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1. A. R. Kovscek, T. W. Patzek, and C. J. Radke. Mechanistic Foam Flow Simulation in Heterogeneous and Multidimensional Porous Media. Society of Petroleum Engineers Journal, 2(4):511--526, December 1997.
   [pdf]
   Keywords: Foam, EOR, Mobility Control.

   Abstract

   Gases typically display large flow mobilities in porous media relative to oil or water, thereby impairing their effectiveness as displacing fluids. Foamed gas, though, is a promising agent for achieving mobility control in porous media. Because reservoir-scale simulation is a vital component of the engineering and economic evaluation of any enhanced oil recovery (EOR) or aquifer remediation project, efficient application of foam as a displacement fluid requires a predictive numerical model. Unfortunately, no such model is currently available for foam injection in the field where flow is multidimensional and the porous medium is heterogeneous. We have incorporated a conservation equation for the number density of foam bubbles into a fully implicit, three-dimensional, compositional, and thermal reservoir simulator and created a fully functional, mechanistic foam simulator. Because foam mobility is a strong function of bubble texture, the bubble population balance is necessary to make accurate predictions of foamflow behavior. Foam generation and destruction are included through rate expressions that depend on saturations and surfactant concentration. Gas relative permeability and effective viscosity are modified according to the texture of foam bubbles. In this paper, we explore foam flow in radial, layered, and heterogeneous porous media. Simulations in radial geometries indicate that foam can be formed deep within rock formations, but that the rate of propagation is slow. Foam proves effective in controlling gas mobility in layered porous media. Significant flow diversion and sweep improvement by foam are predicted, regardless of whether the layers are communicating or isolated.

   
   
   
   [Bibtex-key = Kovscek_1997]
   [BibTex Entry]
2. A. R. Kovscek. Mechanistic Modeling of Solution Gas Drive in Viscous Oils. In , Porlarmar, Margarita Island, Venezuela, March 2001.
   [pdf]
   Keywords: Solution Gas Drive, Heavy Oil.

   Abstract

   Solution gas drive in reservoirs containing heavy and viscous oil is not well understood. This paper develops a mechanistic population balance model for describing the process of bubble nucleation and growth. The model is applied to both light and viscous oils. The primary modeling concept is a continuum bubble population balance. Appropriate rate equations are derived for two theories of bubble nucleation described in the literature—instantaneous nucleation (IN) and progressive nucleation (PN). The results of simulations for the IN and PN models are compared to experimental data reported elsewhere for light oil and to new data for viscous oils. Model parameters are all physically based. Within the IN model, the number density of bubbles must be specified while the PN model requires the cavity size distribution of the porous medium as input. The PN model matches the experiments somewhat better, but is more demanding computationally. Interestingly, the population balance description of either model does not require a critical supersaturation to be exceeded before the onset of bubble nucleation and growth. Supersaturation is the difference between the equilibrium and dynamic liquid pressure of a system. Liberation of gas from solution at the thermodynamic bubble point and the bubble growth equations presented here well describe the kinetics of the gas phase and pressure response of the systems examined.

   
   
   
   [Bibtex-key = SPE69717]
   [BibTex Entry]
3. D. Zhou, L. Jia, J. Kamath, and A. R. Kovscek. An Investigation of Counter-Current Imbibition Processes in Diatomite.. In , Bakersfield,CA, USA, March 2001.
   [pdf]
   Keywords: Imbibition, Diatomites, Analytical Work.

   Abstract

   Oil recovery from low permeability reservoirs is strategically important because of the large resources locked in such formations. Imbibition is fundamental to oil recovery from such reservoirs under most secondary and improved recovery processes of practical interest. It is also characteristic of porous medium wettability. The rate and the extent of imbibition depend critically on the viscosity of the wetting and nonwetting phases. In this study, we present our recent work on imaging imbibition in low permeability porous media (diatomite) with X-ray computed tomography. The viscosity ratio between nonwetting and wetting fluids is varied over several orders of magnitude yielding different levels of imbibition performance. We also perform a mathematical analysis of counter-current imbibition processes and develop a modified scaling group incorporating the mobility ratio. This modified group is physically based and appears to improve scaling accuracy of countercurrent imbibition significantly.

   
   
   
   [Bibtex-key = SPE68837]
   [BibTex Entry]
4. O. G. Apaydin and A. R. Kovscek. Transient Foam Flow in Homogeneous Porous Media: Surfactant Concentration and Capillary End Effects.. In , Tulsa, OK, USA, April 2000.
   [pdf]
   Keywords: Foam, Mobility Control, Interfacial Tension.

   Abstract

   Foaming injected gas is a useful and promising technique for achieving mobility control in porous media. Typically, such foams are aqueous. In the presence of foam, gas and liquid flow behavior is determined by bubble size or foam texture. The thin-liquid films that separate foam into bubbles must be relatively stable for a foam to be finely textured and thereby be effective as a displacing or blocking agent. Film stability is a strong function of surfactant concentration and type. This work studies foam flow behavior at a variety of surfactant concentrations using experiments and a numerical model. Thus, the foam behavior examined spans from strong to weak. Specifically, a suite of foam displacements over a range of surfactant concentrations were monitored in a roughly 7 mm2, one-dimensional sandpack using X-ray computed tomography (CT). Sequential pressure taps were employed to measure flow resistance. Nitrogen was the gas and an alpha olefin sulfonate (AOS 1416) in brine was the foamer. Surfactant concentrations studied varied from 0.005 to 1 wt%. Because foam mobility depends strongly upon its texture, a bubble population balance model is both useful and necessary to describe the experimental results thoroughly and self consistently. Excellent agreement is found between experiment and theory.

   
   
   
   Annotation: 3-5 April 2000
   
   [Bibtex-key = SPE59286]
   [BibTex Entry]
5. E. R. Rangel-German and A. R. Kovscek. Matrix-Fracture Interactions in Single Matrix Blocks. In , Stanford University, CA, USA, January 2000.
   [pdf]
   Keywords: Fractures, Imbibition, Experimental Work.

   Abstract

   Capillary imbibition is an important mechanism during water reinjection in fractured porous media. Using an X-ray computerized tomography (CT) scanner, and a novel, CT-compatible core holder, we performed a number of experiments to study air expulsion from rock samples by capillary imbibition of water in a three-dimensional geometry. Different injection rates and fracture apertures were utilized. The existence of two flow periods during imbibition by the matrix was observed. The early-time period can be understood as an infinite acting media and the square root of time model of imbibition with the appropriate characteristic time and length can be used. Although the late-time period has not been analyzed fully, a set of both characteristic times and lengths is proposed. Two different fracture flow regimes were also identified. The first one, named “filling-fracture” shows a variable length plane source due to relatively slow water flow through fractures; the second flow regime, named “instantly-filled fracture”, where the time to fill the fracture is much less than the imbibition time, shows a constant plane source imbibition. The behavior of the second regime is very similar to that observed in both counter current and cocurrent one-dimensional imbibition experiments reported previously in the literature.

   
   
   
   [Bibtex-key = ERGerman_2000]
   [BibTex Entry]
6. Y. Wang and A. R. Kovscek. A Streamline Approach for History-Matching Production Data. In , Tulsa, OK, USA, April 2000.
   [pdf]
   Keywords: Streamlines, History-Matching, Inverse Problems.

