Heterogeneous Carbonate Formations Research Articles

Potential of polymer’s viscosity and viscoelasticity for accessible oil recovery during low salinity polymer flooding in heterogeneous carbonates

Despite the usual improvement in sweep efficiency during polymer flooding, the polymer’s viscoelastic characteristics were reported to contribute to residual oil recovery in sandstone reservoirs at high flux conditions. In carbonate reservoirs, besides high-salinity, high-temperature, and non-water-wet nature, heterogeneity is a key variable that may impair the viscoelastic fluid flow in the porous media and recovery performance. However, no attempts were made to study the polymer’s viscoelastic influence on residual oil recovery in heterogeneous carbonate formations and the objective of this paper is to systematically examine the recovery performance of high molecular weight viscoelastic sulfonated polymer (AN-125-SH) in comparison to viscous xanthan gum polymer with the low salinity injection water of 5957 ppm total dissolved solids (TDS) in heterogeneous outcrop carbonate rocks at fluxes ranging from shear thinning to shear thickening using the combination of bulk shear rheometry, NMR, single-phase in-situ studies and two-phase core flooding experiments.Nuclear magnetic resonance (NMR) imaging ensured that the chosen cores are characterized with similar pore-size distribution. The steady-shear rheological experiments showed that 2500 ppm AN-125-SH polymer exhibits a lower viscosity at the lower shear rate and an early shear thickening (indicating higher non-linear viscoelasticity) than 2000 ppm xanthan gum. Then single-phase flow experiments are conducted using two polymer systems to determine the desired flux rates before the eventual multi-rate two-phase core flood experiments. Core flooding results revealed following an extensive secondary water flooding, at the shear thinning flux of 4 ft/day, 2000 ppm high viscous xanthan gum injection leads to an incremental recovery factor of 8.3 % with the generated pressure gradient of 20.48 psi/ft compared to 3.6 % recovery obtained using 2500 ppm AN 125-SH polymer with a pressure gradient of 16.2 psi/ft. However, at shear thickening fluxes of 20 ft/day and 30.5 ft/day, the higher elastic polymer enhanced the recovery by 3.3 % and 1.2 %, respectively. Conversely, the less elastic xanthan gum showed minimal to no incremental recovery at these fluxes.The novel findings of this work convey that the viscosity of xanthan gum provides a comparative advantage over the viscoelasticity of synthetic sulfonated polymers on oil recovery at relatively low fluxes in the studied heterogeneous formation at low salinity conditions.

The impact of chelating agent pH on the stability and viscosity of CO2 foam under harsh reservoir conditions

The injection of CO2 foam into the carbonate reservoir for enhanced oil recovery (EOR) has attracted special interest in the last decades; nevertheless, the understanding of the effect of liquid solution chemistry on foam stability at high temperatures and salinities is limited. Hence, this paper fully investigates the effect of chelating agents L-glutamic acid-N, N-diacetic acid (GLDA) pH, and hydrochloric acid (HCl) on the stability and viscosity of generated CO2 foam for heterogeneous carbonate formation under reservoir conditions. In this paper, Duomeen TTM and Armovis VES surfactants were utilized due to their capabilities to produce viscous CO2 foam under harsh conditions. The foamability, foam stability, and foam structure were studied at 100 °C and 1000 psi using a high-temperature and high-pressure (HPHT) foam analyzer. The measurement of CO2 foam viscosity was determined at 100 °C, 1000 psi, and 70 % foam quality using the HPHT foam rheometer. Rheology experiments and dynamic light scattering investigated the micelle’s size or aggregation behavior of surfactants. The obtained results showed that the Duomeen TTM generated unstable foam; however, foam stability and foamability improved with the decrease in GLDA pH. Armovis VES showed excellent CO2 foam performance, where the foam half-life time of Armovis VES systems was 240 min. The liquid drainage and bubble coarsening were delayed due to the formation of the viscoelastic liquid phase. The foamability of Armovis VES was improved as the GLDA pH decreased. Furthermore, the addition of HCl to Armovis VES solution presented the highest foamability. The outcomes of the HPHT foam analyzer and HPHT viscometer proved that as the pH of Armovis VES solution decreased, higher foamability was produced. The highest foam viscosity was obtained using the synergic effect of 0.5 wt% Duomeen TTM and 0.5 wt% Armovis VES (39 cp at 100/s). In comparison, 1 wt% Armovis VES presented the lowest foam viscosity (30 cp at 100/s). The outcomes of this research can provide insight into the effect of chemistry on CO2 foam and extend its application in oilfield development. This work broadens the design of novel CO2 foam formulation, leading to the improvement of sweep efficiency in CO2-EOR methods and enhance the gas trapping in carbon storage.

