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

Determining Gas Flow Rate and Formation Thermal Conductivity from Pressure and Temperature Profiles in Vertical Well

A simple and effective method of the gas rate prediction from temperature and pressure data is discussed in this paper. Solving the inverse problem allows de termination of the flow rate by matching the gas pressure and temperature distri butions with measured profiles. Results of field data treatment show good agree-ment with the model prediction.

/pdf/determining-gas-rate-distribution-from-temperature-and-4tdkndzin0.pdf

Determining gas rate distribution from temperature and pressure profiles in gas well


 
 
 In order to account for dissolution of CO2 in water, the core must be initially saturated by carbonized water, which have been in equilibrium with CO2. To account for evaporation of water in CO2, the injected CO2 must be put in contact with water until thermodynamic equilibrium. To account for both, reservoir water with CO2 is put in the tank until the thermodynamic equilibrium is established.
 
 
 
 Steady-state coreflood test is a widely accepted industrial method to determine relative permeability (Kr), but the capillary pressure (Pc) must be known from other sources (porous plate, mercury injection, and centrifuge tests). Significant difference between the capillary pressure determined from corefloods and by other methods is widely presented in the literature.
 We developed a novel coreflood method for simultaneous determination of relative permeability (Kr) and capillary pressure (Pc) − steady-state-transient test (SSTT). The main idea is to use the stabilized data of the steady-state method along with the transient data of the pressure drop. Therefore in the SSTT, the transient data on the pressure drop across the core, between the steady-states, are used instead of the traditionally utilized Pc-curve.
 The aim of this work is the development of laboratory procedure and mathematical method of the lab data treatment for SSTT.
 
 
 
 We run the following SSTT for two Berea cores:
 – Preliminary mathematical modelling of SSTT to determine optimal test parameters (flow rate, injected water fractions, sampling volumes and frequencies) and type curves for measured pressure drop and water-cut; – Performing water-oil injections with water cuts 0.02, 0.05, 0.1, 0.25, 0.5, 0.75, 0.9, 0.95, 0.98, and 1.00; – Approximation of the measured transient pressure-drop data by the type curves to regularise the inverse problem of Kr and Pc calculations; – Kr and Pc calculations by the inverse modelling.
 To approximate the scattered, raw transient pressure-drop data, we determine the type curves within the stabilization-time interval. The S-shape pressure-drop curves are observed for low water fractions in the injected fluid; the exponential form is observed at high water fraction values.
 
 
 
 After determination of Kr and Pc curves from the steady-state and transient pressure-drop data by the inverse solver, we compared the measured and modelled values of transient water-cut. High agreement was observed for two Berea corefloods: R2 varies from 0.88 to 0.99. Besides, the matched modelling lines for pressure-drop and saturation are located within the respective error bars in both tests.
 We also applied the SSTT method developed to treat the published steady-state data of 3 gas-water and 3 oil-water tests, where steady-state saturation profiles were determined by X-ray CT. The close match validates the SSTT.
 
 
 
 For the first time, a lab method for simultaneous determination of Kr and Pc from coreflood for gas-water and oil-water fluids has been developed and validated.


A Novel Method to Determine Relative Permeability and Capillary Pressure from Corefloods Application to CO2 Storage

Formation damage by fines migration during low-salinity water injection can greatly affect field-scale waterflooding projects. In this paper, we present the basic governing equations for single-phase flow with detachment, migration and straining of natural reservoir fines. We perform laboratory corefloods with low-salinity water injections and monitor the breakthrough particle concentration and pressure drop across the core. The analytical model for linear flow matches the laboratory data with high accuracy. The analytical model for radial flow predicts well behaviour from laboratory-tuned coefficients. The calculations show that fines migration during low-salinity water injection causes significant injectivity decline. For typical values of fines-migration model coefficients, injectivity index declines 2–8 times during 10−3 pore volumes injected and the radius of the damaged zone does not exceed a few metres. We present two field cases on waterflooding and low-salinity water injection. The radial model presents good agreement with well injectivity field data.

Pavel Bedrikovetsky

Papers

Determining Gas Flow Rate and Formation Thermal Conductivity from Pressure and Temperature Profiles in Vertical Well

Determining gas rate distribution from temperature and pressure profiles in gas well

A Novel Method to Determine Relative Permeability and Capillary Pressure from Corefloods Application to CO2 Storage

Injectivity formation damage due to fines migration

Productivity decline in a Salamander geothermal well: experiment, modelling and case study