   Abstract

   This study proposes and develops a streamline approach for inferring field-scale effective permeability distributions based on dynamic production data including producer water-cut curve, well pressures, and rates. The approach simplifies the history-matching process significantly. The basic idea is to relate the fractional-flow curve at a producer to the water breakthrough of individual streamlines. By adjusting the effective permeability along streamlines, the breakthrough time of each streamline is found that reproduces the reference producer fractional-flow curve. Then the permeability modification along each streamline is mapped onto cells of the simulation grid. Modifying effective permeability at the streamline level greatly reduces the size of the inverse problem compared to modifications at the gridblock level. The approach outlined here is relatively direct and greatly reduces the computational work by eliminating the repeated inversion of a system of equations. It works well for reservoirs where heterogeneity determines flow patterns. Example cases illustrate computational efficiency, generality, and robustness of the proposed procedure. Advantages and limitations of this work, and the scope of future study, are also discussed.

   
   
   
   [Bibtex-key = SPE59370]
   [BibTex Entry]
7. S. Akin, L. M. Castanier, and W. E. Brigham. Effect of Temperature on Heavy Oil/Water Relative Permeabilities. In , Bakersfield, CA, USA, March 1999.
   [pdf]
   Keywords: Relative Permeability, JBN Model, Experimental Work.

   Abstract

   In the first part of this study, the accuracy of the JBN technique for the determination of heavy oil/water relative permeabilities, and the effect of temperature on relative permeabilities is examined by giving numerical as well as experimental examples. Using the JBN technique leads to a false temperature dependence of relative permeability curves. In the second part, we present unsteady state relative permeability experiments with initial brine saturation at differing temperatures conducted using South Belridge sand and heavy oil. A new three step experimental technique and an analysis procedure were developed to test the effect of temperature on relative permeabilities. In this technique, an ambient temperature unsteady-state relative permeability run is conducted in the first stage, and following that the temperature is increased twice (i.e. 122°F and 150°F). Two phase saturation profiles along the sand pack are measured using a CT scanner. A commercial black oil simulator, coupled with a global optimization code is then used to estimate two phase relative permeabilities. Experimental saturation profiles, differential pressure and recovery data collected from both the ambient and higher temperature data are used in the numerical model. It has been observed that a single set of relative permeability curves can represent both the ambient and high temperature parts of the experiment. This suggests that relative permeability is not a function of temperature at least for the system tested.

   
   
   
   [Bibtex-key = SPE54120]
   [BibTex Entry]
8. S. Akin and A. R. Kovscek. Imbibition Studies of Low-Permeability Porous Media. In , Anchorage, AK, USA, May 1999.
   [pdf]
   Keywords: Imbibition, Diatomites, Experimental Work.

   Abstract

   A systematic investigation of capillary pressure, relative permeability, and fluid flow characteristics within diatomite (a high porosity, low permeability, siliceous rock) is reported. Using an X-ray computerized tomography (CT) scanner, and a specially constructed imbibition cell, we study spontaneous cocurrent water imbibition into diatomite samples at various initial water saturations. Air-water and oil-water systems are used. Despite a marked difference in rock properties between diatomite and sandstone, including permeability and porosity, we find similar trends in saturation profiles and dimensionless weight gain versus time functions. Diatomite is roughly 100 times less permeable than sandstone, yet it imbibes water at rates rivaling sandstone. Importantly, the spontaneous imbibition data when combined with CT-scan images provides a means to determine dynamic relative permeability and capillary pressure functions.

   
   
   
   [Bibtex-key = SPE54590]
   [BibTex Entry]
9. K. T. Elliot and A. R. Kovscek. A Numerical Analysis of the Single-Well Steam Assisted Gravity Drainage Process (SW-SAGD). In , Enghien-les-Bains, France, September 1999.
   [pdf]
   Keywords: SAGD, Thermal Recovery, Analytical Work.

   Abstract

   Steam assisted gravity drainage (SAGD) is an effective method to produce heavy oil and bitumen. In a typical SAGD approach, steam is injected into a horizontal well located directly above a horizontal producer. A steam chamber grows around the injection well and helps displace heated oil toward the production well. Single-well (SW) SAGD attempts to create a similar process using only one horizontal well. This may include steam injection from the toe of the horizontal well with production at the heel. To improve early-time response of SW-SAGD, it is necessary to heat the near-wellbore area to reduce oil viscosity and allow gravity drainage to take place. Ideally heating should occur with minimal circulation or bypassing of steam. Since project economics are sensitive to early production response, we have investigated early-time processes to improve reservoir heating. A numerical simulation study was performed to gauge combinations of cyclic steam injection and steam circulation prior to SAGD in an effort to better understand and improve early-time performance. Results from this study, include cumulative recoveries, temperature distributions, and production rates. Variances are displayed within the methods. It is found that cyclic steaming of the reservoir prior to SAGD offers the most favorable option for heating the near-wellbore area to create conditions that improve initial SAGD response. Additionally, a sensitivity analysis was performed with regard to reservoir height, oil viscosity, horizontal to vertical permeability anisotropy, and dead versus live oil. More favorable reservoir conditions such as low viscosity, thick oil zones, and solution gas, improved reservoir response. Under unfavorable conditions, response was limited and could prove to be uneconomical in actual field cases.

   
   
   
   [Bibtex-key = S-10]
   [BibTex Entry]
10. K. T. Elliot and A. R. Kovscek. Simulation of Early-Time Response of Single-Well Steam-Assisted Gravity Drainage. In , Anchorage, AK, USA, May 1999.
    [pdf]
    Keywords: SAGD, Thermal Recovery.

    Abstract

    Steam assisted gravity drainage (SAGD) is an effective method of producing heavy oil and bitumen. In a typical SAGD approach, steam is injected into a horizontal well located directly above a horizontal producer. A steam chamber grows around the injection well and helps displace heated oil toward the production well. Single-well (SW) SAGD attempts to create a similar process using only one horizontal well. This may include steam injection from the toe of the horizontal well with production at the heel. Obvious advantages of SW-SAGD include cost savings and utility in relatively thin reservoirs. However, the process is technically challenging. To improve early-time response of SW-SAGD, it is necessary to heat the near-wellbore area to reduce oil viscosity and allow gravity drainage to take place. Since project economics are sensitive to early production response, we are interested in optimizing the start-up procedure. An investigation of early-time processes to improve reservoir heating will be discussed. We performed a numerical simulation study of combinations of cyclic steam injection and steam circulation prior to SAGD in an effort to better understand and improve early-time response. Results from this study, including cumulative recoveries, temperature distributions, and production rates display variances within the methods. It is found that cycling steaming of the reservoir prior to SAGD offers the most favorable option for heating the near-wellbore area and creating conditions that will improve initial SAGD response.

    
    
    
    [Bibtex-key = SPE54618]
    [BibTex Entry]
11. E. R. Rangel-German, S. Akin, and L. M. Castanier. Multiphase Flow Properties of Fractured Porous Media. In , Anchorage, AK, USA, May 1999.
    [pdf]
    Keywords: Fractures, Experimental Work, Imbibition.

