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Abstract

The use of the acoustic well sounding (AWS) technique to determine bottomhole pressure (BHP) requires an estimate of the gas-void fraction (f.) in the liquid column of a pumping well annulus. Three correlations relating the annular superficial gas velocity to fg are available for saturated oil columns. These correlations were developed by Godbey and Dimon, Podio et al., and Gilbert as reported by Gipson and Swaim. Use of these correlations for determining the BHP, either flowing or shut in, involves a stepwise numerical integration often performed by a computer.

This work addresses three aspects of estimating the BHP from AWS data: (1) estimation of the superficial gas velocity, (2) development of analytical solutions for a single-step BHP calculation, and (3) comparison and interpretation of the predicted BHP's by use of the three correlations for the field examples.

A mathematical model, based on the principle of mass balance of the annular. gas phase, is used to determine the superficial gas velocity. This model rigorously accounts for the time-dependent pressure, volume, and the gas deviation factor in the liquid-free annulus.

Analytical solutions are obtained for both the Godbey-Dimon and Podio et al. correlations to calculate the BHP in a single step. These analytical solutions provide a significant improvement over the numerical stepwise integration technique, because a hand-held calculator can be used for the BHP calculations.

The field examples studied indicate that both the pumping liquid column height and the superficial gas velocity pumping liquid column height and the superficial gas velocity play a key role in estimating the gas void fraction-an play a key role in estimating the gas void fraction-an essential element in calculating the BHP. We observe that only the early-time shut-in pressures are affected by the presence of gas bubbles in the liquid column. Because the presence of gas bubbles in the liquid column. Because the bottomhole flowing pressure (BHFP) is dependent on the correlation used to predict the fg, both skin and productivity index calculations are affected. Estimation of the productivity index calculations are affected. Estimation of the permeability/thickness product and the static reservoir permeability/thickness product and the static reservoir pressure, however, are independent of the fg correlation pressure, however, are independent of the fg correlation used.

Introduction

The majority of the oil wells in North America are on some form of artificial lift system. Brown gives a comprehensive review of these artificial lift systems. Typically, the oil is lifted up the tubing string while the gas is vented through the annulus to avoid gas-locking the pump. Sucker-rod (beam) pumps are the most popular and pump. Sucker-rod (beam) pumps are the most popular and widely used lift system in the industry.

The process of gas venting through the annular liquid column (oil and/or water) has a profound effect on the liquid density. Because knowledge of the gas-lightened liquid column is the key to a meaningful BHP (flowing and/or shut in) estimation, a better understanding of the physical process is essential, so we explored the relevant physical process is essential, so we explored the relevant works available in the literature to provide an overview of the state of the art for estimating BHP's in sucker-rod pumping wells. pumping wells. A knowledge of the BHFP (pf) is an essential element in predicting a well's productivity index (J) and its inflow performance relationship (IPR). This information is instrumental in proper artificial lift design. A pressure buildup test conducted on a pumping well can provide an array of valuable information-such as permeability/ thickness product, skin, and static reservoir pressure. The last piece of information is necessary for a meaningful J estimation.

We will examine the methods available that permit estimation of pwf and subsequent shut-in pressures, pws, for a buildup analysis.

Because of the mechanical constraints, a subsurface pressure recorder normally cannot be run down the pressure recorder normally cannot be run down the tubing string to monitor the in-situ pressure in a sucker-rod pump. After the pump and rods have been pulled, pump. After the pump and rods have been pulled, however a recorder can be run downhole to record pressures in the conventional mariner. This method has several problems. First, a rig is needed to pull the pump and rods and problems. First, a rig is needed to pull the pump and rods and rerun them following the test. The cost of the test may be prohibitive, especially for marginal wells. Second, the early-time data, including the p is lost because of the very nature of the operation.

Permanent downhole recorders are used sometimes to monitor pressures in key wells of a field in certain cases. Because of their permanent nature, the recorders have a very limited application.

Nind described several other alternatives-such as depression of the annular liquid column and two methods involving the use of a dynamometer. These methods are time-consuming and have other limitations. They are capable of estimating only the pf, and, consequently, have no application in pressure buildup testing.

The use of AWS with an echometer has been a very popular method for estimating both the flowing and popular method for estimating both the flowing and shut-in pressures in pumping wells. Thomas et al. and McCoy describe the principle of the method.

