A new closed-form analytical solution to the radial transport of tracers in porous media under the influence of linear drift is presented. Specifically, the transport of tracers under convection–diffusion-dominated flow is considered. First, the radial transport equation was cast in the form of the Whittaker equation by defining a set of transformation relations. Then, linear drift was incorporated by considering a coordinate-independent scalar velocity field within the porous medium. A special case of low-intensity tracer injection where molecular diffusion controls tracer propagation but convection with linear velocity drift plays a significant role was presented and solved in Laplace space. Furthermore, a weak-form numerical solution of the nonlinear problem was obtained and used to analyse tracer concentration behaviour in a porous medium, where drift effects predominate and influence the flow pattern. Application in enhanced oil recovery (EOR) processes where linear drift may interfere with the flow path was also evaluated within the solution to obtain concentration profiles for different injection models. The results of the analyses indicated that the effect of linear drift on the tracer concentration profile is dependent on system heterogeneity and progressively becomes more pronounced at later times. This new solution demonstrates the necessity to consider the impact of drift on the transport of tracers, as arrival times may be significantly influenced by drift intensity.
This paper presents some new close-form analytical solutions to equations describing radial transport of reactive tracers in porous media under conditions of tracer adsorption, nonuniform convection, and variable dispersion coefficient. Three different types of variable dispersion coefficients were considered and exact solutions presented in Laplace space. The special case where shear mixing or convection dominates dispersion, which is important for tracer test studies, was programmed on a computer to obtain concentration profiles for the continuous-and slug-injection test models. Ai[[ (3 ]';' 1/(rD)1 C)(k,+s) J x Ai[[ /3 ]\(rD=l)I················ (56) C)(k,+s) J Eqs. 55 and 56 were programmed with Stehfest's Laplace numerical routine. Figs. 1 and 2 represent the results from these equations.
S.M. El-Hadidi, Abu Dhabi National Oil Company (ADNOC); G.K. Falade, C. Dabbouk, and F. Al-Ansari, Zakum Development Company (ZADCO); Abu Dhabi U.A.E. SPE Members Abstract The main focus of this paper is the applications of polymer treatment in controlling injectivity profiles and the improvement of the conformance of the near-wellbore injection profiles. Reservoir high permeability zones causing distortions of water injection profiles at the wellbore, and the possible existence of layer barriers were identified using conventional investigation tools such as Open Hole Logs, Production Logging Tools, Formation and Micro Scanners. A polymer screening procedure was put in place so that appropriate polymer formulations for use as agents for reducing fluid mobility in the high permeability zones at the wellbore can be identified. The use of these polymer formulations facilitated the improvement of near-wellbore conformance of injectivity profiles. The field performance of the polymer treatment program was ascertained by using a monitoring program which combined the application of the Production Logging Tools with well test analyses. Introduction The presence of high permeability streaks and fractures is a common occurrence in stratified carbonate reservoirs. If these reservoirs are subjected to patterned water-flooding operations, it is not uncommon for the highly permeable zones to accept most, if not all, of the water injected. This tends to distort the injectivity profile at the wellbore, and raises the possibility of an eventual poor reservoir coverage and sweep efficiency. Therefore, a successful water-flood project necessarily demands a clear understanding of reservoir characteristics with a view to identifying the incidence of high permeability streaks, channels, and layer barriers, so that adequate remedial actions that can reduce their adverse effects on water-flood performance can be put in place. One of such remedial actions which have gained prominence in the recent past, is the use of Polymer and Non-polymer agent for injection/Production wellbore profile modification. In this paper, we present the screening, monitoring and evaluation procedures for a successful application of a cross-linked polymer formulation on water injection wells in order to improve the wellbore conformance of injectivity profiles. Background History The reservoir under consideration is a mature reservoir under five spot patterned water injection. The injection pattern size has been under continual modification by implementing a carefully planned program of infill drilling and conversion of some original producers to injectors. This progressive review of pattern size has reduced the distance of producers to injectors from an original value of 2.8 km to a current value of about 1.4 km. Simulation studies indicated that water production from this reservoir is not expected to start before 2010. However, it has been observed that some of the producing wells have started experiencing premature water breakthrough. Analysis of produced water confirmed that water being produced by these wells comes largely from injected sea water. Field wide investigation as to the cause(s) of premature water breakthrough in some wells was initiated. These investigations involved a complete reevaluation of all available open- and cased-hole logs of all producers and the neighboring injectors within the pattern in which premature water breakthrough has been observed. In addition to the newly acquired data, special consideration was given to PLT logs, particularly newly acquired PLT, Dynamic Testing, Pulse Neutron Logs and Core data from in-fill drillings. This data acquisition program was designed to correlate injection profiles of the various water injection wells in the reservoir. P. 69^
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