    Abstract

    The fluid transfer parameters between matrix and fracture are not well known. Consequently, simulation of fractured reservoirs uses, in general, very crude and unproved hypothesis such as zero capillary pressure in the fracture and/or relative permeability functions that are linear with saturation. In order to improve the understanding of flow in fractured media, an experimental study was conducted and numerical simulation used to interpret experimental results. A laboratory flow apparatus was built to obtain data on water-air imbibition and oil-water drainage displacements in fractured sandstone systems. During the experiments, porosity and saturation were measured along the core utilizing a Computerized Tomography (CT) scanner. Saturation images were reconstructed in 3-D to observe how matrix-fracture interaction occurred. Differences in fluid saturations and relative permeabilities caused by changes of fracture width have also been analyzed. In the case of water-air imbibition, fracture systems with narrower fracture apertures showed more stable fronts and slower water breakthrough than the wide fracture systems. However, the final water saturation was higher in wide fracture systems, thus showing that capillary pressure in the narrow fracture has more effect on fluid distribution in the matrix. During oil-water drainage, oil saturations were higher in the blocks near the thin fracture, again showing the effect of fracture capillary pressure. Oil fingering was observed in the wide fracture. Fine-grid simulations of the experiments using a commercial reservoir simulator were performed. Relative permeability and capillary pressure curves were obtained by history matching the experiments. The results showed that the assumption of fracture relative permeability equal to phase saturation is incorrect. We found that both capillary and viscous forces affect the process. The matrix capillary pressure obtained by matching an experiment showed lower values than reported in the literature.

    
    
    
    [Bibtex-key = SPE54591]
    [BibTex Entry]
12. H. J. Bertin, O. G. Apaydin, L. M. Castanier, and A. R. Kovscek. Foam Flow in Heterogeneous Porous Media: Effect of Crossflow. In , Tulsa, OK, USA, April 1998.
    [pdf]
    Keywords: Foam, Crossflow, Experimental Work.

    Abstract

    Previous studies of foam generation and transport were conducted, mainly, in one-dimensional and homogeneous porous media. However, the field situation is primarily heterogeneous and multidimensional. To begin to bridge this gap, we have studied foam formation and propagation in an annularly heterogeneous porous medium. The experimental system was constructed by centering a 5.0 cm diameter cylindrical Fontainebleau sandstone core inside an 8.9 cm acrylic tube and packing clean Ottawa sand in the annular region. The sandstone permeability is roughly 0.1 d while the unconsolidated sand permeability is about 7 d. Experiments with and without crossflow between the two porous media were conducted. To prevent crossflow, the cylindrical face of the sandstone was encased in a heat-shrink Teflon sleeve and the annular region packed with sand as before. Nitrogen is the gas phase and an alpha olefin sulfonate (AOS 1416) in brine is the foamer. The aqueous phase saturation distribution is garnered using X-ray computed tomography. Results from this study are striking. When the heterogeneous layers are in capillary communication and cross flow is allowed, foam fronts move at identical rates in each porous medium as quantified by the CT-scan images. Desaturation by foam is efficient and typically complete in about 1 PV of gas injection. When cross flow is prohibited, foam partially plugs the high permeability sand and diverts flow into the low permeability sandstone. The foam front moves through the low permeability region faster than in the high permeability region.

    
    
    
    [Bibtex-key = SPE39678]
    [BibTex Entry]
13. E. R. German, S. Akin, and L. M. Castanier. Experimental and Theoretical Investigation of Multiphase Flow in Fractured Media. In , San Diego, California, USA, September 1998.
    [pdf]
    Keywords: Fractures, Imbibition, Experimental Work, Analytical Model, Relative Permeability.

    Abstract

    A laboratory flow apparatus was built to obtain data on water-air displacements in horizontal single-fractured block systems. For this purpose, two configurations have been used: a two matrixblock system with a 1mm spacer between the blocks, and a two matrix-block system with no spacer. During the experiments, porosity and saturation calculations along the cores have been made utilizing an X-ray Computerized Tomography (CT) scanner. Saturation images were reconstructed in 3-D to observe better matrix-fracture interactions. Differences in fluid saturations and relative permeabilities caused by changes in fracture width have also been analyzed. The fracture system without a spacer showed a more stable front and faster breakthrough than the other. However, the final water saturation was higher in the wide fracture system, thus showing that capillary pressure in the narrow fracture has more effect on recovery. Simulations of the experiments were made using a commercial reservoir simulator (Eclipse). Fracture relative permeability and capillary pressure curves were obtained by history matching the experiments. Sensitivity analysis of parameters such as fracture relative permeability, capillary pressure in the fracture, and fracture width were also conducted. The results showed that the assumption of fracture relative permeability equal to phase saturation is incorrect. Moreover, larger flow resistance in the fractures was observed by comparing the experiments with numerical simulation work . We found that the processes are both capillary and viscous dominated.

    
    
    
    [Bibtex-key = ERGerman]
    [BibTex Entry]
14. A. R. Kovscek. Reservoir Simulation of Foam Displacement Processes. In , Beijing, China, October 1998.
    [pdf]
    Keywords: Heavy Oil, Steam, Thermal Recovery.

    Abstract

    Steam injection has had a profound impact on the production of heavy crude oil. Steam, however, is inviscid compared to a viscous oil and is not the ideal displacement agent. Field studies and laboratory tests have shown that foaming the steam phase through the aid of a suitable surfactant in aqueous solution can achieve mobility control of injected gases and mitigate the effects of gravity override. Thus, production is improved. Unfortunately, simulation models and simulation tools that accurately gauge the effects of foam on gas mobility in porous media are not readily available. Recent advances in modeling gas mobility in the presence of foam are reviewed. These include the socalled bubble population balance method, scaling arguments to obtain representative foam texture and hence gas mobility, and semi-empirical alteration of gas mobility. The bubble population balance is then illustrated by means of a few sample calculations.

    
    
    
    [Bibtex-key = unitar]
    [BibTex Entry]
15. J.M. Schembre, S. Akin, L. M. Castanier, and A. R. Kovscek. Spontaneous Water Imbibtion in Diatomite. In , Bakersfield, CA, USA, May 1998.
    [pdf]
    Keywords: Experimental Work, Diatomites, Capillary Pressure.

    Abstract

    A systematic experimental investigation of capillary pressure characteristics and fluid flow in diatomite has been accomplished. Using an X-ray CT scanner and a specially constructed imbibition cell, we study spontaneous water imbibition processes in diatomite and for reference Berea sandstone and chalk. The mass of water imbibed as a function of time is also measured. Imbibition is restricted to cocurrent flow. Despite a marked difference in rock properties including permeability and porosity, we find similar trends in saturation profiles and weight gain versus time functions. Imbibition in diatomite is relatively rapid when initial water saturation is low due to large capillary forces.

    
    
    
    [Bibtex-key = SPE46211]
    [BibTex Entry]
16. Y. Wang, A. R. Kovscek, and W. E. Brigham. Effect of Mobility Ratio on Areal Sweep Efficiency and Pattern Flood Behavior. In , Carmel, CA, USA, October 1998.
    [pdf]
    Keywords: Mobility Control, Sweep Efficiency, Simulation.

    Abstract

    It is well known, for unit mobility ratio, that the areal sweep efficiency of a staggered-linedrive pattern is always better than a five-spot pattern. However, this observation does not hold for very favorable mobility ratios. We present simulation results and, with the help of streamline and saturation distributions, explain the differences between unit and favorable mobility ratios. Simulations compare well with experiments conducted elsewhere. Accurate definition of breakthrough time is also discussed for multiphase, streamline, simulation results. The exact definition of breakthrough is difficult due to physical dispersion in experiments and numerical dispersion in simulations.

    
    
    
    [Bibtex-key = Wang_1998]
    [BibTex Entry]
17. R.G. Hughes, W.E. Brigham, and L. M. Castanier. CT Measurements of Two-Phase Flow in Fractured Porous Media. In , January 1996.
    [pdf]
    Keywords: Experimental Work, Imbibition.

