We investigate the deep-bed filtration of micron-sized hematite particles suspended in distilled water during flow in siliceous granular porous media, where particle retention is mostly due to surface ͑van der Waals and electrostatic͒ interactions. We show that x-ray computed tomography enables three-dimensional images of the filtration process to be generated. The one-dimensional filtrate concentration profiles obtained by averaging the images over sections perpendicular to the flow direction are rapidly decaying functions of the distance from the porous medium inlet and slide upward in the course of time, consistently with the filtration model presented by Herzig et al. ͓Ind. Eng. Chem. 62, 8 ͑1970͔͒. Finally, the filtration coefficient is found to decrease rapidly as a function of time: This indicates that the attractive interaction responsible for the retention of the hematite particles is strongly attenuated as the particles accumulate of the pore surfaces.

The injector impairment due to suspended particles during waterflood project happens in two stages: firstly particles penetrate into a reservoir and are captured by the rock (deep bed filtration); at the second stage, after the reservoir inlet is plugged by particles, the particles build up a filter cake. Prediction of injectivity decline is based on mathematical modelling of deep bed filtration and filter cake formation. The model parameters are determined from either laboratory tests or field data. The model parameters for deep bed filtration - the filtration and formation damage coefficients - can be determined from laboratory pressure measurements using so-called 3-point pressure method. The method for determination of the critical porosity fraction, which is necessary for calculation of the time of transition from deep bed filtration to filter cake buildup, is not available in the literature. In the current paper, the 3-point pressure method was used for determination of the critical porosity fraction. The data from 18 laboratory tests were treated, and the correlation between the formation damage coefficient and the critical porosity fraction was obtained. This correlation allows determining of the deep bed filtration and filter cake buildup parameters from either routine coreflood test or well injectivity history. Introduction Injection well impairment during sea/produced water flooding is a widespread problem in offshore field development. It happens due to solid and liquid particles, which are present in the injected water and are captured by rock, resulting drastic permeability decline1,2. It resulting in drastic increase of operation costs. Impairment of injectors during poor quality water injection occurs in two stages: first the particles penetrate into the reservoir making formation damage (so called deep bed filtration), at the second stage the particles form an external cake after plugging the inlet cross section3–5. The injectivity decline prediction is performed using mathematical models of deep bed filtration3,4,6 and external cake formation3–5. The data for reservoir formation damage simulation are obtained from laboratory coreflood tests. The mathematical model for deep bed filtration contains two empirical constants - filtration and formation damage coefficients. These parameters can be determined from measurements of the particle outlet concentration and pressure drop during coreflooding3,4,6. The concentration measurements are cumbersome and complex while the pressure measurement is a routine laboratory procedure. Measurements of pressure in some intermediate core point together with its measurements at core inlet and effluent (so-called 3-point pressure method) allows determination of both filtration and formation damage coefficients7,8. The transition time of switching from deep bed filtration to external cake formation is determined by a critical porosity fraction, which should be filled by deposited particles in order to prevent further particle penetration into porous rock. Due to lack of method for critical porosity fraction measurement, it is proposed to use the value 0,53,4. In the current paper, a method for laboratory determination of the critical porosity fraction is developed. The method uses pressure measurements in three core points. The data of 18 laboratory corefloods were treated, and the model parameters were obtained. Analysis of the results allows for correlating the formation damage coefficient with the critical porosity fraction. This correlation allows for complete characterisation of deep bed filtration and filter cake buildup systems from either routine coreflood or well injectivity history. Analytical Model for Deep Bed Filtration and External Cake Formation Fig. 1 shows two stage of injectivity impairment: deep bed filtration described by eq. (A-1)-(A-11) from Appendix A, and external filter cake formation modelled by (D-1)-(D-4).