SPEJ

P. 823

annular, artificial lift system, BHP, buildup, calculation, column, correlation, data, formation evaluation, gas, gas velocity, Gilbert, Gilbert Correlation, machine learning, Podio, prediction, pressure transient testing, production control, production logging, production monitoring, rate, reservoir simulation, solution, value, velocity, well

SPE Disciplines: Reservoir Description and Dynamics > Formation Evaluation & Management > Drillstem/well testing (1.00)

Abstract

This paper investigates the role of oil aromaticity in miscability development and in the deposition of heavy hydrocarbons during CO2, flooding. The results of phase equilibrium measurements, compositional studies, sandpack displacements, and consolidated corefloods are presented. Reservoir oil from the Brookhaven field and presented. Reservoir oil from the Brookhaven field and synthetic oils that model natural oil phase behavior are examined. Phase compositional analyses Of CO2/synthetic-oil mixtures in static PVT tests demonstrate that increased oil aromaticity correlates with improved hydrocarbon extraction into a CO2-rich phase. The results of tertiary corefloods performed with the synthetic oils show that CO2-flood oil displacement efficiency is also improved for the oil with higher aromatic content. These oil aromaticity influences are favorable. Reservoir oil experiments show that a significant deposition of aromatic hydrocarbon material occurs when CO2, contacts highly asphaltic crude. Solid-phase formation was observed in phase equilibrium and displacement studies and led to severe plugging during linear flow through Berea cores. It is unclear how this solid phase will affect oil recovery on a reservoir scale.

Introduction

Several reports suggest that oil aromaticity affects the CO2, displacement process of reservoir oil. Henry and Metcalfe noted the absence of multiple-liquid phase generation in displacement tests performed with a crude oil of low aromatic content. Holm and Josendal showed that when a highly paraffinic oil was enriched with aromatics, the slim-tube minimum miscibility pressure (MMP) decreased and oil recovery improved. Qualitative differences in the phase behavior of two crudes with contrasting aromatic contents prompted the suggestion by Monger and Khakoo that increased oil aromaticity correlates with improved hydrocarbon extraction into a CO2-rich phase. Clementz discussed how the adsorption of petroleum heavy ends, like the condensed aromatic ring structures found in asphaltenes, can alter rock properties. Laboratory studies have shown that improved oil properties. Laboratory studies have shown that improved oil recoveries in tertiary CO2 displacements benefited from changes in wetting behavior apparently , induced by asphaltene adsorption. Tuttle noted that CO2, appears to reduce asphaltene solubility and can cause rigid film formation. In these respects, oil aromaticity may also account for phase-behavior/oil-recovery synergism. Asphaltene deposition, though not a problem during primary and secondary recovery operations, was primary and secondary recovery operations, was reported in the Little Creek CO2 -injection pilot in Mississippi. Wettability alteration from asphaltene precipitation appears to have explained the results of low residual oil at high water-alternating-gas ratios in the Little Knife CO2, flood minitest in North Dakota. This paper provides detailed laboratory data from phase equilibrium measurements, compositional studies. sandpack displacements, and consolidated corefloods that illuminate the role of aromatics in miscibility development and in solid-phase formation during CO2 - flooding. The results for synthetic oils that model crude-oil behavior suggest that CO2-flood performance will benefit from increased oil aromaticity. The interpretation of reservoir oil results is more difficult. The precipitation of highly aromatic hydrocarbon material is observed when CO2, contacts Brookhaven crude. One purpose of this paper is to examine the variables that influence asphaltene precipitation. Near the wellbore, solid-phase formation might precipitation. Near the wellbore, solid-phase formation might reduce injectivity or impair production rates. Perhaps in other regions of the reservoir, altered permeability and/or wettability caused by solid-phase deposition might improve the ability of CO2, to contact oil. Additional work is needed to determine which potential benefits of oil aromaticity are significant on the reservoir scale. Advances in computer-implemented equations of state are making the prediction of CO2,/hydrocarbon phase behavior easier and more reliable. When an equation of state with CO2/reservoir-oil mixtures is used, an important consideration is the characterization of the heavy hydrocarbon components. One characterization method that appears to match the experimental data accurately in the critical point region for rich-gas/reservoir-oil mixtures is based on assigning separate paraffinic, aromatic, and naphthenic cuts. An additional aim of this study is to provide experimental data in assisting similar modeling provide experimental data in assisting similar modeling efforts for CO2/reservoir-oil mixtures. Experimental phase equilibrium data for mixtures containing CO2, and phase equilibrium data for mixtures containing CO2, and heavy hydrocarbons, particularly aromatics, are scarce. The behavior of multicomponent CO2,/hydrocarbon systems is not readily deduced from the phase equilibria of binary or ternary systems.

Materials and Methods

Phase Equilibrium Studies. A schematic diagram of the Phase Equilibrium Studies. A schematic diagram of the apparatus used in the phase-behavior experiments appears in Fig. 1. A detailed description of the equipment, procedures, chemicals, and analytical methods used is given procedures, chemicals, and analytical methods used is given in Ref. 10.