    Abstract

    This paper describes the design, construction, and preliminary results of an experiment that stud- ies imbibition displacement in two fracture blocks. Three core configurations were constructed. The configurations are a compact core, a two-block system with a 1 mm spacer between the blocks, and a two-block system with no spacer. The blocks are sealed in epoxy so that saturation measurements can be made throughout the displacement experiments using a Computed Tomography (CT) scanner. Preliminary results are presented from a water/air experiment. These results suggest that it is incorrect to assume negligible capillary continuity between matrix blocks as is often done.

    
    
    
    [Bibtex-key = Hugues_1996]
    [BibTex Entry]
18. S. Qadeer, W. E. Brigham, and L. M. Castanier. Techniques to Handle Limitations in Dynamic Relative Permeability Measurements.. Technical report, Stanford University, CA, USA, May 2002.
    [pdf]
    Keywords: Relative Permeability, JBN Model, Experimental Work, Analytical Model.

    Abstract

    The objective of this work was to understand the limitations of the conventional methods of calculating relative permeabilities from data obtained from displacement experiments. The Johnson, Bossler and Neumann (JBN) method is the industry standard for measuring relative permeabilities from field cores. It is known that the relative permeabilities calculated by the JBN method from low rate displacements are often in error due to the capillary forces. Sometimes history matching methods are used to calculate the relative permeabilities. Generally 1-D numerical models, that assume uniform initial saturation distribution, are used for this purpose. The pressure drop and recovery data generated from 2-D, r-z numerical simulations were used to study the errors introduced in the calculated relative permeability curves when using the JBN method. The results indicate that, because of the saturation gradients in the core, the relative permeabilities obtained from the JBN method show large errors at low water saturations. In this study, using the CT scanner to measure in situ saturations, it was observed that even at relatively high rates there are saturation gradients in the core after the drainage displacements. These saturation gradients cause additional pressure drop through the core. It is therefore recommended that control experiments should be conducted using some in situ saturation measurement technique to determine the extent of the end effects and the saturation gradients in the cores. The Berea sandstone cores, used in this study even after baking to deactivate the clays, were found to be sensitive to the brine used in the experiments. It is therefore necessary to conduct the laboratory experiments using fluids which are compatible with the rock.

    
    
    
    [Bibtex-key = TR128]
    [BibTex Entry]
19. I. Diabira, L. M. Castanier, and A. R. Kovscek. Porosity and Permeability Evolution Accompanying Hot Fluid Injection Into Diatomite.. Technical report, Stanford University, CA, USA, March 2001.
    [pdf]
    Keywords: Permeability, Diatomites, Porosity, Experimental work.

    Abstract

    An experimental study of silica dissolution was performed to probe the evolution of permeability and porosity in siliceous diatomite during hot fluid injection such as water or steam flooding. Two competing mechanisms were identified. Silica solubility in water at elevated temperature causes rock dissolution thereby increasing permeability; however, the rock is mechanically weak leading to compression of the solid matrix during injection. Permeability and porosity can decrease at the onset of fluid flow. A laboratory flow apparatus was designed and built to examine these processes in diatomite core samples. At the core level, we measured the pressure drop as a function of time for fixed injection rates to determine permeability variation and utilized an X-ray Computerized Tomography (CT) scanner to measure in-situ porosity. At the pore level, a scanning electron microscope (SEM) was used to observe changes in pore morphology. We found that porosity decreased initially due to compaction caused by the imposed pressure drop across the core. Later, porosity increased as silica dissolved. Dissolution of the rock matrix appeared to be relatively uniform; wormholes were not observed even after tens of pore volumes of fluid injection.

    
    
    
    [Bibtex-key = TR123]
    [BibTex Entry]
20. K. T. Elliot and A. R. Kovscek. A Numerical Analysis of the Single-Well Steam Assisted Gravity Drainage Process.. Technical report, Stanford University, CA, USA, June 2001.
    [pdf]
    Keywords: SAGD, Steam, Heavy Oil, Thermal Recovery.

    Abstract

    Steam assisted gravity drainage (SAGD) is an effective method to produce heavy oil and bitumen which are important energy resources. In a typical SAGD approach, steam is injected into a horizontal well located directly above a horizontal producer helping to displace heated oil. Single-well (SW) SAGD attempts to create a similar process using only one horizontal well. To improve early-time response of SW-SAGD, it is necessary to heat the near-wellbore area to reduce oil viscosity and allow gravity drainage to begin. Ideally heating should occur with minimal circulation or bypassing of steam. We have investigated early-time processes to improve reservoir heating. A numerical simulation study was performed to gauge combinations of cyclic steam injection and steam circulation prior to SAGD in an effort to better understand and improve early-time performance. Results from this study, include cumulative recoveries, temperature distributions, and production rates. It is found that cyclic steaming of the reservoir offers the most favorable option for heating the near-wellbore area to create conditions that improve initial SAGD response. More favorable reservoir conditions such as low viscosity, thick oil zones, and solution gas, improved reservoir response. Under unfavorable conditions, response was limited.

    
    
    
    [Bibtex-key = TR124]
    [BibTex Entry]
21. D. S. George and A. R. Kovscek. Visualization of Solution Gas Drive in Viscous Oil.. Technical report, Stanford University, CA, USA, July 2001.
    [pdf]
    Keywords: Solution Gas Drive, Heavy Oil.

    Abstract

    Several experimental studies of solution gas drive are available in the literature, but almost all of the studies have used light oil. Solution gas drive behavior, especially in heavy oil reservoirs, is poorly understood. Hence, experiments were performed in which pore-scale solution gas drive phenomena were viewed in water/carbon dioxide and viscous oil/carbon dioxide systems. A new pressure vessel was designed and constructed to house silicon-wafer micromodels that previously operated at low (< 3 atm) pressure. The new apparatus is used for the visual studies. Several interesting phenomena were viewed. The repeated nucleation of gas bubbles was observed at a gas-wet site occupied by dirt. Interestingly, the dissolution of a gas bubble into the liquid phase was previously recorded at the same nucleation site. Gas bubbles in both systems grew to span one or more pore bodies before mobilization. Liquid viscosity affected the ease with which gas bubbles coalesced. More viscous solutions result in slower rates of coalescence. The transport of solid particles on gas-liquid interfaces was also observed.

    
    
    
    [Bibtex-key = TR126]
    [BibTex Entry]
22. A. R. Kovscek, L. M. Castanier, and W. E. Brigham. Heavy and Thermal Oil Recovery Mechanisms Annual Report for 2000-2001.. Technical report, Stanford University, CA, USA, 2001.
    [pdf]
    Keywords: Multiphase Flow, Reservoir Definition, In-Situ Combustion, EOR, Heavy Oil.

    Abstract

    Supri-A yearly research report.

    
    
    
    [Bibtex-key = TR127]
    [BibTex Entry]
23. E. R. Rangel-German and A. R. Kovscek. Experimental and Analytical Study of Multidimensional Imbibition in Fractured Porous Media.. Technical report, Stanford University, CA, USA, October 2001.
    [pdf]
    Keywords: Imbibition, Fractures, Analytical Model.