Summary Permeability decline occurs during injection of sea or produced water, resulting in well impairment. Solid and liquid particles dispersed in the injected water are trapped by the porous medium and may significantly increase hydraulic resistance to the flow. We discuss a mathematical model for deep bed filtration containing two empirical parameters - the filtration and the formation damage coefficients. 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 with expensive and difficult particle-concentration measurements of the core effluent, and 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 proved in an earlier work 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. A new method for the simultaneous determination of both coefficients is developed here. The method's new feature is using pressure data at an intermediate core point, 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. In this work, the proposed method is used for analysis of laboratory test data on deep bed filtration. The values of filtration and formation damage coefficients are obtained for flow of solid and liquid particle dispersions in a number of different cores. Effects of particle type and porous media wettability on permeability decline are analyzed. Introduction Injectivity decline of oilfield injection wells is a widespread phenomenon during sea- or produced-water injection. This decline may result in significant cost increases in waterflooding projects. Reliably predicting this decline is important for waterflood design as well as for choice and preventative treatment of injected water. 1,2 One of the reasons for well injectivity decline is the permeability decrease caused by rock matrix plugging from solid or liquid particles suspended in the injected water. The flow and deposition of particles in the rock matrix is called deep bed filtration. A mathematical model for deep bed filtration presented by Herzig et al.3 and by Sharma and Yortsos4 contains two empirical parameters - the filtration coefficient ? and the formation damage coefficient ß. Knowledge of these two parameters is essential for predicting well injectivity decline during sea/ produced water injection. These parameters are empirical; therefore, they should be determined from laboratory coreflood tests by flowing water with particles through rock. Pang and Sharma5 and Wennberg and Sharma6 showed that both parameters can be inferred from the combined measurements of core pressure drop and of suspended particle concentration in core outlet water. The method is based on the analytical model for linear deep bed filtration with constant filtration and formation damage coefficients. In general, the filtration coefficient lambda and the permeability are arbitrary functions of deposited concentration that can also be found from the pressure drop and the outlet concentration by solving functional and integral equations.7 A coreflood test is usually accompanied by pressure-drop measurements. These measurements are inexpensive and simple to perform; therefore, they are widely mentioned in the literature.1,3-6,8 Nevertheless, suspended-particle-concentration data in core outlet water during laboratory tests are almost unavailable in the literature because measuring concentration data requires special equipment and is difficult compared to pressure-drop measurements.8,9 These difficulties are the motivation for attempting to determine the constants ? and ß from the total pressure drop along the core measured at different times during flow. Here we show that the mathematical solution to this problem has limitations. This is discussed in the main part of the text heuristically and in Appendix C rigorously. In summary, only a combination of these two parameters can be found. At best, only ranges of each of these two parameters can be obtained. This limited result is unfortunate for common engineering practice. For example, certain existing software packages for predicting well injectivity loss provide the option of adjusting the pressure- drop curve by matching both parameters ? and ß, under the implicit assumption that these two parameters can be found from the test. A method for determining the filtration and formation damage coefficients from pressure measurements at an intermediate point of the core as well as at core entrance and exit during deep bed filtration, was proposed in a previous work10 (the so-called three point pressure method). The main part of this paper describes the laboratory procedure and the mathematical recovery method. The method is proven to furnish unique values for the two coefficients and verifies that the solution of the inverse problem is unique and stable. The precise mathematical description of the model is contained in Appendix A. Appendix B contains the expressions for impedance, and the final equation for solution of the inverse problem is derived in Appendix C. Laboratory data on deep bed filtration with pressure measurements at two intermediate points have been presented in the literature. 11,12 In the current work, the results of 34 laboratory tests11,12 have been analyzed with the three-point pressure method. The objective of this study is to determine statistical relationships between the filtration and formation damage coefficients and the ratio of pore radius to particle size.13 The results should help in predicting well injectivity decline with permeability and porosity without performing special coreflood tests. A system of dimensionless parameters has been selected, and the forms of dependencies on the parameters have been derived. The results are presented in Tables 1 through 4 for different groups of tests, such as water with solid, liquid, or with both types of particles.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractWhen oil is produced under high water-cut conditions, oil in water emulsions can be formed. The break-up of oil droplets predominantly takes place in the choke valve. We have conducted laboratory experiments to investigate the effect of flow through a choke valve on the oil-droplet-size distribution in the emulsion. In these experiments the choke is modeled as a circular orifice in a pipe. The droplet sizes after break-up can be correlated to the mean energy dissipation rate per unit mass in the orifice. The experiments have been conducted with two set-ups on a different scale. The relation, which we have derived for the maximum stable droplet diameter downstream of the orifice can be applied to both scales. Furthermore the effect of oil viscosity on the droplet sizes after break-up has been investigated.

The importance of produced water re-injection (PWRI) is unquestionable. It is in many cases the cheapest and most environmentally friendly solution for wastewater disposal. It is also a feasible method for EOR as a water flooding mechanism. PWRI, however, suffers from a major limitation, which is the current inability in accurately predicting the lifespan and performance of its injection wells. This is due to the multitude of parameters that affect it. Current models1–2 exist that incorporate the thermal effects3 of PWRI leading to fracture growth. However, the leak-off pattern of this injection differs from that of clean water (seawater) injection due to the damage caused by the produced water onto the formation and especially the fracture faces. Thus, static filtration experiments with refined post-mortem analysis have been conducted to obtain quantitative deposition profiles along the core. This allows for the testing and verification of existing models4–7. The post-mortem analysis introduced in this paper will be used for future dynamic filtration experiments as well as experiments specifically devised to simulate the fracture tip area. A unified model that will accurately reproduce the permeability decline and deposition profile for all three sets of experiments will flow, thus advancing the predictability of injectivity decline associated with PWRI. A detailed description of the post-mortem analysis will be presented. Testing of existing heuristic models Wennberg5 and Bedrikovedski7 will be published in the near future. Introduction Produced water re-injection (PWRI), when first introduced, was seen as a breakthrough solution for water disposal. It is both environmentally friendly and economically among the cheapest options. Thus, it garnered much interest. However, the associated injectivity decline remains a major issue. In order to simulate and predict the extent of formation damage inflicted by produced water re-injection it is necessary to have a competent model of the damage inflicted as a function of injection flow rate and particle concentration among other parameters. Different models exist in the literature - each having their merits and weaknesses. Thus, the authors of this article undertook controlled static filtration experiments with the addition of detailed post-mortem analysis. The post-mortem analysis is a new development that presents quantitative data that can be used to affirm or refute the predictions of existing heuristic models; thereby lending a guiding hand to the direction modelling should follow. The static filtration experiments were conducted using a 5-port sleeve, to obtain six pressure drop data channels over a 5.0 inch Bentheim sandstone core of 1-inch diameter. Bentheim sandstone is homogeneous with a porosity of 22%, permeability of approximately 1.4D and pore throat diameter of 10–15 (m. Distilled water containing 0.1 µm - 5 (m hematite (Fe2O3) particles (65% of which were less than 1 (m in diameter) was injected at different concentrations (20 ppm, 40 ppm and 80 ppm) and flow rates (5.4 l/hr and 10 l/hr) into the core - each experiment having only one injection concentration and one injection flow rate. The concentration of the effluent solution of the experiment was either measured online using a laser diffraction unit (Figure 1) or by collecting samples and quantifying the concentration at a later stage using chemical analysis (Figure 2). The data gathered used the guideline suggested by Wennberg8 as a compliance criterion. The post-mortem analysis consisted of quantitative visual analysis of core cross-sections as well as quantitative chemical analysis. Using these two techniques an accurate deposition profile of the injected solid along the length of the sandstone core was obtained. These two techniques will be discussed in detail in the next section.