SPEJ

P. 865

Behavior, Brookhaven, chemical flooding, coreflood, displacement, flow assurance, formation evaluation, hydrocarbon, miscible method, oil, oil aromaticity, Oil Recovery, oilfield chemistry, Phase, Phase Behavior, pressure, production control, production monitoring, PVT measurement, recovery, reservoir simulation, result, sandpack, scaling method, Table, temperature, waterflooding

Industry:

- Materials > Chemicals > Commodity Chemicals > Petrochemicals (1.00)
- Energy > Oil & Gas > Upstream (1.00)

SPE Disciplines:

Mobil Research and Development Corporation Field Research Laboratory Dallas, Texas

Abstract

The organic carbonaceous matter found intimately associated with the uranium mineral in some Crownpoint ore trends appears to shield some of the uranium from contact by a chemically-mild leaching system. Sodium hypochlorite (NaOCl) is an oxidant strong enough to attack this carbonaceous matter and contact the trapped uranium mineral. Batch and pack laboratory tests showed that alkaline bicarbonate solutions containing 0.1-5.0 wt-% NaOCl were effective for rapid recovery of uranium from Crownpoint refractory ore. Recoveries of 90% and greater were obtained In the laboratory tests. However, NaOCl is such a strong oxidant that it reacts extensively with gangue minerals also present in the ore as well as with uranium. Since oxidation with NaOCl generates sodium chloride, high chloride levels would tend to build up in the leaching circuit. Electron mlcroprobe studies of ore samples after leaching with NaOCl showed the presence of holes and cracks in the residual carbonaceous matrix as well as the presence of chloride. Leaching with NaOCl is also associated with high levels of dissolved organic carbon. These observations suggest some degree of oxidative breakdown of the encapsulating organic matter by NaOCl, thereby facilitating oxidant attack on the uranium mineral.

Oilfield Places:

- North America > United States > Pennsylvania > Morrison Oil Field (0.98)
- North America > United States > New Mexico > San Juan Basin (0.97)
- North America > United States > Colorado > San Juan Basin (0.97)

Summary

Measuring the rheological properties of crosslinked fracturing fluids is difficult but important. Fluid properties play a key role in the determination of the final geometry of the created fracture and in the distribution of proppant within the fracture; therefore, an accurate knowledge of these parameters is necessary for optimum treatment design. The first paper^{1} in this series described a method to measure accurately and reproducibly the rheological properties of crosslinked fracturing fluids. The technique is the first that applies long-accepted mathematical methods to correct the measurements for the deviations in shear rate caused by the non-Newtonian nature of the fluids. This, in turn, allows the rigorous examination of mathematical fluid models to determine which, if any, best describes the flow properties of the fluids.

Introduction

The problems of characterizing crosslinked fracturing fluids were outlined in the first paper^{1} in this series. These problems made the application of accepted mathematical techniques to correct measurements for deviations caused by the non-Newtonian character of these fluids difficult to justify. As a result, not making corrections has often led to the wrong choice of fluid models when the mathematical description of the fluid flow is attempted.

The technique^{1} that was used to gather data for this study has been described previously. Dynamic mechanical testing provides a quantity - called the complex viscosity (Âµ*) - that has been shown by Cox and Merz^{2} to equal the apparent viscosity (Âµ* _{a}*) determined in steady-shear measurements. Yasuela

The API^{4} currently specifies that the data gathered on fracturing fluids be reported as *n*' and *k*', which have been derived from apparent Newtonian shear rates. This promotes consistency in the presentation of data but can lead to the misinterpretation of the results of an experiment. When necessary, model-independent shear-rate conversions were applied before analysis to all the input data in this study to avoid misinterpretation of the results.

Background: Analysis of Laboratory Rheology Data

The procedure for determining fluid-flow characteristics from laboratory data may be expressed generally as occurring in three distinct, but not independent, steps: (1) data acquisition, (2) analysis and data reduction, and (3) scale-up with the fundamental equations of fluid mechanics or some generalized method, such as that of Metzner and Reed,^{5} that is based on those relationships.

Only the first and second steps are discussed here; a complete discussion of the third step is beyond the scope of this study.

**Data Acquisition.**

Data for scale-up are normally acquired in the laboratory with capillary-, tube- and extrusional-type rheometers or parallel-plate, cone-and-plate, and concentric-cylinder rotational-type rheometers. When crosslinked gels are measured, each measurement technique suffers from the effects of the viscoelastic nature1 of the gels. Slip at the wall in capillary- and tube-type rheometers makes data obtained with this type of measurement difficult to reproduce. Slip at the wall and the Weissenberg effect complicate the interpretation of data derived from the steady-shear mode of rotational-type viscometers. The method of dynamic testing^{1} avoids many of those problems and provides reproducible data for the next step in the scale-up process.

**Analysis and Data Reduction.**

The first step in the data analysis process is the conversion of the experimental measurements - i.e., pressure drop and pump rate or torque and angular velocity - into estimates of shear stress and shear rate. Three methods of conversion can be used: (1) equivalent (apparent) Newtonian shear rate or viscosity, (2) model-dependent conversions, and (3) model-independent conversions.