Estimating Residual Oil Saturation in Carbonate Rocks: A Combined Approach of Direct Simulation and Data-Driven Analysis

Summary Estimating residual oil saturation (Sor) post-waterflooding is critical for selecting enhanced oil recovery strategies, further field development, and production prediction. We established a data-driven workflow for evaluating Sor in carbonate samples using microcomputed tomography (μ-CT) images. The two-phase lattice Boltzmann method (LBM) facilitated the flooding simulation on 7,192 μ-CT samples. Petrophysical parameters (features) obtained from pore network modeling (PNM) and feature extraction from μ-CT images were utilized to develop tree-based regression models for predicting Sor. Petrophysical features include porosity, absolute permeability, initial water saturation (Swi), pore size distribution (PSD), throat size distributions (TSD), and surface roughness (Ra) distribution. Our method excludes vugs and macro/nanoporosity, which complicates multiscale simulations—a recognized challenge in modeling carbonate rocks. When subdividing the image into numerous subvolumes, certain subvolumes may contain vugs exceeding the dimensions of the subvolume itself. Hence, these vugs were omitted given the entirety of the image constitutes a vug. Conversely, vugs with dimensions smaller than those of the subvolume were not excluded. Despite scale limitations, our subsampling, supported by substantial data volume, ensures our microscale porosity predictions are statistically reliable, setting a foundation for future studies on vugs and nanoporosity’s impact on simulations. The results show that features obtained from dry-sample images can be used for data-driven Sor prediction. We tested three regression models: gradient boosting (GB), random forest (RF), and extreme gradient boosting (XGBoost). Among these, the optimized GB-based model demonstrated the highest predictive capacity for Sor prediction [R2 = 0.87, mean absolute error (MAE) = 1.87%, mean squared error (MSE) = 0.12%]. Increasing the data set size is anticipated to enhance the models’ ability to capture a broader spectrum of rock properties, thereby improving their prediction accuracy. The proposed predictive modeling framework for estimating Sor in heterogeneous carbonate formations aims to supplement conventional coreflooding tests or serve as a tool for rapid Sor evaluation of the reservoir.

3D unrestricted fluid-driven fracture propagation based on coupled hydromechanical interface elements

Exploring unconventional reservoirs has raised several engineering challenges to improve oil/gas recovery. In the Brazilian pre-salt fields, highly heterogeneous carbonate formations compose these reservoirs containing fractures in multiple scales. The extracted carbon dioxide is reinjected in the reservoirs to increase oil recovery and reduce greenhouse gas emissions. For that reason, it is essential to develop robust numerical methods capable of simulating fracture propagation in naturally fractured porous media. This paper presents a new 3D mesh fragmentation technique to simulate non-planar hydraulic fracture propagation, considering its interaction with natural fractures. This method is based on discrete fracture representation through hydromechanical interface elements with a cohesive zone model to simulate fluid-driven fracture propagation. The proposed 3D mesh fragmentation algorithm inserts triple noded-interface elements into the continuum finite element faces, ensuring continuity of the fluid pressure field. The approach is successfully validated against experimental fracturing tests and analytical models. Also, by applying the proposed fragmentation technique, we study the influence of pre-existing oriented fractures on hydraulic fracture propagation in different scenarios. The results provide insight into the complex hydraulic fracturing process in naturally fractured formations. Finally, this approach is an attractive alternative to simulate multi-staged fracturing into 3D multilayered fractured rock formations.

