Effect of Temperature on Oil/Water Relative Permeabilities of Unconsolidated and Consolidated Sands

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

Unsteady-State Spherical Flow With Storage and Skin

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

Determining Bottomhole Pressures in Pumping Wells

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:estimation of the superficial gas velocity,development of analytical solutions for a single-step BHP calculation, andcomparison 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

Alternatives to the Power-Law Fluid Model for Crosslinked Fluids

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 paper1 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 paper1 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 technique1 that was used to gather data for this study has been described previously. Dynamic mechanical testing provides a quantity - called the complex viscosity (µ*) - that has been shown by Cox and Merz2 to equal the apparent viscosity (µa) determined in steady-shear measurements. Yasuela et al.3 recently confirmed this relationship with a wide variety of instruments. Use of this relationship, coupled with the increased sensitivity and reproducibility of the mechanical spectrometer, allows an examination of the data analysis techniques currently used in the industry. The API4 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:data acquisition,analysis and data reduction, andscale-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 testing1 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:equivalent (apparent) Newtonian shear rate or viscosity,model-dependent conversions, andmodel-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 testing1 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:equivalent (apparent) Newtonian shear rate or viscosity,model-dependent conversions, andmodel-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.

Some Rock-Mechanical Aspects of Oil and Gas Well Completions

Elementary borehole- and perforation-stability problems in friable clastic formations for unrestricted fluid flow between reservoir rock and underground opening are treated on the basis of linear poroelastic theory. Thermal stress effects caused by a temperature difference between reservoir and borehole fluids can be predicted from the mathematical similarity of poro- and thermoelasticity. A tension-failure condition applies for the prediction of hydraulic fracture initiation in a formation around injection wells. The resulting equations are partially well-known. Similarly, a uniaxial compression-failure condition should predict perforation failure leading to sand influx in production wells. The major difference between these situations is that, at sufficient depth of burial, the tensile strength of a friable rock mass has only a minor effect on the fracturing pressure level, but the actual value of the compressive strength plays a crucial role in the prediction of sand-influx conditions. Practical suggestions for resolving the latter are given. Introduction This paper discusses borehole- and perforation-stability problems as encountered in friable sandstone formations that have in common free fluid flow between a reservoir and an underground opening. Such a condition prevailsduring fluid production through either casing perforations or open hole andduring injection of fluids into a reservoir for pressure maintenance, gas conservation, tertiary oil recovery, or well stimulation. In the absence of a membrane (such as a filter cake) at the rock/hole interface, the effective stress normal to the rock surface is zero. Rock failure can result either in tension during fluid injection or in compression during fluid production. Because one of the principal effective stresses (the radial stress) is zero and the effect of the intermediate principal effective stress is small, failure is of either the unconfined tension or compression type. Rock failure resulting from fluid production from friable sandstones causes sand-particle influx. Failure caused by fluid injection means either planned or unintentional formation fracturing. The production technologist has to foresee such failure conditions as a function of changes in the stress regime with time. He has to start with a best possible estimate of the initial in-situ state of stress. On the basis of log data and core sample analysis, relevant rock deformation and strength properties must be determined next. Finally, an estimate of changes in the stress field resulting from prolonged production or injection must be made. Problem Areas Formation Particle Influx in Production Wells. Although significant improvements have been made in well-completion techniques aimed at sand-particle retention by both gravel packing and sand consolidation, straightforward production through casing perforations is the preferred production method because of minimum costs and maximum usage of well-flow potential. Moreoever, gravel packing long intervals of strongly deviated holes remains a difficult, expensive operation to perform, while sand consolidation processes for oil wells at temperatures above 75 degrees C [167 degrees F] are not available commercially. Friable formation sands i.e., formations that have some strength of their own-do not necessarily present a sand-influx problem initially. Sand production may develop gradually in time, once total drawdown increases and/or water breakthrough occurs. Deviated boreholes may encounter less favorable stress concentrations around perforations than vertical holes. All in all, it is necessary to predict the sand-influx potential of a well as soon as possible after drilling to serve as a basis for a completion policy. A perforation pattern that both results in production from only the more competent zones and enables delivery of the required well production capacity could be implemented. Formation Fracturing Around Injection Wells. A familiar type of formation failure is fracturing in tension around injection wells. Formation fracturing always occurs when the injection pressure surpasses the formation breakdown pressurei.e., the fluid pressure that brings the hoop stress around the opening in a tension equal to the tensile strength. Once initiated at or below this pressure level (because the formation may contain natural fractures), fracturing proceeds while the injection pressure surpasses the least principal in-situ total stress. The instantaneous shut-in pressure recorded during or after a fracturing job provides the best value of the least principal total stress component. The in-situ state of stress is not necessarily a constant during the production life of a reservoir. Changes both in reservoir pressure and in temperature adjacent to a well affect the local stress field in the formation. The effect of reservoir pressure variations on formation fracturing potential is well-known. Breckels and van Eekelen explicitly account for this effect. It is less recognized that in deeper formations cooling of the borehole surroundings by injection of liquids at near-surface temperature causes reservoir-rock shrinkage, leading to a reduction in both fracture initiation and propagation pressure. SPEJ P. 848^

