. The increase in the pH of the effluent samples suggest mineral reactions, which is supported by an increase in the concentration of chemical elements in the effluent samples. Scanning Electron Microscopy (SEM) images show pore enlargement due to dissolution and depict pore blockage due to fines migration, grains redistribution, and mineral precipitation. Mineral reactions dissolved the grain's surface and intergranular cement, releasing silicate fines and rock grains, which in turn reduce the permeability of the rock by 68 % to 99.9 %

Permeability hysteresis in gravity counterflow segregation

Hysteresis effects in two-phase flow in porous media are important in applications such as waterflooding or gas storage in sand aquifers. In this paper, we develop a numerical scheme for such a flow where the permeability hysteresis is modeled by a family of reversible scanning curves enclosed by irreversible imbibition and drainage permeability curves. The scheme is based on associated local Riemann solutions and can be viewed as a modification of the classical Godunov method. The Riemann solutions necessary for the scheme are presented, as well as the criteria that guarantee the well-posedness ofthe Riemann problem with respect to perturbations of left and right states. The numerical and analytical results show strong influence of the permeability hysteresis on the flow. In addition, the numerical scheme accurately reproduces the available experimental data once hysteresis is taken into account in the model.Shaerer, C., Sarkis, M., Marchesin, D. and Bedrikovetski, P

Evaluating transport in irregular pore networks

A general approach for investigating transport phenomena in porous media is presented. This approach has the capacity to represent various kinds of irregularity in porous media without the need for excessive detail or computational effort. The overall method combines a generalized effective medium approximation (EMA) with a macroscopic continuum model in order to derive a transport equation with explicit analytical expressions for the transport coefficients. The proposed form of the EMA is an anisotropic and heterogeneous extension of Kirkpatrick's EMA which allows the overall model to account for microscopic alterations in connectivity (with the locations of the pores and the orientation and length of the throat) as well as macroscopic variations in transport properties. A comparison to numerical results for randomly generated networks with different properties is given, indicating the potential for this methodology to handle cases that would pose significant difficulties to many other analytical models

An investigation into the roles of chlorides and sulphate salts on the performance of low salinity injection in sandstone reservoirs : experimental approach

Numerous studies have been carried out to ascertain the mechanisms of low salinity and smart water flooding technique for improved oil recovery. Focus were often on brine composition and, specifically the cationic content in sandstone reservoirs. Given the importance of the salt composition and concentration, tweaking the active ions which are responsible for the fluids-rock equilibrium will bring into effect numerous mechanisms of displacement which have been extensively debated. This experimental study, however, was carried out to evaluate the extent of the roles of chloride and sulphate-based brines in improved oil recovery. To carry this out, 70,000 ppm sulphates and chloride-based brines were prepared to simulate formation water and 5,000ppm brines of the same species as low salinity displacement fluids. Core flooding process was used to simulate the displacement of oil by using four (4) native sandstones core samples, obtained from Burgan oil field in Kuwait, at operating conditions of 1500 psig and 50oC. The core samples were injected with 70,000 ppm chloride and sulphates and subsequently flooded with the 5,000 ppm counterparts in a forced imbibition process. Separate evaluations of chloride and sulphate-based brines were carried out to investigate the displacement efficiencies of each brine species. The results showed that the in both high and low salinity displacement tests, the SO4 brine presented better recovery of up to 89% of the initial oil saturation (Soi). Several mechanisms of displacement were observed to be responsible for improved recovery during SO4 brine displacement. IFT measurement experiments also confirmed that there was reduction in IFT at test conditions between SO4 brine and oil and visual inspection of the effluent showed a degree emulsification of oil and brines. Changes in pH were observed in the low salinity flooding and negligible changes were noticed in the high salinity floods. These results provide an insight into the roles of chloride and sulphate ions in the design of smart “designer” water and low salinity injection scenarios

Prediction of gas rates from different layers by temperature distributions in wells: application to unconventional fields

A method for determination of gas and water rates from different separate layers based on the data of the temperature and pressure profiles along the wells is developed. The developed physics model is based on the first principles of mass, moment and energy conservations of flowing fluid along the wellbore column. It allows prediction of flow rate depth distribution in the well. Temperature and pressure depth profiles from gas production well in gas field (Australia) have been treated to determine the gas rates from different production layers. The accumulated rates measured in the field are compared to the modeling results, showing good accuracy of the model predictions. Compared to traditional flow metering, the proposed method is advantageous in low-flow-rate unconventional gas reservoirs

Colloidal-suspension flows with delayed fines detachment: analytical model & laboratory study

The effects of confinement and electrostatic interactions on the ion diffusion in the particle-rock contact area yields a delay in particle detachment during low-salinity water injection in porous media. The objective of the work is laboratory and mathematical modelling of the effects of delayed particle detachment on colloid-suspension transport in porous media. We present the governing system for single-phase particulate flow accounting for non-equilibrium fines detachment. The exact solution for one-dimensional flow with varying salinity is derived. Laboratory coreflood tests on low-salinity water injection are performed. The measured breakthrough fine particle concentration and pressure drop across the core are matched by the analytical model with high accuracy. Introduction of delay in the model removes the concentration shocks present in the instant fines detachment model as fines detach continuously throughout the injection period.Thomas Russell, Pavel Bedrikovetsk