Pavel Bedrikovetsky

Characterisation of deep bed filtration system from laboratory pressure drop measurements

Abstract During the injection of sea/produced water, permeability decline occurs, resulting in well impairment. Solid and liquid particles dispersed in the injected water are trapped by the porous medium and may increase significantly the hydraulic resistance to the flow. We formulate a mathematical model for deep bed filtration containing two empirical parameters—the filtration coefficient and the formation damage coefficient. These parameters should be determined from laboratory coreflood tests by forcing water with particles to flow through core samples. A routine laboratory method determines the filtration coefficient from expensive and difficult particle concentration measurements of the core effluent; then, the formation damage coefficient is determined from inexpensive and simple pressure drop measurements. An alternative method would be to use solely pressure difference between the core ends. However, we prove that given pressure drop data in seawater coreflood laboratory experiments, solving for the filtration and formation damage coefficients is an inverse problem that determines only a combination of these two parameters, rather than each of them. Despite this limitation, we show how to recover useful information on the range of the parameters using this method. We propose a new method for the simultaneous determination of both coefficients. The new feature of the method is that it uses pressure data at an intermediate point of the core, supplementing pressure measurements at the core inlet and outlet. The proposed method furnishes unique values for the two coefficients, and the solution is stable with respect to small perturbations of the pressure data.

Particle Detachment Under Velocity Alternation During Suspension Transport in Porous Media

Flow of suspensions in porous media with particle capture and detachment under alternate flow rates is discussed. The mathematical model contains the maximum retention concentration function of flow velocity that governs the particle release and is used instead of equation for particle detachment kinetics from the classical filtration model. An analytical model for suspension injection with alternate rates was derived, and a coreflood by suspension with alternate rates was carried out. The modelling and laboratory data are in a good agreement, which validates the modified particle detachment model with the maximum retention function.

Mathematical Model for Fines-Migration-Assisted Waterflooding With Induced Formation Damage

Permeability decline during corefloods with varying water composition, especially with low-salinity water, has been widely reported in the literature. This effect can provide a relatively simple method for mobility control during waterflooding. In this work, new basic equations for waterflooding with salinity variations causing the detachment of fine particles, their migration, and their straining are derived. The maximum concentration of attached fine particles as a function of water salinity and saturation is used to model the fines detachment. In large-scale approximation, the equivalence between the model for two-phase flow with fines migration and the adsorption-free polymer-flood model is established, which allows applying a commercial polymer flood simulator for modeling the waterflood with induced fines migration. The modeling showed that the permeability decline in the water-swept zone, caused by the alteration of the injected water composition and induced fines migration, may be able to improve waterflood performance by delaying water breakthrough, increasing sweep efficiency, and reducing the water cut, thus providing a relatively simple method for mobility control during waterflooding.

Particle mobilization in porous media: temperature effects on competing electrostatic and drag forces

The fluid flow in natural reservoirs mobilizes fine particles. Subsequent migration and straining of the mobilized particles in rocks greatly reduce reservoir permeability and well productivity. This chain of events typically occurs over the temperature ranges of 20-40 degrees C for aquifers and 120-300 degrees C for geothermal reservoirs. However, the present study might be the first to present a quantitative analysis of temperature effects on the forces exerted on particles and of the resultant fines migration. Based on torque balance between electrostatic and drag forces acting on attached fine particles, we derived a model for the maximum retention concentration and used it to characterize the detachment of multisized particles from rock surfaces. Results showed that electrostatic force is far more affected than water viscosity by temperature variation. An analytical model for flow toward wellbore that is subject to fines migration was derived. The experiment-based predictive modeling of the well impedance for a field case showed high agreement with field historical data (coefficient of determination R-2=0.99). It was found that the geothermal reservoirs are more susceptible to fine particle migration than are conventional oilfields and aquifers.

A fast inverse solver for the filtration function for flow of water with particles in porous media

Models for deep bed filtration in the injection of seawater with solid inclusions depend on an empirical filtration function that represents the rate of particle retention. This function must be calculated indirectly from experimental measurements of other quantities. The practical petroleum engineering purpose is to predict injectivity loss in the porous rock around wells. In this work, we determine the filtration function from the effluent particle concentration history measured in laboratory tests knowing the inlet particle concentration. The recovery procedure is based on solving a functional equation derived from the model equations. Well-posedness of the numerical procedure is discussed. Numerical results are shown.

Size-Exclusion Colloidal Transport in Porous Media--Stochastic Modeling and Experimental Study

Suspension, colloidal, and emulsion flow in rocks with particle size-exclusion may have a strong effect on the reservoir and on the well behavior during fines migration and production, drilling-fluid invasion into oil- or gas-bearing formations, or injection of seawater or produced water. The stochastic microscale equations for size-exclusion colloidal transport in porous media (PM) are derived. The proposed model includes the following new features: It accounts for the accessible flux in the expression for capture rate, it accounts for the increase of inlet concentration caused by the injected particles entering only the accessible area, and it accounts for the dilution of effluent accessible flux in the overall flux of the produced suspension.

