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

Quantitative Theory for Fines Migration and Formation Damage

Characterisation of fines migration system using laboratory pressure measurements

One of the widely spread causes of reservoir formation damage is fines migration. Migration of natural reservoir fines occurs during commingled production of oil or gas with low-salinity water, during high-rate production or injection, with low-salinity waterflooding and its combinations with enhancd oil recovery (EOR). At least 10% of $100 billion annual worldwide expenditure on prevention, mitigation, and removal of formation damage is attributed to fines migration. The current chapter derives basic fundamental equations for fines detachment, migration, and size exclusion in single-phase and two-phase environments. The mathematical model for fines detachment derived in this chapter significantly differs from the classical approach: the maximum attached concentration as a function of velocity, salinity, and pH captures fines lifting due to change of the abovementioned variables. Exact analytical solutions are obtained for 1D linear flows with fines migration during rate increase and salinity decrease. Laboratory coreflood data are matched by the analytical models, providing the tuned parameter values. The laboratory-based parameters are used for field-scale predictions of behavior of injection and production wells during fines migration.

Formation Damage by Fines Migration: Mathematical and Laboratory Modeling, Field Cases

Sulfate scaling in offshore waterflood projects, in which sulfate from the injected seawater (SW) reacts with metals from the formation water (FW), forming salt deposit that reduces permeability and well productivity, is a well known phenomenon. Its reliable prediction is based on mathematical models with well-known parameters. Previous research presents methods for laboratory determination of model coefficients using breakthrough concentration during coreflooding. The concentration measurements are complex and cumbersome, while the pressure measurements are simple and require standard laboratory equipment. In the present work, a new laboratory method is developed for determination of the model coefficients from pressure measurements. Several laboratory core-floods have been performed. The tests show that the proposed method is more precise for artificial cores than for the natural reservoir cores. Further development of the method is required to determine parameters of formation damage caused by sulfate scaling for reservoir core samples.

A New Laboratory Method for Evaluation of Sulfate Scaling Parameters From Pressure Measurements

Injectivity decline of oilfield injection wells is a widespread phenomenon during seawater/produced-water injection. The decline may result in significant cost increase of the waterflooding project. Reliable modeling-based prediction of injectivity-index decrease is important for waterflood design as well as for the planning of preventive injected-water treatment. One of the reasons for well injectivity decline is permeability decrease caused by rock plugging by solid/liquid particles suspended in the injected water. The mathematical model for deep-bed filtration contains two empirical functions: the filtration coefficient and the formationdamage coefficient. These empirical coefficients must be determined from laboratory coreflood tests by forcing water with particles to flow through the core samples. A routine laboratory method determines the filtration coefficient from expensive and difficult particle-concentration measurements at the core effluent; then, the formation-damage coefficient is determined from inexpensive and simple pressure-drop measurements. An alternative three-point-pressure method uses pressure data at an intermediate point of the core, supplementing pressure measurements at the core inlet and outlet. The method provides unique and stable values for constant-filtration and formation-damage coefficients. In the current work, we consider a more complex case in which both coefficients are linear functions of retained-particle concentration. In this case, the model is fully determined by four constants. The three-point-pressure method furnishes unique values for the four model parameters. A new semianalytical model for axisymmetric suspension filtration was developed to predict well-injectivity decline from the linear coreflood data with pressure measurements in three core points.

Pavel Bedrikovetsky

Papers

Quantitative Theory for Fines Migration and Formation Damage

Characterisation of fines migration system using laboratory pressure measurements

Formation Damage by Fines Migration: Mathematical and Laboratory Modeling, Field Cases

A New Laboratory Method for Evaluation of Sulfate Scaling Parameters From Pressure Measurements

Formation-damage evaluation from nonlinear skin growth during coreflooding