Reduction of Grid-Orientation Effects in Reservoir Simulation With Generalized Upstream Weighting

A generalization of upstream weighting is proposed as a method for reducing grid-orientation effects in reservoir simulation. For the two sample problems studied,. a piston-flow waterflood and a realistic gas injection, the piston-flow waterflood and a realistic gas injection, the grid-orientation effect was almost completely eliminated. The new generalized upstream weighting (GUW) method is particularly attractive because it is fast and accurate, and particularly attractive because it is fast and accurate, and can be added easily to an existing simulator that uses upstream weighting. Introduction The grid-orientation effect is a well-known phenomenon in finite-difference reservoir simulation. Numerical results are highly dependent on the orientation of the finite-difference grid imposed on the model. In practice it occurs whenever one has a strongly adverse mobility ratio. This happens when one tries to push a viscous oil with a highly mobile fluid, such as steam or hydrocarbon gas. This paper presents a technique for reducing grid-orientation effects that is fast, flexible, and easily added to an existing simulator. A good survey of the research in this area was recently published. With this in mind, we will give an published. With this in mind, we will give an idiosyncratic interpretation of some of the techniques suggested by others. The main numerical difficulty in petroleum reservoir simulation is largely a consequence of the need to estimate individual phase mobilities halfway between finite-difference gridpoints. Because averaging the values from adjacent gridpoints is numerically unstable, the midgridpoint typically is assigned the value at the next upstream point. The idea of looking upstream for information point. The idea of looking upstream for information is found throughout much of computational fluid dynamics. Many improvements on one-point upstream weighting have been proposed in the reservoir simulation literature. The principal attractions of these techniques are that they can be interchanged easily within existing computer codes and do not add significantly to computation time. We found that the upstream weighting procedures have a common feature. If the midgridpoint in procedures have a common feature. If the midgridpoint in question lies, for example, on a grid line in the x direction, these techniques consider only other points on this same grid line in the extrapolation/interpolation process. A second body of literature developed around the idea of using a nine-point (instead of the standard five-point) finite-difference scheme to represent two-dimensional (2D) second derivatives. Because the nine-point scheme is a weighted superposition of two 5-point grids with a common center point and a 45 * relative rotation, the procedure averages away the grid-orientation effect to some extent without explaining it. Nevertheless, the nine-point grid schemes include one attractive feature absent from the upstream schemes: the weighting parameter can be tuned to improve the quality of the results. parameter can be tuned to improve the quality of the results. Perhaps the biggest fault of these procedures is that they Perhaps the biggest fault of these procedures is that they do not extend easily to three dimensions. The widening of the matrix bandwidth also increases the computation time. Our proposed technique is a modification of a procedure used successfully in the convective-heat transfer literature. It amounts to a generalization of one-point upstream weighting, accomplished by the introduction of mobility values from nearby points that lie in the true upstream direction rather than along a single grid line. This is explained in more detail in the next section. Note that the technique requires very little computer time. In fact, because most reservoir simulators use an automatic timestep adjustment, the improved stability of the technique, relative to standard upstream procedures, allows larger timesteps to be taken. Also, two adjustable parameters that permit the grid-orientation effect to be almost parameters that permit the grid-orientation effect to be almost completely eliminated are introduced. Finally, because the procedure works well with the standard five-point finite-difference representation of 2D second derivatives, it generates easily to three dimensions and is completely compatible with most reservoir simulators. Governing Equations The conservation equations for multiphase fluid flow in porous media are well known. However, the porous media are well known. However, the equations for three-phase flow are listed below for completeness. The continuity equations are as follows. SPEJ P. 902