Effect of heterogeneity on engineered water injection in carbonates using five-spot sector model: A numerical study

One of the promising and emerging enhanced oil recovery techniques in both sandstones and carbonates is engineered water injection (EWI). However, few studies discussed the field-scale applications of this technique in heterogeneous carbonate formations. This paper is an extension of our previous work of the EWI technology at core-scale. This research numerically investigates heterogeneity effect on EWI technique in carbonates at field-scale using five-spot models. Three synthetic five-spot sector models were considered including homogeneous, heterogeneous with permeability channeling, and heterogeneous with gravity underride. The results showed that EWI improves both volumetric and displacement sweep efficiencies compared to conventional formation water injection (FWI) for all models investigated. Also, tracer method is recommended for better estimation of volumetric sweep efficiency as opposed to fractional flow method. Moreover, secondary EWI outperforms other techniques including secondary FW and tertiary EWI. In addition, the observed delay in tertiary EWI can be reduced by increasing well injection pressure and sulfate concentration in the engineered water. An optimum sulfate concentration of 25,000 ppm is recommended for achieving the highest oil recovery by EWI. This study gives more insight into understanding the performance of the EWI technique at field-scale. Recommendations for boosting the performance of this technique have been discussed, which assure more certainty and lower risk.

Infill drilling and well placement assessment for a multi-layered heterogeneous reservoir

This paper presents an assessment of infill drilling opportunities in a complex multi-layered heterogeneous carbonate formation located in Abu Dhabi offshore. The subject field was developed last century and is currently undergoing further development with line drive horizontal wells. The field is being redeveloped for improved oil recovery at higher production rates with long horizontal wells. An infill assessment process is defined using sector model reservoir simulations for the specific reservoir. Reservoir simulations are performed on pattern sector models to establish the optimum grid for infill evaluation. Also, the models with an appropriate grid size are used to optimize infill placement (vertical and lateral well placement) and infill drilling timing for a couple of geologically similar areas. In the second step, the sector model results are applied to test the full-field infill development plan. The relatively homogeneous geological area shows very uniform displacement with 1-km spaced wells and gives no considerable benefit of incremental recovery through infill drilling. However, in a comparatively heterogeneous geological area, considerable incremental oil recovery is quantified. In brief, this paper presents a detailed infill drilling and well placement assessment process workflow for the re-development of a multi-layered heterogeneous reservoir.

Assessing Subwavelength VHF Radar Scattering Losses in Hyperarid Carbonate Formations

Subsurface scattering losses associated with very high frequency (VHF) subwavelength heterogeneities are crucial for assessing the total radar signal attenuation in fractured and heterogeneous environments such as carbonate formations, which represent one of the most predominant aquifer types in hyperarid areas. Yet, the resulting signal losses are largely unquantified due to the difficulties in constraining their sources, amplitude, and frequency dependence on the VHF spectrum, hence, compromising the ability to perform large-scale characterization of shallow aquifers using radar probing in these areas. To address this deficiency, we present an experimental model quantifying volumetric scattering losses in heterogeneous carbonate formations accounting for wavelength-sized structural elements and subwavelength-sized heterogeneities ranging from 1 mm to 2 cm for the VHF radar signals. In particular, we use an analytical model that estimates the overall scattering effects produced by the interaction of an electromagnetic plane wave with randomly distributed vugs scatterers. We then compare our analysis with field radar measurements collected in the karst limestone aquiferous formation in the Qatar Peninsula at 80 MHz (10-dB bandwidth (BW): 30-150 MHz). Our results estimate that the total losses in karstic environments range between ~0.6 and 1.4 dB/m, of which 20%-65% is due to volume scattering. Furthermore, we find that despite being usually underestimated, subwavelength volumetric scattering accounts for a considerable portion (~40%) of the overall radar attenuation: between ~0.045 and 0.35 dB/m. The results of our analysis can constrain the degree of karstification associated with vertical artesian movements in fossil aquifer systems in hyperarid environments.

A novel acidizing technology in carbonate reservoir: In-Situ formation of CO2 foamed acid and its self-diversion

The serious fingering and nonuniform injectivity profile of acid liquid result from the features of heterogeneity in most carbonate reservoir, leading to a poor effect on the acidizing process. In the present contribution, for the first time, we report a novel diversion acidizing strategy that uses acid-rock reaction between the acidizing fluid itself and carbonate core to produce CO2 at supercritical state. Under the action of a mixture of foaming agent and stabilizer contained in this working fluid, a CO2 foamed acid fluid is in-situ formed in the acidizing layer, which would play a diverting role in carbonate matrix acidizing operations. Experiments on in-situ formation of CO2 microfoams (emulsions) were performed utilizing a visible acid-rock reaction simulation device and a self-made high pressure and temperature foam generator. A series of divided-flow experiments were undertaken by the core displacement setup.Results based on these experiments indicate that with 0.5% SDBS as a foaming agent and 0.15% CMC as a stabilizing agent, the supercritical CO2 microfoams (emulsions) could be created in-situ in the process of acidizing through the carbonate reservoirs. The foamed acid has the accumulating and plugging effects, with divided-flow selectivity not only in the parallel cores of oil saturation and water saturation, but also in the parallel cores of different permeability. This foamed acid fluid could provide better diversion acidizing operations for heterogeneous carbonate formation. Finally, the mechanism of this novel diversion acidizing technology was uncovered in detail. It is suggested that the whole working process is actually an interface effect in the dynamic system of gas/liquid/solid multiphase fluid. Such findings are potentially important for a better understanding on the mechanisms of in-situ formation of CO2 foamed acid and its self-diversion. Looking out to the future, our report attempts to provide a new and efficient technology for the improvement of acid stimulation in the carbonate reservoirs.