Method 1 is specified by API as the method of reporting fluid data. The shear rate, computed as if the fluid were a Newtonian liquid, is used to estimate parameters for non-Newtonian fluid models. It can be shown that this technique is adequate for certain two-parameter models, provided that restrictions are applied to the range of scale-up shear rates and that the rheological parameters are used without modification in generalized methods of scale-up. This method is inadequate, however, if the object of the experiment is both fluid-model optimization and fluid-flow scale-up. The assumptions inherent to this technique will introduce a bias toward three-parameter models that will be carried through the scale-up process, if not isolated and minimized during error determination.

Data Acquisition.

Data for scale-up are normally acquired in the laboratory with capillary-, tube- and extrusional-type rheometers or parallel-plate, cone-and-plate, and concentric-cylinder rotational-type rheometers. When crosslinked gels are measured, each measurement technique suffers from the effects of the viscoelastic nature1 of the gels. Slip at the wall in capillary- and tube-type rheometers makes data obtained with this type of measurement difficult to reproduce. Slip at the wall and the Weissenberg effect complicate the interpretation of data derived from the steady-shear mode of rotational-type viscometers. The method of dynamic testing^{1} avoids many of those problems and provides reproducible data for the next step in the scale-up process.

Analysis and Data Reduction.

The first step in the data analysis process is the conversion of the experimental measurements - i.e., pressure drop and pump rate or torque and angular velocity - into estimates of shear stress and shear rate. Three methods of conversion can be used: (1) equivalent (apparent) Newtonian shear rate or viscosity, (2) model-dependent conversions, and (3) model-independent conversions.

Method 1 is specified by API as the method of reporting fluid data. The shear rate, computed as if the fluid were a Newtonian liquid, is used to estimate parameters for non-Newtonian fluid models. It can be shown that this technique is adequate for certain two-parameter models, provided that restrictions are applied to the range of scale-up shear rates and that the rheological parameters are used without modification in generalized methods of scale-up. This method is inadequate, however, if the object of the experiment is both fluid-model optimization and fluid-flow scale-up. The assumptions inherent to this technique will introduce a bias toward three-parameter models that will be carried through the scale-up process, if not isolated and minimized during error determination.

analysis, chemical treatment, conversion, data mining, determination, Flow, method, model, Newtonian, oilfield chemistry, parameter, production control, production logging, production monitoring, rate, rock/fluid interaction, shear, shear rate, shear stress, solution, stress, technique, value, viscometer, viscosity, yield

SPE Disciplines:

Abstract

The expected loss of useful alkalinity caused by, the slow dissolution of silica from pure quartz sand is shown for some typical alkaline flooding solutions (about 1 % NAOH or 1.25% sodium orthosilicate) to be only about 10 to 20%. This conclusion is based on the observation that alkaline solutions equilibrate with quartz and on the methodology proposed here for determining the useful alkalinity of a solution. Furthermore, the dissolution of quartz in alkaline flooding can be eliminated by the use of solutions saturated in silica with respect to quartz. Such formulations may be useful in controlling the erosion of the wellbore and gravel pack.

Introduction

Research results emphasize the importance of silica dissolution reactions, both in steamflooding and in alkaline flooding. Rapid dissolution of silica can quickly form a large cavity adjacent to the injection well. In unconsolidated reservoir sands, this cavity could collapse and produce lateral stresses that sever the well casing. Furthermore, for alkaline flooding it is uncertain whether alkaline pulses can propagate through reservoir sands before hydroxide concentrations drop to ineffective levels. Although many mechanisms that consume alkali exist in the reservoir, a recent paper by Bunge and Radke proposed that the slow silica dissolution reaction is of primary proposed that the slow silica dissolution reaction is of primary importance. When scaled to reservoir residence times, their calculations for the dissolution of silica by alkali predict dire conclusions: for many practical well predict dire conclusions: for many practical well spacings and flow rates, hydroxide concentrations drop to ineffective levels after - 15% of the interwell distance is traversed. Important assumptions inherent in their calculations are that (1) the dissolution of silica by hydroxide can be treated as an irreversible reaction because the solubility of amorphous silica is not approached, which allows short-term dissolution rates to be extrapolated to reservoir times, and (2) loss of hydroxide ion concentration (or pH,) with time is the critical parameter in estimating alkaline-pulse migration. In this paper, alkaline dissolution experiments are performed with a pure quartz sand. A methodology is performed with a pure quartz sand. A methodology is proposed for estimating the amount of useful alkalinity lost proposed for estimating the amount of useful alkalinity lost because of silica dissolution, and estimates for wellbore erosion are given. It is not the intent of this paper to determine the total alkaline consumption for reservoir sands. Consumption reactions important for reservoir sands such as precipitation of alkali by multivalent cations, and clay transformations-are not considered. However, discussions of the effect that clay minerals and cation precipitation might have on silica dissolution are presented. precipitation might have on silica dissolution are presented. Experimental Procedure