    Abstract

    Capillary imbibition is an important mechanism during water injection and aquifer influx in fractured porous media. Better understanding of matrix-fracture interaction and imbibition in general is needed to model effectively these processes. Using an X-ray computerized tomography (CT) scanner, and a novel, CT-compatible core holder, we performed a series of experiments to study air and oil expulsion from rock samples by capillary imbibition of water in a three-dimensional geometry. The air-water system is useful in that a relatively large number of experiments can be conducted to delineate physical processes. Different injection rates and fracture apertures were utilized. Two different fracture flow regimes were identified. The "filling-fracture" regime shows a plane source that grows in length due to relatively slow water flow through fractures. In the second, "instantly-filled fracture" regime, the time to fill the fracture is much less than the imbibition time. Here, imbibition performance scales as the square root of time. In the former regime, the mass of water imbibed scales linearly with time. A new analytical model is proposed for filling fractures incorporating implicit matrix/fracture coupling. Good agreement is found between experiments and calculation. This analytic coupling was obtained by means of solving the saturation diffusion equation with appropriate initial and boundary conditions. The solution provides the location of the wetting phase front in the fracture and the saturation distribution in the matrix. The solution is analogous to that obtained by Marx and Langenheim (1959) for the areal extent of an equivalent heated zone in thermal recovery methods. Analogous terms among flow and heat transfer in porous media were found and are also presented.

    
    
    
    [Bibtex-key = TR129]
    [BibTex Entry]
24. Y. Wang and A. R. Kovscek. A Streamline Approach for History Matching Production Data.. Technical report, Stanford University, CA, USA, June 2001.
    [pdf]
    Keywords: History-Matching, Streamlines, Inverse Problems.

    Abstract

    This study proposes and develops a streamline approach for inferring field-scale effective permeability distributions based on dynamic production data including producer water-cut curve, well pressures, and rates. The streamline-based inverse approach simplifies the history-matching process significantly. The basic idea is to relate the water-cut curve at a producer to the water breakthrough of individual streamlines. By adjusting the effective permeability along streamlines, the breakthrough time of each streamline is found that reproduces the reference producer fractionalflow curve. Then the permeability modification along each streamline is mapped onto cells of the simulation grid. Modifying effective permeability at the streamline level greatly reduces the size of the inverse problem compared to modifications at the grid-block level. The approach outlined here is relatively direct and rapid. Limitations include that the forward flow problem must be solvable with streamlines, streamline locations do not evolve radically during displacement, no new wells are included, and relatively noise-free production data is available. It works well for reservoirs where heterogeneity determines flow patterns. Example cases illustrate computational efficiency, generality, and robustness of the proposed procedure. Advantages and limitations of this work, and the scope of future study, are also discussed.

    
    
    
    [Bibtex-key = TR125]
    [BibTex Entry]
25. O. G. Apaydin and A. R. Kovscek. Surfactant Concentration and End Effects on Foam Flow in Porous Media. Technical report, Stanford University, CA, USA, October 2000.
    [pdf]
    Keywords: Foam, Mobility Control, Experimental Work.

    Abstract

    Foaming injected gas is a useful and promising technique for achieving mobility control in porous media. Typically, such foams are aqueous. In the presence of foam, gas and liquid flow behavior is determined by bubble size or foam texture. The thin-liquid films that separate foam into bubbles must be relatively stable for a foam to be finely textured and thereby be effective as a displacing or blocking agent. Film stability is a strong function of surfactant concentration and type. This work studies foam flow behavior at a variety of surfactant concentrations using experiments and a numerical model. Thus, the foam behavior examined spans from strong to weak. Specifically, a suite of foam displacements over a range of surfactant concentrations in a roughly 7 µm2, one-dimensional sandpack are monitored using X-ray computed tomography (CT). Sequential pressure taps are employed to measure flow resistance. Nitrogen is the gas and an alpha olefin sulfonate (AOS 1416) in brine is the foamer. Surfactant concentrations studied vary from 0.005 to 1 wt%. Because foam mobility depends strongly upon its texture, a bubble population balance model is both useful and necessary to describe the experimental results thoroughly and self consistently. Excellent agreement is found between experiment and theory.

    
    
    
    [Bibtex-key = TR120]
    [BibTex Entry]
26. W. E. Brigham. Doublets and Other Allied Well Problems.. Technical report, Stanford University, CA, USA, December 2000.
    [pdf]
    Keywords: Sweep Efficiency, Well Models.
    [Bibtex-key = TR122]
    [BibTex Entry]
27. D. Zhou, L. Jia, J. Kamath, and A. R. Kovscek. Scaling of Counter-Current Imbibition Processes in Low Permeability Porous Media.. Technical report, Stanford University, CA, USA, December 2000.
    [pdf]
    Keywords: Imbibition, Diatomites, Tomography, Experimental Work.

    Abstract

    Oil recovery from low permeability reservoirs is strategically important because of the large resources locked in such formations. Imbibition is fundamental to oil recovery from such reservoirs under most secondary and improved recovery processes of practical interest. It is also characteristic of porous medium wettability. The rate and the extent of imbibition depend critically on the viscosity of the wetting and nonwetting phases. In this study, we present our recent work on imaging imbibition in low permeability porous media (diatomite) with X-ray computed tomography. The viscosity ratio between nonwetting and wetting fluids is varied over several orders of magnitude yielding different levels of imbibition performance. We also perform a mathematical analysis of counter-current imbibition processes and develop a modified scaling group incorporating the mobility ratio. This modified group is physically based and appears to improve scaling accuracy of countercurrent imbibition significantly.

    
    
    
    [Bibtex-key = TR121b]
    [BibTex Entry]
28. W. E. Brigham, A. R. Kovscek, and L. M. Castanier. Research on Oil Recovery Mechanisms in Heavy Oil Reservoirs, Final Report 1996 to 1999.. Technical report, Stanford University, CA, USA, 1999.
    [pdf]
    Keywords: Reservoir Definition, In-Situ Combustion, Heavy Oil, Steam, EOR, Thermal Recovery.

    Abstract

    Supri-A yearly research report.

    
    
    
    [Bibtex-key = TR121]
    [BibTex Entry]
29. W. E. Brigham, A. R. Kovscek, and L. M. Castanier. SUPRI Heavy Oil Research Program Twenty Second Annual Report.. Technical report, Stanford University, CA, USA, 1999.
    [pdf]
    Keywords: Reservoir Definition, In-Situ Combustion, Heavy Oil, Steam, EOR, Formation Evaluation.

    Abstract

    Supri-A yearly research report.

    
    
    
    [Bibtex-key = TR117]
    [BibTex Entry]
30. U. K. Diwan and A. R. Kovscek. An Analytical Model for Simulating Heavy-Oil Recovery by Cyclic Steam Injection Using Horizontal Wells. Technical report, Stanford University, CA, USA, July 1999.
    [pdf]
    Keywords: Thermal Recovery, Steam, Analytical Work, Horizontal Wells.

    Abstract

    In this investigation, existing analytical models for cyclic steam injection and oil recovery are reviewed and a new model is proposed that is applicable to horizontal wells. A new flow equation is developed for oil production during cyclic steaming of horizontal wells. The model accounts for the gravitydrainage of oil along the steam-oil interface and through the steam zone. Oil viscosity, effective permeability, geometry of the heated zone, porosity, mobile oil saturation, and thermal diffusivity of the reservoir influence the flow rate of oil in the model. The change in reservoir temperature with time is also modeled, and it results in the expected decline in oil production rate during the production cycle as the reservoir cools. Wherever appropriate, correlations are incorporated to minimize data requirements. A limited comparison to numerical simulation results agrees well, indicating that essential physics are successfully captured. Cyclic steaming appears to be a systematic method for heating a cold reservoir provided that a relatively uniform distribution of steam is obtained along the horizontal well during injection. A sensitivity analysis shows that the process is robust over the range of expected physical parameters.

