A common assumption for annular flow used in the petroleum industry is that the inner pipe is concentrically located inside the flow geometry; however, this is rarely the case, even in slightly deviated wells. Considering the increasing number of directional and horizontal wells, the flow behavior of drilling fluids and cement slurries in eccentric annuli is becoming particularly important. In this paper, the governing equation of laminar flow is numerically solved using a finite differences technique to obtain velocity and viscosity profiles of yield-power law fluids (including Bingham plastic and power law fluids). Later, the velocity profile is integrated to obtain flow rate. Results show that the velocity profile is substantially altered in the annulus when the inner pipe is no longer concentric. Stagnant regions of flow were calculated in the low side of the hole. Viscosity profiles predicted for an eccentric annulus show how misleading the widely used single-value apparent viscosity term can be for non-Newtonian fluids. Profiles of velocity and viscosity in concentric and varying eccentric annuli are presented in 3-D and 2-D contour plots for a better visualization of annular flow. Frictional pressure loss gradient versus flow rate relationship data for power law fluids is generated using the computer program. Later, this data is fitted to obtain a simple equation utilizing regressional analysis, allowing for a quick calculation of friction pressure losses in eccentric annuli. For a given flow rate, frictional pressure loss is reduced as the inner pipe becomes eccentric. In most cases, about a 50-percent reduction in frictional pressure loss is predicted when the inner pipe lies on the low side. IntroductionFlow of drilling fluids and cement slurries in annuli is an everyday event in petroleum engineering. In many of the calculation techniques used by petroleum engineers for prediction and design, the annular flow of fluids accounts for a significant part. However, a quick review of the present state of annular flow-related models readily reveals that our equations are for concentric annuli, and also are filled with approximations such as average velocity, average viscosity, and equivalent diameter. Here, through a basic study of non-Newtonian fluid flow in annuli, we will show how crude some of these approximations can be.A few researchers have already pointed out the importance of removing the assumption that the annulus is concentric. Heyda (1959) showed how dramatically the velocity profile of a laminar flowing Newtonian fluid would differ when the annulus is eccentric. Since the fluids of petroleum engineering are typically non-Newtonian in behavior, the studies of nonNewtonian fluid flow in eccentric annuli followed. Unfortunately, a number of investigators have built their eccentric annular flow studies on an equation of flow which is valid for a concentric annulus only and, therefore, have failed to obtain
TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractFeasibility of drilling with pure supercritical carbon dioxide to serve the needs of deep underbalanced drilling operations has been analyzed. A case study involving underbalanced drilling to access a depleted gas reservoir illustrates the need for such a study. For this well, nitrogen was initially considered as the drilling fluid. Dry nitrogen, due to its low density, was unable to generate sufficient torque in the downhole motor. Mixture of nitrogen and water, stabilized as foam, generated sufficient torque, but made it difficult to maintain underbalanced conditions. This diminished the intended benefit of using nitrogen as the drilling fluid. CO 2 is likely to be supercritical at downhole pressure and temperature conditions, with density similar to that of a liquid and viscosity comparable to a gas. A computational model was developed to calculate the variation of density and viscosity in the tubing and the annulus with pressure, temperature and depth. A circulation model was developed to calculate the frictional pressure losses in the tubing and the annulus, and also calculates important parameters such as the jet impact force and the cuttings transport ratio. An attempt was made to model the temperatures in the well using an analytical model. Corrosion aspects of a CO 2 based drilling system are critical and were addressed in this study. The results show that the unique properties of CO 2 , which is supercritical in the tubing and changes to vapor phase in the annulus, are advantageous in its role as a drilling fluid. It has the necessary density in the tubing to turn the downhole motor and the necessary density and viscosity to maintain underbalanced conditions in the annulus. The role of a surface choke is crucial in controlling the annular pressures for this system. A carefully designed corrosion control program is essential for such a system. Results of this study are also important for CO 2 sequestration and CO 2 based enhanced oil recovery operations.
The process of formation permeability damage due to solids movement and capture was quantitatively modeled by using principles of deep bed filtration and chemical reactions kinetics. The developed theory describes the pore blocking mechanism caused by particles from completion fluids (foreign particles invasion), as well as the mechanism of release and capture of rock fines (in-situ mobilization). For practical applications, this theory was used in the context of pattern recognition, i.e., to examine the experimental data on rock permeability change versus time from the laboratory flow experiments. Thus, a straight line section of data plotted in a certain system of coordinates indicated the type of formation damage occurring. The verification study was performed in two series of laboratory experiments. In the first, a completion fluid, contaminated with drilling mud, was pumped through the simulated synthetic rock. In the second, four typical, solids-free completion brines were pumped through actual samples of water-sensitive, unconsolidated sandstones taken from Adriatic Sea gas fields. The experiments revealed the applicability of the theory and the method of diagnostic plots to describe and analyze formation permeability damage.