Static bottle experiments in which quartz sand is contacted with alkaline solution are used to study silica dissolution. A basic argument in this paper is that the accumulation of silica in alkaline solution during storage with sand at elevated temperatures mimics silica accumulation in a given fluid element as the fluid propacates through the reservoir sand. Two assumptions are inherent in this statement: fluid flow at reservoir rates ft/D f - 0. 3 m/d]) has no effect on the chemical reaction of alkali with solid silica. and the surface area of sand in the static bottle tests does not drop significantly as dissolution proceeds. The first assumption is certainly reasonable, but the second deserves comment. Subsequent results show that the maximum silica dissolution observed in these experiments corresponds to only 0.5% of the quartz sand present in the bottles. Assuming spheres, such a dissolution reduces the surface area of sand grains by about 0.4%; thus the second assumption is also valid. This experimental approach is to determine the changes in soluble silica concentration and alkalinity with increasing time. For this pure quartz sand, soluble silica accumulations can be related directly to reaction rates. (In the absence of clays, aluminum is not present to cause the precipitation of silica in the form of aluminosilicate precipitation of silica in the form of aluminosilicate minerals.) Acid titrations of the alkaline solutions can be particularly useful because they reveal the effects that soluble particularly useful because they reveal the effects that soluble silica has on total alkalinity and buffering capacity.

Methods

Static Bottle Tests. For static bottle tests, 75 quartz sand (Clemtex No. 5, - 100 mesh) was stored with 33 g of alkaline solution in tightly sealed Teflon bottles at constant temperature. Special inserts were fabricated and placed in the necks of the bottles to [minimize vapor loss. placed in the necks of the bottles to [minimize vapor loss. The bottles were not agitated during storage because sufficient mixing is accomplished by Brownian diffusion and because agitation results in the abrasion or grinding of the sand grains, a phenomenon not encountered in reservoir flooding. Calculations show that Brownian diffusion completely distributes concentration changes caused by silica dissolution through the aqueous phase in 3 days.

SPEJ

P. 857

alkaline, alkaline flooding, alkaline solution, alkalinity, calculation, chemical flooding, composition, concentration, dissolution, equilibrium, Fig, loss, production control, production logging, production monitoring, quartz, reservoir, SAGD, sand, silica, silica dissolution, silicate, solubility, solution, steam-assisted gravity drainage, temperature, thermal method, waterflooding

SPE Disciplines:

Abstract

This paper presents a set of curvilinear coordinate transformations that lead to no mixed derivative terms in transformed flow equations. The transformations are created by examining the transformed flow equations and by showing that the mixed derivative terms are zero if the transformation satisfies a system of differential equations that depend on the geometry and rock property distribution within the reservoir. Numerical examples with a black-oil simulator are presented to show the increased accuracy resulting from the use of the curvilinear coordinate system and the importance of eliminating the mixed derivative terms.

Introduction

The accurate and efficient simulation of fluid flow in a reservoir is highly dependent on the choice of the mesh upon which discrete flow equations are to be solved. In many situations, a simulation conducted on a curvilinear coordinate system is advantageous. Many authors have reported on the advantages of solving reservoir simulation problems with a curvilinear coordinate system. problems with a curvilinear coordinate system. These advantages include the elimination of grid-orientation effects, improved modeling of reservoir geometries, and reductions in CPU time.

Solving a problem on a curvilinear coordinate grid system is equivalent to transforming the reservoir into a rectangle and then solving the transformed problem on the rectangle. The transformed reservoir flow equations, however, will generally contain mixed derivative terms. In turn, these terms can alter the structure of the matrix that results from discretizing the flow equations. If the structure of the coefficient matrix is altered, the efficient solvers designed for use in reservoir simulation cannot be used without major modifications. One method for eliminating the mixed derivative terms is to use an orthogonal coordinate system. This system, however, does not eliminate the mixed derivative terms for an anisotropic permeability distribution. Several authors claim that the mixed derivative terms are small and, therefore, may be neglected. This is not the case, however, with large anisotropies. To maintain the inherent advantage of the curvilinear coordinate system, we found it necessary to minimize the effect of the mixed derivatives. This paper presents a class of curvilinear coordinate transformations that lead to no mixed derivative terms. The transformations maintain the advantages of a curvilinear coordinate grid system while avoiding the use of mixed derivative terms. The transformations are generated by examining the transformed flow equations and by showing that the mixed derivative terms are zero if the transformations satisfy a system of differential equations. These equations are based on the geometry and rock property distribution within the reservoir. The resulting system of differential equations is solved by a finite-element method (FEM) developed by Aziz and Leventhal. We begin with the derivation of the curvilinear coordinate transformation and how the mixed derivative terms are eliminated. The FEM is outlined briefly, followed by a description of the inverse transformation used to construct the curvilinear grid. Numerical examples with a black-oil simulator are presented to show the increased accuracy resulting from the use of the curvilinear coordinate system, the importance of accurately representing the reservoir geometry, and the importance of eliminating the mixed derivative terms.