Theoretical Definition of Formation Damage Zone With Applications to Well Stimulation

Flow of particulate suspension in porous media with particle retention and consequent permeability reduction is discussed. Using analytical model for suspension injection via single well, the permeability damage zone size was defined and expressed by transcendental equation. Analysis of field data shows that usually the size of damaged zone does not extend more than 1 m beyond the injector. The definition of damage zone size is used for design of well stimulation via deposition removal. DOI: 10.1115/1.4001800

Size exclusion deep bed filtration: Experimental and modelling uncertainties

A detailed uncertainty analysis associated with carboxyl-modified latex particle capture in glass bead-formed porous media enabled verification of the two theoretical stochastic models for prediction of particle retention due to size exclusion. At the beginning of this analysis it is established that size exclusion is a dominant particle capture mechanism in the present study: calculated significant repulsive Derjaguin-Landau-Verwey-Overbeek potential between latex particles and glass beads is an indication of their mutual repulsion, thus, fulfilling the necessary condition for size exclusion. Applying linear uncertainty propagation method in the form of truncated Taylors series expansion, combined standard uncertainties (CSUs) in normalised suspended particle concentrations are calculated using CSUs in experimentally determined parameters such as: an inlet volumetric flowrate of suspension, particle number in suspensions, particle concentrations in inlet and outlet streams, particle and pore throat size distributions. Weathering of glass beads in high alkaline solutions does not appreciably change particle size distribution, and, therefore, is not considered as an additional contributor to the weighted mean particle radius and corresponded weighted mean standard deviation. Weighted mean particle radius and LogNormal mean pore throat radius are characterised by the highest CSUs among all experimental parameters translating to high CSU in the jamming ratio factor (dimensionless particle size). Normalised suspended particle concentrations calculated via two theoretical models are characterised by higher CSUs than those for experimental data. The model accounting the fraction of inaccessible flow as a function of latex particle radius excellently predicts normalised suspended particle concentrations for the whole range of jamming ratios. The presented uncertainty analysis can be also used for comparison of intra- and inter-laboratory particle size exclusion data.

Deep-Bed filtration under multiple particle-capture mechanisms

This paper (SPE 98623) was accepted for presentation at the International Symposium and Exhibition on Formation Damage Control, Lafayette, Louisiana, 15–17 February 2006, and revised for publication. Original manuscript received for review 24 October 2005. Revised manuscript received for review 1 March 2009. Paper peer approved 21 March 2009. Summary Severe injectivity decline during seawater injection and producedwater reinjection is a serious problem in offshore waterflood projects. The permeability impairment occurs because of the capture of particles from injected water by the rock, both internally in the pores and externally in a filter cake. The reliable modeling-based prediction of injectivity decline is important for injected-watertreatment design and management (injection of seawater or produced water, water filtering, etc.). The classical deep-bed filtration model includes a single overall description of particle capture. During laboratory or field data interpretation using this model, it is usually assumed that several simultaneously occurring capture mechanisms are represented in the model by a single overall mechanism. The filtration coefficient, obtained by fitting the model to the laboratory or field data, represents the total kinetics of the particle capture. The purpose of this study is to justify this approach of using an aggregated single filtration coefficient. A multiple-retention deep-bed filtration model needs to describe several simultaneous capture mechanisms. The kinetics of the different capture mechanisms can differ from one another by several orders of magnitude. This greatly affects the particle propagation in natural reservoirs and the resulting formation damage. In this study, a model for deep-bed filtration taking into account multiple particle-retention mechanisms is discussed. It is proven that the multicapture model can be reduced to a single-capture-mechanism deep-bed filtration model. The method for determination of the capture kinetics for all individual capture processes from the breakthrough curve is discussed. As an example, the complete characterization of filtration with monolayer and multilayer deposition of iron oxide colloids is performed using particle-breakthrough curves from coreflooding.

Laboratory-Based Prediction of Sulphate Scaling Damage

BaSO4 scaling can have a disastrous impact on production in waterflood projects with incompatible injected and formation waters. This is due to precipitation of barium sulphate from the mixture of both waters, the consequent permeability reduction resulting in loss of well productivity. The system where sulphate scaling damage occurs is determined by two governing parameters: the kinetics coefficient characterising the velocity of chemical reaction and the formation damage coefficient reflecting permeability decrease due to salt precipitation. Previous work has derived an analytical model-based method for determination the kinetics coefficient from laboratory corefloods during quasi-steady state commingled flow of injected and formation waters. The current study extends the method and derives formulae for calculation of the formation damage coefficient from pressure drop measurements during the coreflood. The proposed method can be extended for axisymmetric flow around the well allowing calculation of both sulphate scaling damage coefficients from field data consisting of barium concentrations in the produced water and well productivity decline. We analyse several laboratory test data and field data, and obtain values of the two sulphate scaling damage parameters. The values of kinetics and formation damage coefficients as obtained from either laboratory or field data vary in the same range intervals. These results validate the proposed mathematical model for sulphate scaling damage and the analytical model-based method “from lab to wells”. Introduction It has been long recognised that formation and well damage may be caused by incompatibility of injected and formation waters. Precipitation of salts results in permeability decline. Among the most significant of all scaling species are the sulphates, particularly barium and strontium sulphates. Decision making on scale prevention and removal is based on prediction scale precipitation and damage is provided by mathematical modelling. The mathematical models for sulphate scaling during waterflooding consist of mass balance equations for all species with the reaction rate sink terms. Chemical reaction rate must obey law of acting masses or another more complex kinetics law. Several numerical and analytical models describing sulphate scaling under laboratory and field conditions are available in the literature. Nevertheless, the problem of determining model coefficients from either laboratory or field data to use in sulphate scaling simulation is far from resolved. This SPE 100611 Laboratoryand Field Prediction of Sulphate Scaling Damage P. G. Bedrikovetsky, SPE, North Fluminense State University (LENEP/UENF); E. J. Mackay, SPE, Heriot-Watt University; R. P. Monteiro, North Fluminense State University (LENEP/UENF); P. M. Gladstone, Cefet-Campos/UNED Macae; F. F. Rosario, SPE, Petrobras/CENPES