This paper presents a generalized correlation for predicting the minimum miscibility pressure (MMP) required for predicting the minimum miscibility pressure (MMP) required for multicontact miscible displacement of reservoir fluids by hydrocarbon, CO2, or N2 gas.
The equations are derived from graphical correlations given by Benham et al. and give MMP as a function of reservoir temperature, C7+ molecular weight of the oil, mole percent methane in the injection gas, and the molecular weight of the intermediates (C2 through C6) in the gas. CO2 and N2 are represented in the current correlation by "equivalent" methane/propane- and methane/ethane-mixture injection gases, respectively.
The study shows that for hydrocarbon systems, paraffinicity has an effect on MMP. In the equations, the C7+ paraffinicity has an effect on MMP. In the equations, the C7+ molecular weight of the oil is corrected to a K factor of 11.95, thereby accounting for varying paraffinicity.
An additional temperature effect on N2 MMP is related to the API gravity of the oil. The N2 correlation, however, is not tested against measured MMP data other than those used to develop the equation and should be used with care.
A correlation that accounts for the additional effect on CO2 MMP caused by the presence of intermediate components in the reservoir oil is presented.
Predicted MMP's from the correlations developed are compared to experimental slim-tube displacement data from the literature and from our displacement tests on North Sea gas/oil systems. These displacement tests have been performed with a packed slim tube, where the effect of viscous fingering is reduced to a minimum.
Multicontact miscibility is represented most easily with a ternary diagram, where the composition of the driving or displaced fluid is altered. This is obtained by vaporization of light hydrocarbon components into a driving gas or by condensation of hydrocarbon components from a driving gas into the reservoir oil. Miscibility between reservoir oils and hydrocarbon gases is achieved either by vaporization or by condensing-gas-drive mechanism, depending on the reservoir oil and injection-gas composition. With N2 and CO2, miscibility is obtained by vaporization, but with CO2, miscibility usually is achieved at lower pressure because CO2 extracts much higher-molecular-weight hydrocarbons from the reservoir oil than N2 gas.
The prediction of miscibility conditions from ternary diagrams is based on experimentally determined or calculated gas and liquid compositions of a reservoir-oil/injection-gas mixture. The experimental gas and liquid equilibrium data are not easy to obtain and are often time-consuming to determine, especially near the plait point. The method for calculating gas and liquid data with point. The method for calculating gas and liquid data with equations of state to predict miscibility relies largely on gas and liquid compositions near the plait-point region. It is generally accepted that such data may not be sufficiently accurate.
Flow experiments offer the most reliable method to determine the pressure required for miscibility with CO2, N 2, and hydrocarbon gas. The slim-tube method has been most widely used to determine miscibility. Different experimental procedures and interpretation criteria, however, have ted to different definitions of miscibility and have caused considerable confusion. The limitation of the slim-tube test and the problems associated with miscible displacement in porous media have been described by several authors. Phase behavior and mechanisms of miscible flooding with CO2, N2, and hydrocarbon gas have also been described by several authors.
Correlations for predicting MMP have been proposed by a number of investigators and are important tools in the selection of potential reservoirs for gas miscible flooding. Therefore, the correlations must be as accurate as possible.
Several CO2 MMP correlations have been published, but none of these can be used with enough published, but none of these can be used with enough confidence for final project design. They are useful, however, for screening and preliminary work. Correlations on CO2 miscible flooding have shown temperature to be the most important parameter but they disagree regarding the effect of oil type (e.g., C7+ properties of the oil).
Compared with CO2 miscible flooding, very little has been published on high-pressure hydrocarbon gas miscible flooding. A recent publication gives a correlation for predicting MMP with lean hydrocarbon gases and nitrogen.
In 1960, Benham et al. presented empirical curves that can estimate miscibility conditions for reservoir oils that are displaced by rich gas within a pressure range of 1,500 to 3,000 psia [10.34 to 20.68 MPa]. They assumed a limiting tie line (at the critical composition on a ternary diagram) parallel to the C1 -C7+ axis and estimated mole percent methane in the injection gas from calculated percent methane in the injection gas from calculated critical points with pressure, temperature, molecular weights of C2 through C4 in the gas, and the C5+ molecular weight of the oil as variables.
From Benham et al.'s data, the proposed equations have been derived for predicting MMP.
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.
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.
The fundamental linear partial differential equation (PDE) describing fluid flow in an infinite medium characterized by a radial-spherical symmetry is
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.
The quantity rsw is an equivalent or pseudospherical wellbore radius used to represent the actual cylindrical sink (or source) of radius rw.
Mobil Research and Development Corporation Field Research Laboratory Dallas, Texas
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.
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.
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.
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.
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.
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 prevails (1) during fluid production through either casing perforations or open hole and (2) during 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.
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 sandsi.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.
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.
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.
On September 1, 1981 the "Memorandum of Agreement between the Government of Canada and the Government of Alberta relating to Energy Pricing and Taxation" was signed. The Energy Agreement contains very complex oil and gas regulations. The purpose of this study is to provide an easy procedure by which Engineers and Corporate Planners could easily determine the economic limit for non-EOR projects in Alberta. The economic limit in this study is defined as the minimum average daily oil production rate needed to break-even on a Before and/or After Income Tax basis. The study utilizes the current, effective January 1, 1983, Canadian Oil and Gas taxes and royalties. The procedure to determine the economic limit is independent of the current taxes and royalty rates and thus can be used at any period of time.
The economic limit can be expressed by an easy to use set of equations. These equations are developed in the appendices. The values of the constants in the equations are determined by the tax rates, royalty factors, operating costs and wellhead price. Once the constants are calculated for a given project, it is then very simple to calculate the economic limit as well as perform sensitivity analysis for that project. These equations can be used in both the planning stages as well as in every day use in the area office.
The operating costs used in this study are completely arbitrary. They are not representative of any particular field or project. The intent of this paper is to develop and easy method by which a project can be evaluated. paper is to develop and easy method by which a project can be evaluated. It is not the intent of this paper to comment on the economics of any particular project in Alberta. particular project in Alberta. Both single well as well as unit's or project's economic limit can be evaluated by the method outlined below. In calculating the unit's or project's royalty rate an average monthly oil production rate per producer project's royalty rate an average monthly oil production rate per producer must be used.
Mobil Research and Development Corporation Field Research Laboratory Dallas, Texas
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.
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.
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.
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.
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.
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.
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.