Lean HC gas injection pilots analysis and IPR back calculation to examine the impact of asphaltene deposition on flow performance

Gas injection is one of the most economical and effective approach to improve oil recovery. However, outcome of such approach is contingent to reservoir heterogeneities impacting gas override and fingering. Furthermore, injected fluid composition and its compatibility with the reservoir fluid potentially impact flow assurance issues such as asphaltene precipitation into the wellbore and surface facilities.The objective of this paper is to examine the lesson learnt from a couple of field scale 5 spot patterned lean hydrocarbon gas injection pilots which were deployed in a heterogeneous carbonate formation of a giant field located offshore Abu Dhabi under secondary and tertiary drive mechanisms. Said pilots provides a valuable insight on production performance, pressure support, gravity override, fluid composition and evidence of asphaltene deposition that resulted in heavy production loss prior to the solvent treatment.This paper presents the overall pilot performance including pattern recovery, fluid front movement, potential role of heterogeneity in gas breakthrough timings and the operational events to witness asphaltene deposition affecting the flow performance. The deposited asphaltene cake thickness was measured mechanically during routine tubing clearance check operation that was helpful in estimating production loss due to altered production tubing flow opening. Also an integrated approach is applied to confirm the AOP laboratory measurements with the actual deposits of asphaltene that were found in to the production tubing.In order to confirm the effect of asphaltene deposition on inflow from near wellbore formation to the wellbore, a straightforward yet innovative nodal analysis approach was applied to study well performance using the calibrated and history matched well model. It was noticed that not only the outflow was altered because of asphaltene deposition into wellbore but also the inflow (productivity index) was seriously impacted potentially due to asphaltene deposition in near wellbore formation.

Wettability, hysteresis and fracture–matrix interaction during CO2 EOR and storage in fractured carbonate reservoirs

Relative permeabilities show significant dependence on the saturation path during CO2 enhanced oil recovery (EOR) and storage. This dependence (or hysteresis) is particularly important for water-alternating-gas (WAG) injection, a successful CO2 EOR and storage method for clastic and carbonate reservoirs. WAG injection is characterized by an alternating sequence of drainage and imbibition cycles. Hysteresis is hence common and results in residual trapping of the CO2 phase, which impacts the volume of CO2 stored and the incremental oil recovery. The competition between hysteresis and geological heterogeneity during CO2 EOR and storage, particularly in carbonate reservoirs, is not yet fully understood.In this study, we use a high-resolution simulation model of a Jurassic Carbonate ramp, which is an analogue for the highly prolific reservoirs of the Arab D formation in Qatar, to investigate the impact of hysteresis during CO2 EOR and storage in heterogeneous carbonate formations. We then compare the impact of residual trapping (due to hysteresis) on recovery to the impact of heterogeneity in wettability and reservoir structure. End-member wettability scenarios and multiple wettability distribution approaches are tested, while, effective fracture permeabilities are computed using discrete fracture networks (DFN), ranging from sparsely distributed background fractures to fracture networks where intensity varies with proximity to faults.The results enable us to analyze the efficiency of oil recovery and CO2 sequestration in carbonate reservoirs by comparing the impact of physical displacement processes (e.g., imbibition, drainage, residual trapping) and heterogeneous rock properties (e.g., wettability, faults, fractures, layering) that are typical in carbonate reservoirs. We show that although the fracture network properties have the greatest impact on the fluid flow, the effect of wettability and hysteresis is nontrivial. Our results emphasize the need for wettability to be accurately measured and appropriately distributed in a reservoir simulation model. Similarly, our results indicate that hysteresis effects in cyclic displacement processes must be accounted for in detail to ensure that simulation models give accurate predictions.