    
    
    
    [Bibtex-key = TR118]
    [BibTex Entry]
31. K. E. Elliot and A. R. Kovscek. Computer Simulation of Single-Well Steam Assisted Gravity Drainage (SW-SAGD). Technical report, Stanford University, CA, USA, July 1999.
    [pdf]
    Keywords: SAGD, Thermal Recovery, Heavy Oil.

    Abstract

    Steam assisted gravity drainage (SAGD) is an effective method of producing heavy oil and bitumen. In a typical SAGD approach, steam is injected into a horizontal well located directly above a horizontal producer. A steam chamber grows around the injection well and helps displace heated oil toward the production well. Single-well (SW) SAGD attempts to create a similar process using only one horizontal well. This may include steam injection from the toe of the horizontal well with production at the heel. Obvious advantages of SW-SAGD include cost savings and utility in relatively thin reservoirs. However, the process is technically challenging. To improve early-time response of SW-SAGD, it is necessary to heat the nearwellbore area to reduce oil viscosity and allow gravity drainage to take place. Ideally heating should occur with minimal circulation or bypassing of steam. Since project economics are sensitive to early production response, we are interested in optimizing the start-up procedure. An investigation of early-time processes to improve reservoir heating will be discussed. We performed a numerical simulation study of combinations of cyclic steam injection and steam circulation prior to SAGD in an effort to better understand and improve early-time response. Results from this study, including cumulative recoveries, temperature distributions, and production rates, display variances within the methods. It is found that cyclic steaming of the reservoir prior to SAGD offers the most favorable option for heating the near-wellbore area and creating conditions that will improve initial SAGD response.

    
    
    
    [Bibtex-key = TR119]
    [BibTex Entry]
32. E. R. Rangel-German, L. M. Castanier, and S. Akin.. An Experimental and Theoretical Investigation of Multi- Phase Flow in Fractured Porous Media. Technical report, Stanford University, CA, USA, June 1999.
    [pdf]
    Keywords: Experimental Work, Fractures, Tomography.

    Abstract

    The fluid transfer parameters between rock matrix and fracture are not well known. Consequently, simulation of fractured reservoirs uses, in general, very crude and unproven hypotheses such as zero capillary pressure in the fracture and/or relative permeability linear with saturation. In order to improve the understanding of flow in fractured media, an experimental study was conducted and numerical simulations of the experiments were made. A laboratory flow apparatus was built to obtain data on water-air imbibition and oil-water drainage displacements in horizontal single-fractured block systems. For this purpose, two configurations have been used: a two-block system with a 1mm spacer between the blocks, and a two-block system with no spacer. During the experiments, porosity and saturation measurements along the cores have been made utilizing an X-ray Computerized Tomography (CT) scanner. Saturation images were reconstructed in 3-D to observe matrix-fracture interactions. Differences in fluid saturations and relative permeabilities caused by changes in fracture width have also been analyzed. In the case of water-air imbibition, the thin fracture system showed a more stable front and faster breakthrough than the wide fracture system. However, the final water saturation was higher in the blocks near the wide fracture, thus showing that capillary pressure in the narrow fracture has more effect. During oil-water drainage, oil saturations were higher in the blocks near the thin fracture, again showing the effect of fracture capillary pressure. Oil fingering was observed in the wide fracture. Simulations of the experiments have been performed using a commercial reservoir simulator. Relative permeability and capillary pressure curves were obtained by history matching the experiments. Sensitivity analysis of parameters such as fracture relative permeability, capillary pressure in the fracture, and fracture width were also conducted. The results showed that the assumption of fracture relative permeability equal to phase saturation is incorrect. Moreover, higher resistance in the fractures was observed by comparing the experiments with numerical simulation work. We found that the processes are dominated by both capillary and viscous forces.

    
    
    
    [Bibtex-key = TR116]
    [BibTex Entry]
33. O. G. Apaydin, H. J. Bertin, L. M. Castanier, and A. R. Kovscek. An Experimental Investigation of Foam Flow in Homogeneous and Heterogeneous Porous Media. Technical report, Stanford University, CA, USA, June 1998.
    [pdf]
    Keywords: Foam, Experimental Work, Mobility Control.

    Abstract

    Foam is used to reduce the high mobility of gas-drive fluids and improve the contact between oil and these injected fluids. We require a better understanding of the effect of surfactant concentration on foam flow in porous media. Besides this, the literature on foam flow and transport in heterogeneous systems is sparse although the field situation is primarily heterogeneous and multidimensional. In this study, foam flow experiments were conducted first in homogenous sand packs to investigate the effect of surfactant concentration on foam flow and then a heterogeneous experimental setup was prepared to observe heterogeneity and multidimensional flow effects on foam propagation. The homogeneous core experiments were conducted in a cylindrical aluminum core holder that was packed with a uniform Ottawa sand. Sand permeability is about 7.0 Darcy. The experiments were interpreted in terms of evolution of in-situ water saturation as a function of time by the usage of CT scanner, cumulative water recovery, and pressure drop across the core. At very low surfactant concentration, no significant benefit was observed. But when stable foam generation started sweep efficiency (water recovery), breakthrough time, and pressure drop increased as surfactant concentration increased. At the next stage, a Fontainebleau sandstone was centered inside an acrylic tube and the annular region was packed with clean Ottawa sand to construct a heterogeneous porous medium. The permeability contrast between sandstone and sand was 67 to 1. Experiments with and without crossflow between the two porous media were conducted. To prevent crossflow, a heat-shrink Teflon jacket was placed on the cylindrical face of sandstone. In-situ water saturation distribution was garnered using the CT scanner. The results from this study are striking. When the heterogeneous layers were in capillary communication and cross flow was allowed, foam fronts move at identical rates in each porous medium as quantified by the CT-scan images. Desaturation by foam was efficient and typically complete in about 1 PV of gas injection. When cross flow was prohibited, foam partially plugs the high permeability sand and diverted flow into the low permeability sandstone. The foam front moved through the low permeability region faster than in the high permeability region.

    
    
    
    [Bibtex-key = TR112]
    [BibTex Entry]
34. S. K. Bhat and A. R. Kovscek. Modeling Permeability Alteration in Diatomite Reservoirs During Steam Drive. Technical report, Stanford University, CA, USA, July 1998.
    [pdf]
    Keywords: Diatomites, Thermal Recovery, Steam, Network Modeling.