Mathematical Formulation

The scope of this study is limited to two-dimensional (2D) reservoir flow problems. The transformations developed are applicable to complex transient and multiphase problems. However, it is sufficient to consider the model for the flow equations given in Eq. 1.

.......(1)

(See Appendix for more details.) It is assumed that the reservoir is banded by four curves, as shown in Fig. 1. The top and bottom curves represented by f1 and f2 are functions of x, while the sides, g1 and g2, are functions of y. The coordinates of the four corner points, c1, c2, c3, and c4, are (x1,y1), (x2,y2), (x3,y3), and (x4,y4), respectively.

SPEJ

p. 893

boundary, coordinate, Curvilinear, curvilinear coordinate, curvilinear coordinate system, curvilinear grid, domain, equation, Fig, flow metering, formation evaluation, function, grid, inverse, permeability, problem, production control, production monitoring, reservoir simulation, Simulation, simulator development, term, transformation

Abstract

Over the past 20 years, a number of studies have reported temperature effects on two-phase relative permeabilities in porous media. Some of the reported results, however, have been contradictory. Also, observed effects have not been explained in terms of fundamental properties known to govern two-phase flow. The purpose of this study was to attempt to isolate the fundamental properties affecting two-phase relative permeabilities at elevated temperatures.

Laboratory dynamic-displacement relative permeability measurements were made on unconsolidated and consolidated sand cores with water and a refined white mineral oil. Experiments were run on 2-in. [5.1-cm] -diameter, 20-in. [52.-cm] -long cores from room temperature to 300F [149C].

Unlike previous researchers, we observed essentially no changes with temperature in either residual saturations or relative permeability relationships. We concluded that previous results may have been affected by viscous previous results may have been affected by viscous instabilities, capillary end effects, and/or difficulties in maintaining material balances.

Introduction

Interest in measuring relative permeabilities at elevated temperatures began in the 1960's with petroleum industry interest in thermal oil recovery. Early thermal oil recovery field operations (well heaters, steam injection, in-situ combustion) indicated oil flow rate increases far in excess of what was predicted by viscosity reductions resulting from heating. This suggested that temperature affects relative permeabilities.

One of the early studies of temperature effects on relative permeabilities was presented by Edmondson, who performed dynamic displacement measurements with crude performed dynamic displacement measurements with crude and white oils and distilled water in Berea sandstone cores. Edmondson reported that residual oil saturations (ROS's) (at the end of 10 PV's of water injected) decreased with increasing temperature. Relative permeability ratios decreased with temperature at high water saturations but increased with temperature at low water saturations.

A series of elevated-temperature, dynamic-displacement relative permeability measurements on clean quartz and "natural" unconsolidated sands were reported by Poston et al. Like Edmondson, Poston et al. reported a decrease in the "practical" ROS (at less than 1 % oil cut) as temperature increased. Poston et al. also reported an increase in irreducible water saturation. Although irreducible water saturations decreased with decreasing temperature, they did not revert to the original room temperature values. It was assumed that the cores became increasingly water-wet with an increase in both temperature and time; measured changes of the IFT and the contact angle with temperature increase, however, were not sufficient to explain observed effects.

Davidson measured dynamic-displacement relative permeability ratios on a coarse sand and gravel core with permeability ratios on a coarse sand and gravel core with white oil displaced by distilled water, nitrogen, and superheated steam at temperatures up to 540F [282C]. Starting from irreducible water saturation, relative permeability ratio curves were similar to Edmondson's. permeability ratio curves were similar to Edmondson's. Starting from 100% oil saturation, however, the curves changed significantly only at low water saturations. A troublesome aspect of Davidson's work was that he used a hydrocarbon solvent to clean the core between experiments. No mention was made of any consideration of wettability changes, which could explain large increases in irreducible water saturations observed in some runs.

Sinnokrot et al. followed Poston et al.'s suggestion of increasing water-wetness and performed water/oil capillary pressure measurements on consolidated sandstone and limestone cores from room temperature up to 325F [163C]. Sinnokrot et al confirmed that, for sandstones, irreducible water saturation appeared to increase with temperature. Capillary pressures increased with temperature, and the hysteresis between drainage and imbibition curves reduced to essentially zero at 300F [149C]. With limestone cores, however, irreducible water saturations remained constant with increase in temperature, as did capillary pressure curves.

Weinbrandt et al. performed dynamic displacement experiments on small (0.24 to 0.49 cu in. [4 to 8 cm3] PV) consolidated Boise sandstone cores to 175F [75C] PV) consolidated Boise sandstone cores to 175F [75C] with distilled water and white oil. Oil relative permeabilities shifted toward high water saturations with permeabilities shifted toward high water saturations with increasing temperature, while water relative permeabilities exhibited little change. Weinbrandt et al. confirmed the findings of previous studies that irreducible water saturation increases and ROS decreases with increasing temperature.