Technology Focus: Coiled Tubing Applications (June 2012)

Technology Focus The coiled-tubing (CT) industry has experience unparalleled growth in the past year, driven directly by the massive expansion in multistage-fracturing operations in North America. Various sources estimate that the US consumed 50% of the world’s CT in the past 12 months, helping to contribute to a massive 80% growth in product coming off the CT production lines. The growth in the United States was fueled primarily by three applications: milling out composite plugs, milling out fracture-sleeve ball seats, and toe shoots (the name given to the first perforating operation before plug-and-perforate operations). Because toe shoots take place without any pressure on the well, the amount of CT life consumed by fatigue during the operation is small. Plug or seat milling, on the other hand, takes place after fracturing operations are complete and with the wellbore fully pressure charged by the formation; therefore, the CT life consumed by fatigue is high. Superimposed over the wellbore pressures are the pressures arising from circulating fluids through the CT and the milling assemblies. In some of the higher-pressure shale plays, CT strings last only for a few jobs. Accordingly, any technology that reduces the superimposed pressure could lead to longer CT life and potentially to lower completion costs. Two of the papers selected for this month’s issue involve new technologies that might be helpful to operators in this respect. However, of possible greater concern to CT companies in North America is the fact that CT use is now clearly dominated by well-completion operations, or, to put it another way, by rig count. Until recently, the CT intervention business was primarily remedial in nature and, thus, was partially cushioned from the extreme cycles experienced by drillers. However, in North America, a change has already arrived and, with gas prices at historic lows, CT service companies, CT pipe manufacturers, and CT equipment manufacturers probably need to prepare for the same swings that the rest of the well-construction industry is used to. Recommended additional reading at OnePetro: www.onepetro.org. SPE 152351 Comprehensive Approach to Production Stimulation of Massive Cold Heterogeneous Carbonate Formation Using Coiled Tubing by Vladimir Dnistryansky, Schlumberger, et al. SPE 154221 Production Logging on Coiled Tubing in a Marcellus Shale Horizontal Completion by A. McCluskey, Shell Exploration and Production SPE 154060 Best Practices for Composite Plug Milling by Steven Craig, Baker Hughes, et al. SPE 154423 Use of Coiled Tubing Deployed Expandable Technology in Sidetrack Drilling Operations by A. Caccialupi, Mohawk Energy, et al.

Use of X-Ray CT to Measure Pore Volume Compressibility of Shaybah Carbonates

SummaryThe Lower Cretaceous Shu'aiba formation (Shaybah field) in southeastern Saudi Arabia is a heterogeneous carbonate formation with various facies because of diagenetic alteration of the original rock fabric. Preliminary laboratory rock-mechanics studies indicated that the Shu'aiba carbonates are mechanically weak, with the majority of the rocks tested yielding very low strength values (less than 3,000 psi) when compared to samples from other carbonate reservoirs (Salamy and Finkbeiner 2002). On the basis of laboratory-derived rock-strength data from triaxial tests, the formation appears to behave in a plastic manner that strengthens the wellbore. To understand the stress behavior of the Shaybah rocks better, a set of pore volume compressibility tests was conducted in which the changes taking place within the samples were observed and quantified using an X-ray computerized-tomography (CT) scanner. A new technique involving dual-energy CT scanning was used to obtain the pore volume compressibility values, which were compared against the conventional triaxial-cell-generated data and published results by Harari et al. (1995) on cores taken from the same reservoir. Although the magnitude of the pore volume compressibility was the same between different setups, visual data showed some interesting behavior of the Shaybah cores including movement of grains in an irreversible manner even for a relatively low imposed effective stress of 2,000 psi. Some of the advantages of the new CT-based analysis technique include the generation of multiple pore volume compressibility curves from the same plug (a band of data, each at a different slice location), the "visualization" of the changes, the possibility of using either hydrostatic or triaxial cells to make the test more case-specific, and the possibility of measuring permeability under different stress conditions before, during, and after the test.