    Abstract

    There is an estimated 10 billion barrels of original oil in place (OOIP) in diatomaceous reservoirs in Kern County, California. These reservoirs have low permeability ranging from 0.1 to 10 mD. Injection pressure controlled steam drive has been found to be an efficient way to recover oil from these reservoirs. However, steam drive in these reservoirs has its own complications. The rock matrix is primarily silica (SiO2). It is a known fact that silica is soluble in hot water and its solubility varies with temperature and pH. Due to this fact, the rock matrix in diatomite may dissolve into the aqueous phase as the temperature at a location increases or it may precipitate from the aqueous phase onto the rock grains as the temperature decreases. Thus, during steam drive silica redistribution will occur in the reservoir along with oil recovery. This silica redistribution causes the permeability and porosity of the reservoir to change. Understanding and quantifying these silica redistribution effects on the reservoir permeability might prove to be a key aspect of designing a steam drive project in these formations. In this study the first aspect that we examine is the relative importance of the factors that govern the transfer of silica between the rock matrix and the aqueous phase. On the basis of analytical solutions for simple one-dimensional systems and the conditions that typically exist in diatomite reservoirs, we conclude that the silica concentration in the aqueous phase is the equilibrium silica solubility corresponding to the temperature of that location. This is likely true for the whole length of the reservoir, except near injectors and producers. We call this attainment of “local chemical equilibrium”. This implies for a given location, that when we know the temperature variation, we can predict the amount of silica transfer between rock grains and the aqueous phase surrounding it. From a qualitative argument we know that the extent of permeability alteration will depend on the pore-level characteristics of this rock apart from the extent of silica redistribution. We tried to infer the pore-level shapes and distributions of pore-sizes of this rock by a variety of experimental methods including mercury intrusion / retraction porosimetery, scanning electron microscopy, core-level permeability measurements and X-ray computed tomography (CT scanning). On basis of these investigations we inferred the shape of pore-body and pore-throat size distributions for an outcrop sample of diatomite. These were unimodel distributions with a high positive skew. The average pore-throat size was around 6 mm and the average pore-body size was around 40 mm. In the final phase of this study, we found mathematical relations that are useful to predict the permeability alteration with amount of silica transfer between the rock matrix and the aqueous phase given the pore-level information of diatomite. This was done using pore-network models. To start, we correlated the pore dimensions with properties like permeability and porosity. Next, we modeled the deposition / dissolution processes in terms of changing pore dimensions and then used these altered pore dimensions to find the altered permeability and porosity. This way, we were able to quantify the effect of silica redistribution on permeability of the reservoir.

    
    
    
    [Bibtex-key = TR113]
    [BibTex Entry]
35. W. E. Brigham, A. R. Kovscek, and L. M. Castanier. SUPRI Heavy Oil Research Program Twenty First Annual Report. Technical report, Stanford University, CA, USA, 1998.
    [pdf]
    Keywords: Reservoir Definition, In-Situ Combustion, Heavy Oil, Steam, EOR, Formation Evaluation.

    Abstract

    Supri-A yearly research report.

    
    
    
    [Bibtex-key = TR111]
    [BibTex Entry]
36. G. L. Messner. A Comparison of Mass Rate and Steam Quality Reductions to Optimize Steamflood Performance.. Technical report, Stanford University, CA, USA, July 1998.
    [pdf]
    Keywords: Thermal Recovery, Steam, Heavy Oil.

    Abstract

    Many operators of steamdrive projects will reduce the heat injection rate as the project matures. The major benefit of this practice is to reduce the fuel costs and thus extend the economic life of the project. However, there is little industry consensus on whether the heat cuts should take the form of; (1) mass rate reductions while maintaining the same high steam quality, or (2) steam quality decreases while keeping the same mass rate. Through the use of a commercial three-phase, three-dimensional simulator, the oil recovery schedules obtained when reducing the injected steam mass rate or quality with time were compared under a variety of reservoir and operating conditions. The simulator input was validated for Kern River Field conditions by using the guidelines developed by Johnson, et al. (1989) for four steamflood projects in Kern River. The results indicate that for equivalent heat injection rates, decreasing the steam injection mass rate at a constant high quality will yield more economic oil than reducing the steam quality at a constant mass rate. This conclusion is confirmed by a sensitivity analysis which demonstrates the importance of the gravity drainage/steam zone expansion mechanism in a low-pressure, heavy oil steamflood with gravity segregation. Furthermore, the impact of discontinuous silts and nonuniform initial temperatures within the steamflood zone was studied, indicating again that a decreasing mass rate injection strategy is a superior operating practice.

    
    
    
    [Bibtex-key = TR108]
    [BibTex Entry]
37. J. M. Schembre, S. Akin, and A. R. Kovscek. Spontaneous Imbibition in Low Permeability Porous Media. Technical report, Stanford University, CA, USA, December 1998.
    [pdf]
    Keywords: Imbibition, Experimental Work, Simulation, Relative Permeability, Capillary Pressure.

    Abstract

    A systematic experimental investigation of capillary pressure characteristics and fluid flow in diatomite was begun. Using an X-ray CT scanner and a specially constructed imbibition cell, we study spontaneous water imbibition processes in diatomite and, for reference, Berea sandstone and chalk. The mass of water imbibed as a function of time is also measured. Imbibition is restricted to cocurrent flow. Despite a marked difference in rock properties such as permeability and porosity, we find similar trends in saturation profiles and weight gain versus time functions. Imbibition in diatomite is relatively rapid when initial water saturation is low due to large capillary forces. Using a non-linear regression analysis together with the experimental data, the capillary pressure and water relative permeability curves are determined for the diatomite in the water-air system. The results given for displacement profiles by numerical simulation match the experimental results.

    
    
    
    [Bibtex-key = TR114]
    [BibTex Entry]
38. Y. Wang, A. R. Kovscek, and W. E. Brigham. A Study of the Effect of Mobility Ratios on Pattern Displacement Behavior. Technical report, Stanford University, CA, USA, December 1998.
    [pdf]
    Keywords: Mobility Control, Sweep Efficiency, Simulation.

    Abstract

    It is well known, for unit mobility ratio, that the areal sweep efficiency of a staggered line drive pattern is always better than a five-spot pattern. However, this observation does not hold for very favorable mobility ratios. I studied the effect of mobility ratios on pattern behavior by the means of simulation using a streamline simulator. In this report, I present simulation results and, with the help of streamline and saturation distributions, explain the differences between displacements with unit and favorable mobility ratios. Simulations compare well with experiments conducted elsewhere. Accurate definition of breakthrough time is also discussed for multiphase, streamline, simulation results. The exact definition of breakthrough is difficult due to physical dispersion in experiments and numerical dispersion in simulations.

    
    
    
    [Bibtex-key = TR115]
    [BibTex Entry]
39. W. E. Brigham. Water Influx, and Its Effect on Oil Recovery Part 1. Aquifer Flow. Technical report, Stanford University, CA, USA, June 1997.
    [pdf]
    Keywords: Aquifer, Analytical Work.

    Abstract

    Natural water encroachment is commonly seen in many oil and gas reservoirs. In fact, overall, there is more water than oil produced from oil reservoirs worldwide. Thus it is clear that an understanding of reservoir/aquifer interaction can be an important aspect of reservoir management to optimize recovery of hydrocarbons. Although the mathematics of these processes are difficult, they are often amenable to analytical solution and diagnosis. Thus this will be the ultimate goal of a series of reports on this subject. This first report deals only with aquifer behavior, so it does not address these important reservoir/aquifer issues. However, it is an important prelude to them, for the insight gained gives important clues on how to address reservoir/aquifer problems. In general when looking at aquifer flow, there are two convenient inner boundary conditions that can be considered; constant pressure or constant flow rate. There are three outer boundary conditions that are convenient to consider; infinite, closed and constant pressure. And there are three geometries that can be solved reasonably easily; linear, radial and spherical. Thus there are a total of eighteen different solutions that can be analyzed. The information in this report shows that all of these cases have certain similarities that allow them to be handled fairly easily; and, though the solutions are in the form of infinite series, the effective results can be put into very simple closed form equations. Some equation forms are for shorter time results, and others are for longer time results; but, remarkably, for all practical purposes, the solutions switch immediately from one to the other. The times at which they switch depend on the sizes of the systems being considered; and these, too, can be defined by simple equations. These simple equation forms provide great insight on the nature of the behavior of these systems. Real field aquifer data are never at constant pressure or constant flow rate. This fact, however, can be handled easily using the superposition integral. This report also discusses this idea and its application, and shows how the simpler analytic solutions make this superposition process considerably easier to perform.