Solubility of Silica in Alkaline Solutions: Implications for Alkaline Flooding

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 thatthe 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, andloss 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

In-Situ Leaching Of Crownpoint, New Mexico, Uranium Ore. III. Laboratory Study Of Strong Leaching Systems: Sodium Hypochlorite

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.

Water/Oil Displacement Characteristics in Crossbedded Reservoir Zones

Kortekaas, T.F.M., SPE, Shell Research B.V. Abstract Festoon crossbedding is a typical sedimentary structure in sandstone reservoirs. It is especially common in fluvial deposits. The important elements are the foreset laminae, which vary in permeability, and the bottomsets of lower permeability. To understand the complex, direction-dependent displacement characteristics of a crossbedded reservoir zone, we first conducted numerical simulations on a centimeter scale in a small part of a water-wet crossbedded reservoir zone. The simulations indicate that, during water/oil displacement, considerable amounts of movable oil initially are left behind in the higher-permeability foreset laminae with fluid flow perpendicular to the foreset laminae, while with flow parallel to the foreset laminae the displacement efficiency is good. To describe the displacement characteristics on a reservoir scale, we developed a procedure for calculating direction-dependent pseudo relative-permeability and capillary-pressure curves to be used as input for the simulations of water/oil displacement in a crossbedded reservoir zone. On a reservoir scale, the displacement characteristics in a water-wet crossbedded reservoir zone are slightly more favorable with the main fluid flow perpendicular to the foreset laminae. perpendicular to the foreset laminae. In addition, the sensitivity of the displacement characteristics to moderate reductions in interfacial tensions (IFT's) and to increases in water viscosity was investigated, both on a centimeter scale and on a reservoir scale. The simulations indicate the potential for substantial improvement in recovery from crossbedded reservoir zones if diluted surfactant or polymer is added to the drive water. Introduction Detailed studies of the effect of reservoir heterogeneities on water/oil displacement characteristics have been conducted on a well-to-well (layering) scale and on a pore scale, but few studies on an intermediate scale have been done. Therefore, we embarked on a study of the effect of centimeter-scale heterogeneities on water/oil displacement characteristics. We studied festoon crossbedding, one of the typical sedimentary structures in sandstone reservoirs, particularly common in fluvial deposits. A schematic particularly common in fluvial deposits. A schematic representation of a small part of a crossbedded reservoir zone is given in Fig. 1A. The important elements are the foreset laminae, which vary in permeability, and the bottom-sets, which are of lower permeability. The width of the foreset laminae is exaggerated in Fig. 1A; typically it is a few centimeters. First, we will discuss a mathematical simulation study in a very limited area of a water-wet crossbedded reservoir zone (1.97 × 26.2 × 0.66 ft [0.6 × 8 × O.2 m]). After a brief discussion of the water/oil displacement characteristics near a single permeability transition, we present the water/oil displacement characteristics in some cross sections of a simplified model (Fig. 1B) of a small part of a crossbedded reservoir zone. In addition, their sensitivity to moderate reductions in IFT's and increases in water viscosity are discussed. Second, we describe the effect of crossbedding on water/oil displacement characteristics on a reservoir scale, discuss a procedure for calculating dynamic, direction-dependent pseudo relative-permeability and capillary-pressure curves, and present the results of a reservoir-scale mathematical simulation study, including the pseudo-properties. Also, the sensitivity of the results to changes pseudo-properties. Also, the sensitivity of the results to changes in IFT and water viscosity is discussed. One-Dimensional Water/Oil Displacement Characteristics Near an Abrupt Permeability Transition Permeability Transition suppose we have a one-dimensional (1D) system consisting of two zones with different absolute, but identical relative, permeabilities. Furthermore, the system is horizontal and contains oil and connate water. The Buckley-Leverett first-order partial differential equation describes the water/oil displacement in each zone.In the absence of capillary and gravitational forces, the water fractional flow Fwo) is given byEq. 1, together with Eq. 2, usually leads to a sharp shock front: at each location, water saturation will instantaneously jump from connate water to shock-front saturation when the water arrives. SPEJ p. 917