Enhanced Reservoir Description of Heterogeneous Carbonate Reservoirs

Abstract This study is conducted to test and evaluate the use of current methods of reservoir characterization, namely the permeabilityporosity correlation, the J-function, and the Reservoir Quality Index (RQI) concepts, for reservoir description of heterogeneous carbonate formations. These approaches were compared with a new technique developed in this paper for improved reservoir description of carbonate reservoirs. This technique is called the Characterization Number (CN) technique and it is based upon considering fluid, rock, rock-fluid properties, and flow mechanics of oil reservoirs. To compare these reservoir characterization techniques, measurements of porosity, absolute permeability, oil and water relative permeability, and irreducible water saturation for 83 actual core samples extracted from eight different wells for a new oil reservoir in the U.A.E. were obtained. These experimental data are used first to develop a permeability-porosity correlation. Then, the J-function and the RQI concepts along with the newly developed CN approach are applied and evaluated for the reservoir description of the UAE carbonate reservoir under investigation. The results show that the Reservoir Quality Index concept is capable of identifying the flow units while the J-function concept is quite poor. Also, a more refined identification of flow units is obtained by using the newly-developed Characterization Number. This improved description for the Characterization Number approach may be attributed to the consideration of rock/fluid properties of flowing fluid(s) and flow dynamic conditions of its containing formation. Introduction and Review Reservoir characterization techniques are quite valuable as they provide a better description of the storage and flow properties of a petroleum reservoir and thus provide the basis for developing its simulation model. Also, carbonate reservoirs, in particular, present a tougher challenge to engineers and geologists to characterize because of their tendency to be tight and heterogeneous. Permeability and porosity of the reservoir rock have always been considered as two of the most important parameters for formation evaluation, reservoir description, and characterization. Beyond evaluating permeability and porosity, one can also use combinations of two or more rock properties to gain insight into the character of flow through porous media. The J-function and the Reservoir Quality Index (RQI) are two of the concepts that the oil industry has used to characterize the reservoir media. They incorporate parameters such as porosity and permeability into a single quantity that describes/characterizes the formation. The application of the J-function and/or the Reservoir Quality Index (RQI) concepts, however, may or may not determine whether a formation can be considered to have a single flow unit or multiple ones(1–4). It is well recognized that an improved and effective reservoir description is a prerequisite for efficient development of oil reservoirs. The following is a brief review of the most common techniques available for reservoir description. Permeability-Porosity Correlation Technique The effective porosity(1) of a rock is defined as the ratio of its interconnected pore volume to its bulk volume. The permeability of the reservoir rock is defined as the ability of that rock to allow fluids to flow through its interconnected pores.

Solids production prediction in a highly heterogeneous carbonate formation

One of the main physical characteristics defining oil recovery during water injection is the phase relative permeability. Salinity of the formation water can significantly differ from the injected water and consequently affect the relative permeabilities.In the current work, we investigate the effect of fines migration on water and oil relative permeability. First, flow tests with piece-wise constant decreasing water salinity without oil are performed in order to identify the movable fine particles. Then the oil is displaced by the formation water from the sister-cores for a recovery assessment excluding the ion exchange processes. After re-saturation, oil is displaced by water with alternate salinity. The conditions of large-scale approximation, where the capillary pressure and dispersion effects are negligible, have been achieved in the tests. This allows the derivation of the modified Welge–JBN method to determine relative permeability from the performed tests. The obtained relative permeability curves for water exhibits an abnormal decline at high saturations, which is attributed to fines mobilization and straining yielding the water permeability decline.

Thermal Effects on Single-Well Chemical-Tracer Tests for Measuring Residual Oil Saturation

Summary The single-well chemical-tracer (SWCT) test for measuring residual oil saturation, Sσr, often involves injecting cool fluid containing a reactive tracer into a warm formation. The Sor estimation with this method depends on the separation between reactant and product tracers. Because the reaction rate is temperature-dependent, accounting for the thermal effects may be necessary to obtain reliable results. Two simulator models are normally used to interpret SWCT tests. The ideal model is used for relatively homogeneous sandstone formations. The pore-diffusion model is used for heterogeneous carbonate formations. Both models have now been solved with appropriate heat-balance equations. These nonisothermal models have been used to reinterpret several previously reported field tests. For the worst case, the estimated Sor value from the nonisothermal model is 5% PV higher than that from the isothermal model. Inequality conditions have been developed that divide the parameter space of SWCT tests into two regions, depending on the location of the temperature front relative to the tracer bank during the reaction period. In the "safe" region, the estimated Sor values from isothermal and nonisothermal models are essentially equal. The inequality conditions have been extended to include the effects of over-and underburden layers and intervening shales in layered systems.