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

Summary Understanding the behaviour of the hydrocarbon flow during secondary migration greatly helps geologists and petroleum engineers to identify the potential hydrocarbon traps in geological basins in the exploration stage. Basin modeling is, therefore, necessary to curtail resource-consuming challenges such as dry-hole drilling. However, building accurate basin models to predict secondary migration and dynamics of trap filling is still a formidable problem due to the complexities associated with hydrocarbon movement at large time scales. Despite several commercial basin simulators for modelling secondary migration, they are primarily based on numerical algorithms and require high volumes of data and computation time, adversely affecting effective exploration decision-making. Analytical models, yet, are fast and require moderate data for multivariant analysis of the secondary migration of hydrocarbons while accounting for relevant geological and physical factors. The analytical models proposed in literature for secondary migration offer limited precision when evaluating the combined effects of physical, chemical, and biological reactions. This study proposes novel analytical models that simulate the dynamics of hydrocarbon propagation below seals and accounts for; (i) chemical reactions including oil biodegradation, (ii) areal variation of cross-section of stringers, and (iii) hydrological water flow below the migrating hydrocarbons for cases of pulse and continuous expulsions. 

Secondary Migration Modelling for Multivariant Exploration Planning: An Analytical Approach

E15 h ysteres sin tu ree=p ase por u

Identifying the Source and Magnitude of Formation Damage from Pressure and Temperature Profiles

Fines migration is a common cause of permeability and, consequently, injectivity and productivity decline in subterranean reservoirs. Many practitioners implement prevention or remediation strategies to reduce the impact of fines migration on field productivity and injectivity. These efforts rely on careful modelling of the underlying physical processes. Existing works have demonstrated the ability to predict productivity decline by quantifying the extent of particle decline at different fluid velocities. Fluid flows in porous media often involve multiple phases, which has been shown in laboratory experiments to influence the extent of particle detachment. However, no theory has directly accounted for this in a particle detachment model. In this work, a new model for fine particle detachment, expressed through the critical retention function, is presented, explicitly accounting for the immobile fines trapped within the irreducible water phase. The new model utilises the pore size distribution to allow for the prediction of particle detachment at different velocities. Further, an analytical model is presented for fines migration during radial flow into a production well. The model accounts for single-phase production in the presence of irreducible water, which has been shown to affect the extent of fines migration significantly. Combining these two models allows for the revealing of the effects of connate water saturation on well impedance (skin factor growth) under fines migration. It is shown that the higher the connate water saturation, the less the effect of fines migration. The appropriateness of the model for analyzing production well data is verified by the successful matching of 10 field cases. The model presented in this study is an effective tool for predicting the rate of skin growth, its stabilization time and final value, as well as the areal distribution of strained particles, allowing for more intelligent well remediation design. Further, the findings of this study can help for a better understanding of the distribution of fines within porous media and how their detachment might be influenced by pore structure and the presence of a secondary immobile phase.

/pdf/treatment-of-oil-production-data-under-fines-migration-and-1bj1wz4q.pdf

Treatment of Oil Production Data under Fines Migration and Productivity Decline

Non-monotonic retention profiles (NRP) have been observed in numerous studies of colloidal-nano flows in porous media. For the first time, we explain the phenomenon by distributed particle properties (size, shape, surface charge). We discuss colloidal-nano transport with fines attachment considering stochastically distributed filtration coefficient (particle attachment probability) and the influence of area occupation by particles on the rock surface. The distributed dynamic system allows for exact averaging (up-scaling) yielding a novel 3x3 system of equations for total concentrations. Besides the traditional equations of particle mass balance and capture-rate, the novel system contains a third independent equation for kinetics of site occupation during particle attachment. Ten laboratory tests exhibiting NRP have been successfully matched by the upscaled system for binary colloids. Ten laboratory tests with 7-parametric data arrays have been successfully matched by the 5-parameter model, which validates the model. The tuned parameters belong to their common intervals. The laboratory data tuning was significantly simplified by deriving the exact solution of upscaled equations. These results provide valuable insights for understanding the transport mechanisms and environmental impact in colloidal-nano flows exhibiting NRP. Besides, the upscaled system and the analytical model for 1D transport facilitate interpretation of the laboratory coreflood data and allows for the laboratory-based predictions for 3D colloidal-nano transport at the field scale.

Pavel Bedrikovetsky

Papers

Secondary Migration Modelling for Multivariant Exploration Planning: An Analytical Approach

E15 h ysteres sin tu ree=p ase por u

Identifying the Source and Magnitude of Formation Damage from Pressure and Temperature Profiles

Treatment of Oil Production Data under Fines Migration and Productivity Decline

Non-monotonic solutions for colloid-transport of size-distributed particles in porous media