SPE Members Abstract The process of formation permeability damage due to solids movement and capture was quantitatively modeled by using principles of deep bed filtration and chemical reactions kinetics. The developed theory describes the pore blocking mechanism caused by particles from completion fluids (foreign particles invasion) as well as the mechanism of release and capture of rock fines (in-situ mobilization). For practical applications, this theory was used in the context of pattern recognition, ie, to examine the experimental data on rock permeability change vs time from the laboratory flow experiments. Thus, a straight line section of data plotted in a certain system of coordinates indicates the type of formation damage occurring. The verification study was performed in two series of laboratory experiments. In the first, a drilling mud, consisting of a contaminated completion fluid, was pumped through the simulated synthetic rock. In the second, four typical, solids-free completion brines were pumped through actual samples of water sensitive, unconsolidated sandstones taken from Adriatic Sea gas fields. The experiments revealed the applicability of the theory and the method of diagnostic plots to describe and analyze formation permeability damage. Introduction The last two decades have seen significant progress made in understanding the mechanisms of formation damage. In summary:all sandstones are water sensitive to some degreepermeability damage is associated with particles movement and clay swelling effectsthere is a strong correlation between fluid salinity and permeability impairment Traditionally, permeability damage has been classified as chemical or mechanical, the latter being broken into two categories: foreign particles invasion and in-situ mobilization of formation fines. Most conventional studies on mechanical permeability damage allowed for qualitative statements regarding a bridging mechanism and a cake invasion zone critical size of the damaging particles, qualitative relationships between permeability vs time and suspended solids, and non-harmful size of mobile solids. Recent developments include x-ray analysis of formation fines [51 showing that mobile particles are not only clay minerals, but fine particles are present in all formations in sufficient quantities to cause formation damage. The mechanism of water sensitivity of sandstones containing clay has been quantitatively analyzed [71 revealing an existence of a critical salt concentration below which the permeability varies with salt concentration as well as the dynamic effects of the rate of salinity change or, permeability reduction. A fully quantitative description of permeability damage due to solids movement was attempted previously [61, by developing a phenomenological model of the rock where a system of plugging and non-slugging pathways is postulated. In this research, an intuitive guess is made on rock permeability as a function of the mobile solids concentration. A mathematical predictive model was developed previously, to describe water sensitivity in Berea sandstone. This model, based on an exponential model of clay release and capture, was used to find correlations between the release/capture coefficients as well as the effects of temperature and flowrate. A sophisticated statistical model of the interactions between particles size distribution and formation pore size distribution was recently presented. This model was used for simulation studies only without experimental verification. The approach applied in this work was to derive a mathematical theory concerning all types of mechanisms of permeability damage and then analyze experimental data on permeability damage. A similar analysis was attempted for foreign particle capture alone. P. 449^
Mechanistic modeling of an underbalanced drilling operation using carbon dioxide has been developed in this research. The use of carbon dioxide in an underbalanced drilling operation eliminates some of the operational difficulties inherent with gaseous drilling fluids, such as generating enough torque to run a downhole motor. The unique properties of CO2, both inside the drill pipe and the annulus are shown in terms of optimizing the drilling operation by achieving a low bottom hole pressure window. Typically, CO2 becomes supercritical inside the drill pipe at this high density; it thus can generate enough torque to run a downhole motor. As the fluid exits the drill bit it will evaporate to a gas, hence achieving the required low density for underbalanced drilling. The latest CO2 equation of state to calculate the required thermodynamic fluid properties is used. In addition, a heat transfer model that takes into account varying properties of both pressure and temperature has been developed. A marching algorithm procedure is developed to calculate the circulating fluid pressure and temperature, taking into account the varying parameters. Both single phase CO2 and a mixture of CO2 and water have been studied to show the effect of produced water on corrosion rates. The model also is capable of handling different drill pipe and annular geometries. The recent increase in oil prices during the recent years has led to re-investing in reservoirs that were previously not economical. In addition, most of the reservoirs had been partially depleted, and the current industry trend is to infill drill and/or sidetrack abandoned reservoirs, seeking new reserves. The existence of such reservoirs has led to the extensive use of underbalanced drilling (UBD), in an effort to minimize formation damage. UBD is the best available technology for low pressure and/or depleted reservoirs. A UBD operation is considered a success when it achieves the required underbalanced pressure. Alternate UBD techniques may not achieve the required wellbore pressures. For example two-phase drilling fluids have been used extensively, but these tend to generate high bottom hole pressure. In many situations, the high pressure generated is not the best solution for UBD. In cases such as deep wells with low bottomhole pressure, the use of these fluids will not achieve the required circulating downhole pressure. The use of gases as drilling fluids may achieve the required circulating pressure but generate other problems. One such problem, the circulating gas density in the drill pipe, is not able to rotate down-hole motors. Recently, super critical carbon dioxide (SC-CO2) has been used in a few applications of interest. The unique features of SC-CO2 make it an ideal candidate for a UBD drilling fluid, since at higher pressure and temperature it will become super critical, which gives it both gaseous and liquids properties. Recent authors have showed the benefits of using SC-CO2 in drilling operations[i],[ii]. Proper hydraulic modeling will optimize the drilling operation in terms of optimum pressure control and project design. In addition, developing a complete hydraulic model, which takes into account a detailed study of the thermodynamic properties of CO2, is needed, since the operation is very sensitive to these parameters.
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