Thermal Effects on Single-Well Chemical-Tracer Tests for Measuring Residual Oil Saturation
- Y.J. Park (U. of Houston) | H.A. Deans (U. of Houston) | T.E. Tezduyar (U. of Minnesota)
- Document ID
- Society of Petroleum Engineers
- SPE Formation Evaluation
- Publication Date
- September 1991
- Document Type
- Journal Paper
- 401 - 408
- 1991. Society of Petroleum Engineers
- 5.2.1 Phase Behavior and PVT Measurements, 5.3.4 Reduction of Residual Oil Saturation, 4.1.5 Processing Equipment, 5.6.5 Tracers, 4.1.2 Separation and Treating, 4.3.4 Scale, 5.6.1 Open hole/cased hole log analysis, 5.4.1 Waterflooding
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Summary. The single-well chemical-tracer (SWCT) test for measuring residualoil saturation, Sor, often involves injecting cool fluid containing a reactivetracer into a warm formation. The Sor estimation with this method depends onthe separation between reactant and product tracers. Because the reaction rateis temperature-dependent, accounting for the thermal effects may be necessaryto obtain reliable results. Two simulator models are normally used to interpretSWCT tests. The ideal model is used for relatively homogeneous sandstoneformations. The pore-diffusion model is used for heterogeneous carbonateformations. Both pore-diffusion model is used for heterogeneous carbonateformations. Both models have now been solved with appropriate heat-balanceequations. These nonisothermal models have been used to reinterpret severalpreviously reported field tests. For the worst case, the estimated Sor valuefrom the nonisothermal model is 5% PV higher than that from the isothermalmodel. Inequality conditions have been developed that divide the parameterspace of SWCT tests into two regions, depending on the location of thetemperature front relative to the tracer bank during the reaction period. Inthe "safe" region, the estimated Sor values from isothermal andnonisothermal models are essentially equal. The inequality conditions have beenextended to include the effects of over-and underburden layers and interveningshales in layered systems.
The SWCT method was developed to measure Sor after water-flooding. Thistechnology was first reported by Tomich et al. and patented by Deans. Sincethen, more than 200 field tests have been performed. The first 59 of thesetests were reported by Deans and Majoros. In their analysis of the observedresults, the tracer were assumed to be in local equilibrium in the pore space,and the system was taken to be isothermal. This is referred to as the"ideal" model. In many SWCT tests, the tracer profiles in the producedfluid showed such nonidealities as multiple peaks and early arrival of poorlydefined peaks, accompanied by extended tailing and poor poorly defined peaks,accompanied by extended tailing and poor material balance. The multipeakfeature can be reproduced by a multilayer version of the ideal model, whichincludes irreversible flow effects and crossflow. The second set of distortionswas first attributed to fluid drift. Several early tests obtained in carbonateformations were matched with the fluid-drift model. It has since beenrecognized that the type of heterogeneity found in the pore structure ofcarbonate formations produces a characteristic distortion in the concentrationprofiles of single-well tracer tests. The pore-diffusion model was developed byDeans and Carlisle to interpret these tests. In this model, the pore space isdivided into two fractions, flowing and stagnant (or dead-end). In the computerprogram, each node in the flowing fraction of pore space is connected with adead-end pore element in which the tracer transport is controlled by diffusion.This heterogeneous model was shown to reproduce all the features observed incarbonate tests. It was also an isothermal model.
All SWCT tests for Sor begin with the injection of a brine bank containing areactive (primary) chemical tracer into a watered-out oil reservoir. Theprimary tracer bank is then pushed away from the well by injectingreactant-free brine solution until the desired radius of investigation isreached by the reactant tracer. Row is then stopped for the shut-in period,during which a part of the primary tracer reacts to form a product (secondary)tracer in the primary tracer reacts to form a product (secondary) tracer in thepore space. pore space. The well is then produced, and the tracer profiles aremeasured in the produced brine. Because the remaining reactant tracer and theproduct tracer have different partition coefficients between the flowing brineand the immobile residual oil phase, they are chromatographically separated ontheir way back to the well. The amount of separation is quantitatively relatedto the saturation of the residual oil phase. The tracer profiles are matched bycomputer simulation to obtain Sor. The simulator solves the equations governingtracer behavior during the three time periods of the test. In particular, therate of reaction to form the product is assumed to be first order in theconcentration of primary tracer. In previous simulators, no attempt was made toinclude temperature dependence of the reaction rate or of the tracer partitioncoefficients because the pore system was assumed to partition coefficientsbecause the pore system was assumed to be isothermal during the test. In thiswork, we consider the effect of the injected brine's temperature on the entiresystem.
The simulation assumes incompressible, radial flow of brine in theaccessible fraction of the pore space. The transport equations for temperatureand tracer concentrations in the predetermined velocity field are written in ageneral form:
where is a vector of unknown variables. The domain must include impermeableover- and underburden layers (and interlayered shales if present) to accountfor the heat gain by conduction. Fluid flow and heat conduction in a wellboreare also considered, as shown in Fig. 1. The center plane of the permeablelayer is assumed to provide Retry conditions for the unknown variables.Therefore the computational domain is taken to be a 2D space, with radial, r,and axial, z, axes consisting of the upper half of the permeable layer and theoverburden impermeable layer. The initial conditions for all the variables areoriginal reservoir conditions. Fig. 2 shows the boundary conditions. Eq. 1 with=0 applies to both layers in the ideal model. In the pore-diffusion model,every node in the permeable layer is connected with a dead-end pore element,which is a 1D space along the y axis. Nonzero elements of appear in thematerial-balance equations in the flowing domain to account for the diffusionflux of tracers between the two domains. Eq. 1 can also be applied to describelocal transient tracer behavior in the stagnant pore spaces. Fig. 3 shows thefinite-element meshes used for the nonisothermal ideal and pore-diffusionmodels. The detail of the independent variable domains, the associateddependent variables, and the appropriate coefficients in Eq.1 are given belowfor each model.
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