Pressure Transient Analysis in an Elongated Linear Flow System

Prominent examples of linear flow behavior in-the well test Prominent examples of linear flow behavior in-the well test literature describe flow within or to a fracture penetrated by a producing well. The characteristic pressure transients generally producing well. The characteristic pressure transients generally are exhibited in the early portion of a well test and are followed by infinite-acting radial flow behavior and/or boundary effects. In contrast, if a formation is of a predominantly linear shape, linear flow is expected to develop in late time. In this paper, analyses of interference, drawdown, and buildup tests that are applicable to linear flow systems are described theoretically and illustrated by practical examples. The necessary equations for the analyses are provided for testing oil, gas, and geothermal steam wells. In elongated linear flow systems, the pressure transient behavior associated with linear flow occurs late in the drawdown or buildup test. The type curves provided in this work show that this pressure behavior is distinguishable from conventional well tests, pressure behavior is distinguishable from conventional well tests, particularly in interference tests. particularly in interference tests. Introduction Interest in linear flow geometry was limited for a long time to water influx applications. Miller I provided solutions for pressure distributions in semi-infinite- or finite-length linear pressure distributions in semi-infinite- or finite-length linear aquifers assuming water influx into the oil zone at a constant flow rate. Ehlig-Economides et al. 2 and Ehlig-Economides and Economides recently developed methods for analyzing geothermal well tests in a predominantly linear flow system. This work was motivated by the presence of parallel linear faults that are predominant in geothermal regions, such as the one shown in Fig. 1. Methods for interference analysis and for drawdown testing of geothermal steam wells were presented. Linear flow geometry currently is cited as a fairly common occurrence in low-permeability gas fields. Kohlhaas et al. provided a case study of linear flow behavior for a gas well completed in a channel-like reservoir and equations for analyzing the linear flow portion of drawdown and buildup tests. Stright and Gordon examined rate-decline behavior in gas wells in the Piceance basin in northwest Colorado that exhibited apparent linear flow behavior. In one case, the well penetrated a fracture in a low-permeability marine sand in which a number of long, natural fractures were present and appeared to be related to extensive faulting in the area. In another case, the well was completed in a long, narrow sand body shown by outcrops in the same area. A recent paper by Nutakki and Mattar provided solutions for drawdown vs. time for linear flow geometry. The solutions are identical to the work done by Ehlig-Economides and Economides for geothermal steam wells. However, the method of analysis, which made use of a "pseudoskin" factor, was distinctly different. In this paper, the previous methods of interference and drawdown analysis for geothermal wells in a linear flow system are reintroduced with additional coefficients for oil- and gas-well testing. In another paper, the drawdown behavior of fractured wells in the predominantly linear flow system is presented in detail. Theory In Fig. 1, the geological map from a geothermal region shows linear faults running parallel for several hundred feet. If the regional faults provide impermeable boundaries to flow, then a particular well may drain a volume best described as a long, narrow particular well may drain a volume best described as a long, narrow channel. In Fig. 2, schematics of several types of depositional environments show possible oil- and gas-reservoir geometries that would result in predominantly linear flow. These formations, which generally are long, narrow shapes, may be the results of river meander point bars, oxbow lakes, river channels, or tectonic breccias. The model used for this work employs the diffusivity equation, which requires assumptions concerning the formation and fluid properties, such as homogeneous and isotropic formation, horizontal monophasic Darcy flow, fluid of small and constant compressibility, and constant viscosity. The boundary conditions and appropriate dimensionless variables are defined separately for interference analysis and for drawdown/buildup analysis. Interference Analysis For interference analysis, the active well is located at the center of a rectangular cylinder of infinite length and is approximated by a planar source, as depicted in Fig. 3. The cross section of the cylinder is assumed to be a rectangle with height h and width b. The planar source boundary condition for the linear flow model is analogous to the vertical line source for horizontal radial flow. For drawdown analysis, a model incorporating wellbore storage and skin is required, as will be discussed later in this paper. SPEJ P. 839