SPEJ

P. 945

breakthrough, core, curve, displacement, effect, formation evaluation, geothermal reservoir, measurement, permeability, permeability curve, pressure, production control, production logging, production monitoring, reservoir simulation, residual oil saturation, result, Run, SAGD, sand, steam-assisted gravity drainage, study, temperature, Temperature Effect, thermal method, viscosity, water saturation, waterflooding

Abstract

Homogeneous core samples are needed for EOR experiments. We have devised a simple test for detecting the presence of nonuniformities in cores. The test consists of presence of nonuniformities in cores. The test consists of measuring the pressure drop across the core during a two-phase immiscible displacement experiment. We show that for a constant injection rate, the pressure drop will be linear with time provided that the core is homogeneous. In situations for which the initial section of the core is homogeneous, but the properties are not uniform in a latter section of the core, the location of the position where the rock properties fast change may be approximately determined. The effect of heterogeneities on the pressure-drop profile is demonstrated with analytical solutions and profile is demonstrated with analytical solutions and laboratory experiments.

Introduction

Core samples are used routinely for EOR or relative permeability experiments. For such experiments, selection permeability experiments. For such experiments, selection of a homogeneous core sample is necessary. Visual inspection of the core is not sufficient to ensure homogeneity. Often, vugs or shale barriers may be present, which may invalidate experimental results. In this paper, a simple test to detect the presence of core heterogeneities is devised.

The scale of heterogeneities considered corresponds to the usual macroscopic description of porous medium properties. The properties of a porous medium (e.g., the properties. The properties of a porous medium (e.g., the porosity and permeability) at any particular location refer porosity and permeability) at any particular location refer to average quantities for some appropriate (small) representative volume element. In this way, each (locally averaged) property is defined at every point within the medium, the collection of which defines the representation of each property as a function of position. If each macroscopic property has the same value at all positions, the medium is said to be homogeneous. Otherwise, the medium is heterogeneous. A more complete discussion of macroscopic properties and heterogeneities can be found in Refs. 1 through 3.

The macroscopic scale is a natural one to use for core selection because attempts to model coreflood experiments or to estimate properties of the porous medium on the basis of measured flow data generally will use mathematical models that use macroscopic properties. A homogeneous core sample is necessary for the experimental determination of relative permeabilities from displacement experiments. Explicit methods for estimating relative permeabilities from displacement data are based on the permeabilities from displacement data are based on the Buckley-Leverett model, in which the core is assumed to be homogeneous. The absolute permeability generally is determined from a single-phase flow experiment and thus represents an average value for the entire core. If the core is not homogeneous, so that the absolute permeability takes on different values in different locations permeability takes on different values in different locations in the core, errors will appear in the relative permeability estimates. Although the magnitude of the errors will depend on many factors, a macroscopically homogeneous sample is always preferred.

Note that heterogeneities may also be defined on a microscopic scale. A porous medium that is macroscopically homogeneous may be microscopically heterogeneous. In fact, this typically would be the case because few real porous media structures are microscopically homogeneous.

In this paper, we develop a test for detecting the presence of macroscopic heterogeneities in core samples. presence of macroscopic heterogeneities in core samples. The test is conducted by displacing the fluid that initially saturates the porous medium with a second fluid that is immiscible with the displaced fluid. The pressure drop across the core is recorded up to the time of breakthrough of the displacing fluid. The test is based on the observation that, with a constant injection rate and incompressible fluids, the pressure drop will be linear with time provided that the core is homogeneous. It is also shown provided that the core is homogeneous. It is also shown that, if the porosity and permeability for a heterogeneous core may be approximated as functions of the longitudinal spatial dimension, the pressure drop will be linear with time provided that the region in which both fluid phases are flowing simultaneously has uniform properties. The detection of heterogeneities by this method is discussed and illustrated with analytical solutions for the displacement process and with laboratory experimental data.

Theory

We consider here a displacement experiment with two incompressible fluids. Initially, the core is saturated with one fluid and the other fluid is injected at one end. For example, if the core initially contains only oil or air, water might be injected at one end. The core could contain the irreducible saturation of the displacing fluid initially, although this is not experimentally convenient and is not necessary for conducting the test. The pressure drop across the core is recorded through the time of breakthrough of the displacing fluid at the core outlet.

SPEJ

P. 909

case, core, core analysis, core sample, displacement, experiment, flow in porous media, Fluid Dynamics, formation evaluation, geomechanics, heterogeneity, Injection Rate, location, multiphase flow, permeability, porosity, pressure drop, production control, production logging, production monitoring, property, reservoir simulation, saturation, scaling method, time, uniform, value, water, wellbore integrity

SPE Disciplines:

Abstract

This paper presents short-time interpretation methods for radial-spherical (or radial-hemispherical) flow in homogeneous and isotropic reservoirs inclusive of wellbore storage, wellbore phase redistribution, and damage skin effects. New dimensionless groups are introduced to facilitate the classic transformation from radial flow in the sphere to linear flow in the rod. Analytical expressions, type curves (in log-log and semilog format), and tabulated solutions are presented, both in terms of pressure and rate, for all flow problems considered. A new empirical equation to estimate the duration of wellbore and near-wellbore effects under spherical flow is also proposed.

