N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

With the decline in oil discoveries during the last decades it is believed that EOR technologies will play a key role to meet the energy demand in years to come. This paper presents a comprehensive review of EOR status and opportunities to increase final recovery factors in reservoirs ranging from extra heavy oil to gas condensate. Specifically, the paper discusses EOR status and opportunities organized by reservoir lithology (sandstone and carbonates formations and turbiditic reservoirs to a lesser extent) and offshore and onshore fields. Risk and rewards of EOR methods including growing trends in recent years such as CO2 injection, high pressure air injection (HPAI) and chemical flooding are addressed including a brief overview of CO2-EOR project economics.

Enhanced Oil Recovery: An Update Review

http://abollegend.persiangig.com/Theory_of_Gas_Injection_Processes_-_Franklin.pdf

Theory of Gas Injection Processes

Particle detachment from the rock during suspension transport in porous media was widely observed in laboratory corefloods and for flows in natural reservoirs. A new mathematical model for detachment of particles is based on mechanical equilibrium of a particle positioned on the internal cake or matrix surface in the pore space. The torque balance of drag, electrostatic, lifting and gravity forces, acting on the particle from the matrix and the moving fluid, is considered. The torque balance determines maximum retention concentration during the particle capture. The particle torque equilibrium is determined by the dimensionless ratio between the drag and normal forces acting on the particle. The maximum retention function of the dimensionless ratio (dislodging number) closes system of governing equations for colloid transport with particle release. One-dimensional problem of coreflooding by suspension accounting for limited particle retention, controlled by the torque sum, allows for exact solution under the assumptions of constant filtration coefficient and porosity. The explicit formulae permit the calculation of the model parameters (maximum retention concentration, filtration and formation damage coefficients) from the history of the pressure drop across the core during suspension injection. The values for maximum retention concentration, as obtained from two coreflood tests, have been matched with those calculated by the torque balance on the micro scale.

Modified Particle Detachment Model for Colloidal Transport in Porous Media

Laboratory tests have been done to investigate the effect of kaolinite content on the behaviour of unconsolidated sandstone rocks during the injection of low-salinity water. Artificial cores comprised of kaolinite and chemically washed sand were prepared and compacted for this study. Five cores with kaolinite weight percentages ranging from 1% to 10% were injected sequentially with sodium chloride solutions of stepwise decreasing salinity. The permeability of the cores declined to as little as 1/54 times the initial permeability. Negligible permeability decline was observed when the kaolinite content was only 1% of the total mass. Generally, the extent of permeability decline was greater in cores with a larger percentage of kaolinite. The results are explained by the effect of kaolinite not only on the abundance of detachable clays, but also on the pore size. The results from the laboratory test were fitted with an exact solution of a model for fines migration. The parameters from these tests were input into a model for radial injection of low-salinity water to predict the extent of injectivity decline. The results serve as a benchmark for correlating injectivity decline due to fines migration between wells using the rock mineralogy. The tests suggest that mineralogy alone is not sufficient to fully predict formation damage, and that pore geometry and the nature of particle detachment are still critical factors for this process.

Effect of kaolinite content on formation damage due to fines migration: systematic laboratory and modelling study

Theoretical and laboratory studies are performed aiming at the development of a predictive model for transport and retention of particles from produced water and crude oil/gas based on grain size distribution and particle sizes only. The particle capture by straining is thoroughly investigated. In the laboratory, injections of different sized particles suspended in fluid with different salinity and pH values have been carried out into the newly designed porous media holder with single-layer grains and into the column packed engineering porous media. The retained particles are filmed using microscope; their breakthrough concentrations are measured by particle counter. A new mathematical model accounting for pore connectivity and triangular pore throat shape is derived and applied to the experimental conditions. Agreement between test data and modelling results supports application of the model to the evaluation of straining effect on the produced water management and injectivity enhancement. Copyright 2012, Society of Petroleum Engineers.

Study of particle straining effect on produced water management and injectivity enhancement

Colloidal transport in anisotropic porous media: Kinetic equation and its upscaling


 Fines migration is one of the most drastic causes for formation damage - the detached clays migrate and impairs well productivity. Two types of damaging clays are encountered in petroleum reservoirs: authigenic clays that grew on the grain surfaces during geological times, and detrital clays that have been broken off the grains by local stresses. Detailed laboratory and mathematical modelling have been carried out for detrital-clay formation damage. The theory for formation damage by authigenic clays is not available. The aim of this work is the development of a laboratory procedure to estimate formation damage by authigenic clays and the derivation of a mathematical model for core scale. We performed two test of corefloods using Castlegate core samples. In the first test, injection rate increased in a stepwise manner up to 100 mL/min and in the second one up to a 200mL/min to make sure both detrital and authigenic particles are detached. The pressure drop across the overall core and the concentration of the fine in the produced fluid have been measured. We have derived equations for authigenic-fines detachment using the beam theory and the von Mises failure criteria to obtain analytical solutions for linear system of equations. Matching the laboratory data by the analytical model allows determining the percentage of authigenic and detrital clays in the cores. The laboratory data exhibit a good match with the mathematical model for the two coreflood tests. The non-monotonic change of the concentration of the detached fine, with the initial and final risings, determines the type curve that evidence the mobilization of both, authigenic and detrital clays. The treatment of the measured data in test#2 shows that 82% of the initial attached particles are authigenic. The model parameters in order of decrease of their sensitivity are contact-bond radius, pore radius, particle size, lever-arm ratio, tensile strength and aspect ratio. A novel experimental procedure to determine fines-migration formation damage by authigenic and detrital clays was developed. A newly derived mathematical model allows determining the model coefficients from the laboratory tests and predict future detachment rate of authigenic and detrital particles.

Formation Damage by Fines Breakage and Migration


 Fines migration causes significant formation damage during oil and gas production. The reliable prediction of well performance and extend of the damaged zone allow for planning and design of well stimulation for prevention, mitigation and removal of the damage. We derive a novel analytical model for production well performance during fines migration. The model includes explicit formulae for concentrations of suspended and strained fines, and the expressions for skin factor and well impedance. Ten field cases exhibit close match with the analytical model. Moreover, the tuned parameters belong to common intervals of their variation. The work provides means for reliable well behaviour prediction based on production history and coreflood data.

Pavel Bedrikovetsky

Papers

Effect of kaolinite content on formation damage due to fines migration: systematic laboratory and modelling study

Study of particle straining effect on produced water management and injectivity enhancement

Colloidal transport in anisotropic porous media: Kinetic equation and its upscaling

Formation Damage by Fines Breakage and Migration

Well Inflow Performance Under Fines Migration: Analytical Model, Production Data Treatment