    
    
    
    [Bibtex-key = TR103]
    [BibTex Entry]
40. W. E. Brigham and L. M. Castanier. SUPRI Heavy Oil Research Program Twentieth Annual Report. Technical report, Stanford University, CA, USA, June 1997.
    [pdf]
    Keywords: Reservoir Definition, In-Situ Combustion, Heavy Oil, Steam, EOR, Formation Evaluation.

    Abstract

    Supri-A yearly research report.

    
    
    
    [Bibtex-key = TR109]
    [BibTex Entry]
41. R. G. Hughes, W. E. Brigham, and L. M. Castanier. CT Measurements of Two-Phase Flow in Fractured Porous Media. Technical report, Stanford University, CA, USA, June 1997.
    [pdf]
    Keywords: Experimental Work, Fractures, Imbibition.

    Abstract

    The simulation of flow in naturally fractured reservoirs commonly divides the reservoir into two continua: the matrix system and the fracture system. Flow equations are written presuming that the primary flow between grid blocks occurs through the fracture system and that the primary fluid storage is in the matrix system. The dual porosity formulation of the equations assumes that there is no ow between matrix blocks while the dual permeability formulation allows fluid movement between matrix blocks. Since most of the fluid storage is contained in the matrix, recovery is dominated by the transfer of uid from the matrix to the high conductivity fractures. The physical mechanisms influencing this transfer have been evaluated primarily through numerical studies. Relatively few experimental studies have investigated the transfer mechanisms. Early studies focused on the prediction of reservoir recoveries from the results of scaled experiments on single reservoir blocks. Recent experiments have investigated some of the mechanisms that are dominant in gravity drainage situations and in small block imbibition displacements. The mechanisms active in multiphase flow in fractured media need to be further illuminated, since some of the experimental results appear to be contradictory. This report describes the design, construction, and preliminary results of an experiment that studies imbibition displacement in two fracture blocks. Multiphase (oil/water) displacements will be conducted at the same rate on three core configurations. The configurations are a compact core, a two-block system with a 1 mm spacer between the blocks, and a two-block system with no spacer. The blocks are sealed in epoxy so that saturation measurements can be made throughout the displacement experiments using a Computed Tomography (CT) scanner. Preliminary results are presented from a water/air experiment. These results suggest that it is incorrect to assume negligible capillary continuity between matrix blocks as is often done.

    
    
    
    [Bibtex-key = TR104]
    [BibTex Entry]
42. N. S. Sagar and L. M. Castanier. Oil-Foam Interactions in a Micromodel.. Technical report, Stanford University, CA, USA, November 1997.
    [pdf]
    Keywords: Foam, Micromodels, Interfacial Tension, Experimental Work.

    Abstract

    This report presents results of a pore-level visualization study of foam stability in the presence of oil. Many laboratory investigations have been carried out in the absence of oil, but comparatively few have been carried out in the presence of oil. For a field application, where the residual oil saturation may vary from as low as 0 to as high as 40% depending on the recovery method applied, any effect of the oil on foam stability becomes a crucial matter. Sandstone patterns were used in this study. The micromodels used are two-dimensional replicas of the flow path of Berea sandstone etched on to a silicon wafer to a prescribed depth, adapting fabrication techniques from the computer chip industry. After flooding the models up to connate water and residual oil saturations, surfactant flood followed by gas injection to generate foam was done. Starting with lower concentrations of surfactant and gas injection the procedure was followed up to higher concentrations of surfactant. Visual observations were made using a high resolution microscope and pictures were recorded on videotape before being processed as they appear in this report. The single most important reason for this study on silicon micromodels compared to previous micromodel work is pore dimensions. With glass micromodels, for example, the reaction kinetics of acid etching makes it necessary to enlarge the pores by a factor of 5 to 50 thus providing a serious limitation for their use in studying processes that depend critically on capillary forces or involve thin films as compared to real rock pores. Two different surfactants were used, a fluoro-surfactant (for generating an oil foam) and an Alpha-Olefin Sulfonate. Oseberg crude was the non-wetting phase in the first set of experiments, and Kerosene in the next two sets. While the fluoro-surfactant created a strong static gas-blocking foam in the presence of oil, the Alpha-olefin Sulfonate (AOS) foamer did not. The fluoro-surfactant foam gave the oil-tolerant behavior expected from its non-entering, non-spreading characteristics. The AOS on the other hand, did not behave in accordance with its bulk observations and its behavior was seen to be controlled by formation of oil/foam emulsions. Generation sites for both foam and the emulsions were seen to be controlled by pore geometry and local saturation. For the foam, no obvious link could be found with the number of films observed and the strength of gas blockage. A lot of other interesting observations included snap-off, emulsion formation and breakdown sequences, foam lamella formation and breakdown sequences, and static emulsion and foam in different configurations within the model usually at higher concentrations of surfactant.

    
    
    
    [Bibtex-key = TR110]
    [BibTex Entry]
43. B. C. Sharma, W. E. Brigham, and L. M. Castanier. CT Imaging Techniques for Two-Phase and Three-Phase In-Situ Saturation Measurements. Technical report, Stanford University, CA, USA, June 1997.
    [pdf]
    Keywords: Steam, Thermal Recovery, Experimental Work, 3-phase Saturation.

    Abstract

    The aim of this research is to use the SUPRI 3D steam injection laboratory model to establish a reliable method for 3-phase in-situ saturation measurements, and thereafter investigate the mechanism of steamflood at residual oil saturation. Demiral et al. (1992) designed and constructed a three-dimensional laboratory model that can be used to measure temperature, pressure and heat loss data. The model is also designed so that its construction materials are not a limiting factor for CT scanning. We have used this model for our study. In this study, we saturated the model with mineral oil, and carried out waterflood until residual oil saturation. Steamflood was then carried out. A leak appeared at the bottom of the model. Despite this problem, the saturation results, obtained by using 2-phase and 3-phase saturation equations and obtained from the Cat scanner, were compared with the saturations obtained from material balance. The errors thus obtained were compared with those obtained by an error analysis carried out on the saturation equations. This report gives details of the experimental procedures, the data acquisition and data processing computer programs, and the analysis of a steamflood experiment carried out at residual oil saturation.

    
    
    
    [Bibtex-key = TR107]
    [BibTex Entry]
44. S. Joshi, W. E. Brigham, and L. M. Castanier. Techno-Economic and Risk Evaluation of a Thermal Recovery Project. Technical report, Stanford University, CA, USA, March 1996.
    [pdf]
    Keywords: Thermal Recovery, Risk Analysis.

    Abstract

    The thermal project studied in this work is a tertiary steam flood recovery project started in May 1989 by Union Pacific Resources Company (UPRC), in the Tar Zone reservoir of Fault Block II Unit located in the Wilmington Field, Los Angeles County, California. An analytical steam flood model was applied to determine an overall heat balance for the project and predict future production rates. An important feature of the analysis is the determination of heat losses due to produced fluids from the wellbore, a factor sometimes not taken account of in analytical methods. The model gave a fairly close history match with the production data. An economic analysis of the project was carried out using capital budgeting and discounted cash flow techniques. Since many of the input parameters for the models were uncertain, a risk evaluation was carried out for both the technical and the economic analysis, by using Monte-Carlo simulation.

    
    
    
    [Bibtex-key = TR102]
    [BibTex Entry]


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