Introduction

The majority of the reported research on unsteady-state flow theory applicable to well testing usually assumes a cylindrical (typically a radial-cylindrical) flow profile because this condition is valid for many test situations. Certain well tests, however, are better modeled by assuming a spherical flow symmetry (e.g., wireline formation testing, vertical interference testing, and perhaps even some tests conducted in wellbores that do not fully penetrate the productive horizon or are selectively penetrate the productive horizon or are selectively completed). Plugged perforations or blockage of a large part of an openhole interval may also promote spherical flow. Numerous solutions are available in the literature for almost every conceivable cylindrical flow problem; unfortunately, the companion spherical problem has not received as much attention, and comparatively few papers have been published on this topic. papers have been published on this topic. The most common inner boundary condition in well test analysis is that of a constant production rate. But with the advent of downhole tools capable of the simultaneous measurement of pressures and flow rates, this idealized inner boundary condition has been refined and more sophisticated models have been proposed. Therefore, similar methods must be developed for spherical flow analysis, especially for short-time interpretations. This general problem has recently been addressed elsewhere.

Theory

The fundamental linear partial differential equation (PDE) describing fluid flow in an infinite medium characterized by a radial-spherical symmetry is

(1)

The assumptions incorporated into this diffusion equation are similar to those imposed on the radial-cylindrical diffusivity equation and are discussed at length in Ref. 9. In solving Eq. 1, the classic approach is illustrated by Carslaw and Jaeger (later used by Chatas, and Brigham et al.). According to Carslaw and Jaeger, mapping b=pr will always reduce the problem of radial flow in the sphere (Eq. 1) to an equivalent problem of linear flow in the rod for which general solutions are usually known. (For example, see Ref. 17 for particular solutions in petroleum applications.) Note that in this study, we assumed that the medium is spherically isotropic; hence k in Eq. 1 is the constant spherical permeability. This assumption, however, does not preclude analysis in systems possessing simple anisotropy (i.e., uniform but unequal horizontal and vertical permeability components). In this case, k as used in this paper should be replaced by k, an equivalent or average (but constant) spherical permeability. Chatas presented a suitable expression (his Eq. 10) obtained presented a suitable expression (his Eq. 10) obtained from a volume integral. It is desirable to transform Eq. 1 to a nondimensional form, thereby rendering its applicability universal. The following new, dimensionless groups accomplish this and have the added feature that solutions are obtained directly in terms of the dimensionless pressure drop, PD, not the usual b (or bD) groups.

......................(2)

.......................(3)

.........................(4)

The quantity rsw is an equivalent or pseudospherical wellbore radius used to represent the actual cylindrical sink (or source) of radius rw.

SPEJ

p. 804

condition, effect, Flow, Fluid Dynamics, formation evaluation, formation testing, phase redistribution, pressure transient testing, problem, production control, production logging, production monitoring, Redistribution, sandface flow rate, skin, solution, storage, time, transform, wellbore, wellbore storage

SPE Disciplines: Reservoir Description and Dynamics > Formation Evaluation & Management > Drillstem/well testing (1.00)

Mobil Research and Development Corporation Field Research Laboratory Dallas, Texas

Abstract

In this paper we present laboratory data on the effectiveness of a fairly severe leaching system ---- sulfuric acid (H2SO4) and an oxidant ---- in recovery of uranium from refractory Crown- point uranium ore. In combination with a strong mineral acid such point uranium ore. In combination with a strong mineral acid such as H2SO4, oxidants such as oxygen or hydrogen peroxide (H202) should be able to degrade the organic matter intimately associated with uranium in slow-leaching uranium ores, thus increasing exposure of the uranium mineral sites to contact by the leachate. Scoping batch leach tests showed that a leachate such as H2SO4 with H2O2 and with ferric ion added gave good racoveries at a fast rate from Crownpoint refractory ore. For detailed study of the H2SO4-oxygen system, a composite core was fabricated with ore segments from several wells in an area In which ore leached slowly with mild leachates. With this system, comprising 0.5% H2SO4, 24.5 gm/liter Na2SO4, 1 gm/liter NaCl and 0.2 gm/liter CO2 with 800 psig (~520 kPa) 02, 65% recovery of uranium was observed rapidly in about 30 pore volumes. This is almost double the recovery observed with a mild leaching system (02-NaHC03) in the same number of pore volumes. Plugging that occurred twice during the leach run appears related to movement of feldspar and quartz fines rather than gypsum deposition.

Oilfield Places:

- North America > United States > Wyoming > Shirley Basin (0.99)
- North America > United States > Wyoming > Powder River Basin (0.99)
- North America > United States > Montana > Powder River Basin (0.99)
- North America > United States > Montana > Lake Basin (0.98)

SPE Disciplines: