Material Balance Calculations Research Articles

Subsurface ammonium maxima in Northern Bay of Bengal

Chemical oceanographic data collected on RV Gaveshani cruises 181 and 182 in the Bay of Bengal during March–April, 1987 showed subsurface ammonium maxima in the water column in northern Bay of Bengal. While there is no regular trend either in horizontal or in vertical distribution of ammonium in the central Bay (Lat. 12–14°N), two prominent maxima, one in the euphotic zone near the oxycline (75–150 m) and the other in the oxygen deficient zone (400–600 m) are observed in the vertical distribution of ammonium in the northern Bay of Bengal (Lat. 18–20°N). The subsurface maximum (2·0–3·5 μmol dm −3) in the euphotic zone is attributed to the regeneration of ammonium by zooplankton excretion associated with the stratification of water column during summer (spring). The spatial distribution of recycled nitrogen (ammonium) along the transects showed an increasing trend of regenerated nitrogen from inshore to offshore regions in the northern Bay. The second ammonium maximum (4·0–6·0 μmol dm −3) observed in oxygen deficient region (< 50 μmol dm −3) is assumed to be due to the bacterial reduction of nitrate to ammonium in the denitrification process. Nitrate deficits ( ΔN = 9–12 μmol dm −3) derived from material balance calculations are in close agreement with those reported earlier. Nitrogen transformations in the water column are schematically represented by distinguishing three zones of biological activity on the basis of oxygen concentration levels.

The Sean North and Sean South Fields, Block 49/25a, UK North Sea

Abstract Sean North and Sean South are two small prolific gas fields located on the Indefatigable Shelf in the Southern North Sea. They, like most of the other fields in the area, have a Carboniferous source, a Rotliegend aeolian sandstone reservoir and a Zechstein evaporite cap rock. They have been developed to fullfil a peak-shaving role, being produced for only a few days per year in times of high gas demand when they produce at a rate of 600 MMSCFD. Initially thought to be two equally sized accumulations, there is now some evidence from material balance calculations that the Sean South is bigger than North Sean. The contractual recoverable reserves for the two fields are 425 BCF.

Dynamic Leakage of Faults During Differential Depletion: Theory, Models, and Examples from the Niger Delta

Previous studies of fault sealing have addressed possible fault leakage during secondary migration due to the effects of increased hydrocarbon-water capillary pressure, fracturing, or small-scale incremental fault movements. Of equal importance to production geologists is the failure and leakage of faults during field development due to differential depletion of adjacent fault blocks. This paper examines the unique problems associated with this dynamic leakage of faults. It is theoretically shown that the fault sealing mechanism, and the extent of the seal, directly influences the failure process which in turn results in a variety of favorable and unfavorable effects on field development. The qualitative models give considerable insight into such aspects as oil-column expansion and resaturation losses, interfault block aquifer support (with important implications to material balance calculations), possible leakage or spillage of oil across faults, and potential fault failure during (re)injection projects. Examples of dynamic fault leakage are presented from selected fields of the Niger delta.

Reservoir Simulation (includes associated papers 21606 and 21620 )

"... the precision with which variations In reservoir properties can be modeled Is determined by the number of blocks In the model." Introduction In the past 30 years, reservoir simulation has evolved from a research area into one of the most flexible and widely used tools in reservoir engineering. Use of reservoir simulation has grown because of its ability to predict the future performance of oil and gas reservoirs over a wide range of operating conditions. Reservoir simulators use numerical methods and high-speed computers to model multidimensional fluid flow in reservoir rock. Reliable simulators and adequate computing capacity are available to most reservoir engineers, so simulation is usually practical for all reservoir sizes and all types of reservoir performance studies. Although the use of simulation frequently is optional, it may be the only reliable way to predict the performance of a large, complex reservoir, especially if such external considerations as government regulations influence the production schedule. Even for small reservoirs where simple calculations or extrapolations may be adequate, simulation is often faster, cheaper, and more reliable than alternative methods for predicting performance. Modeling Concepts A reservoir simulator models a reservoir as if it were divided into a number of individual blocks (gridblocks). Each block corresponds to a designated location in the reservoir and is assigned properties-porosity, permeability, relative permeability, etc. -believed to be representative of the reservoir at that location. In the simulator, fluids can flow between neighboring blocks at a rate determined by pressure differences between blocks and flow properties assigned to the interfaces between blocks. In essence, the mathematical problem is reduced to a calculation of flow between adjacent blocks. For every block-to-block interface, a set of equations must be solved to calculate the flow of all mobile phases. The equations generally incorporate Darcy's law and the concept of material balance and contain terms describing the permeability "between" blocks, fluid mobilities (relative permeability and viscosity), and rock and fluid compressibilities. Fig. 1 illustrates the most common types of models used in simulation. Models range in complexity from a single block, useful only for classical material-balance calculations, to fully 3D models capable of modeling all major factors that influence reservoir performance. Each gridblock in a model has only one set of properties; there is no variation in any property within a block. For example, phase saturations in a model block will be volumetric averages of the saturations in that part of the reservoir represented by the block. In this respect, a model block can be visualized as a well-stiffed tank (i.e., its contents are homogeneous)connected to adjacent tanks with pipes whose flow capacities are determined by reservoir flow properties. This visualization, although simplistic, demonstrates that the precision with which variations in reservoir properties can be modeled is determined by the number of blocks in the model. A simulator also divides the life of a reservoir into discrete increments. Changes in a reservoir (pressure, saturation, etc.) are computed over each of many time increments, or timesteps. Conditions are defined only at the beginning and end of each timestep; nothing is defined at any intermediate time within a time interval. The accuracy with which reservoir behavior can be calculated generally will be influenced by the length of the timesteps as well as the number of gridblocks. The preceding discussion implies that for any size gridblock and any length of timestep, there will always be abrupt changes in reservoir conditions from one block to the next and from one timestep to the next. Fig. 2 illustrates this point. At the top of Fig. 2 are plan views of a hypothetical two-well reservoir being waterflooded and a four-gridblock simulator model of the reservoir. The two plots show-water-saturation distribution at a given time in both the reservoir and the model. JPT P. 692⁁

Recovery of Mineral Salts and Potable Water from Desalting Plant Effluents by Evaporation. Part II. Proposed Simulation System for Salt Recovery

Abstract Salt recovery from rejected brines of the Al-Khobar Water Desalination Plant, Saudi Arabia, is studied through the simulation of a modified MSF system. Two phases of concentrations are planned: Phase I will concentrate the main effluent from 6.4 wt% total salt to 28.8%, while Phase II will use the effluents from Phase I as a feed to undergo further evaporation and cooling. NaCl and water are produced throughout this phase, while the end residue product will be essentially MgCl2, since it is the most soluble. A mathematical model is developed and used to perform stage-to-stage material and heat balance calculations. Concentrations of NaCl and MgCl2 in the streams entering and leaving a stage are determined by using the solubility correlation developed in Part I. Simulation results show that by using 5210 tons/h brine as a feed for Phase I, we can recover 4430 tons/h fresh water, 277 tons/h NaCl, and 502 tons/h bittern (in which the ratio of MgCl2/NaCl is increased to 12) as the very final products of the integrated scheme. This bittern provides 30 tons/h MgCl2 as an end product.

Beryllium isotopes in the ocean.

Vertical profiles of 9Be and 10Be have been determined in the ocean. The nutrient-like recycling behavior for both Be isotopes, involving surface scavenging and deep-water regeneration, is manifested by their vertical profiles in the borderland basin off southern California, in the Pacific and in the Bering Sea. In contrast, in the western N. Atlantic, the concentrations of 9Be are almost vertically constant (or slightly higher in the surface than in the deep), and the concentrations of 10Be generally show minor surface depletion and are lower than those of the Pacific. The 9Be profiles in the S. Atlantic are generally similar to those of the Pacific except for a station close to the plume of Saharan desert dust, which shows surface enrichment. We interpret the vertical distributions and their differences among stations in terms of intense surface 9Be input (especially eolian input) to the Atlantic, a relatively uniform oceanwide pluvial input of 10Be, the particle reactive nature of Be, and the oceanic residence time of Be. Material balance calculations using a two-box (coastal and open oceans) model point to the importance of coastal ocean as a sink for both Be isotopes and eolian dusts as a source of oceanic 9Be.

Rose City: A Synergistic Approach to Proration of a Prairie du Chien Field, Ogemaw County, Michigan: ABSTRACT

Proration of gas fields in Michigan is required by law and is regulated by the Michigan Public Service Commission (MPSC). The recent discovery of Prairie du Chien (Ordovician) gas reservoirs necessitate redefining proration rules, formulas, and assumptions. Existing proration standards predicated on the Niagaran (Silurian) Pinnacle reef play are not appropriate for the Prairie du Chien. Shell Western prepared a proposal for proration of the Rose City field, Ogemaw County, Michigan, that was accepted by the working interest owners and presented to the MPSC. The proposal is based on a comprehensive, synergistic subsurface study that will help set the standards for proration of other Prairie du Chien fields. To accomplish the authors goal of presenting the first thorough proration proposal to the MPSC, a multidisciplinary approach was used to analyze the extensive data available at Rose City. Examination of cores and thin sections from three of the seven wells in the field led to the definition of five lithofacies. Petrophysical responses could be related to lithofacies type. The lithofacies distributions and calibrated log responses were combined with seismic structural interpretations to characterize the reservoir system and map the distribution of hydrocarbon-bearing pore volume (SgOeH). A computer mapping program was usedmore » for manipulating data, calculating volumetrics, and preparing display. Volumetrics and material balance calculations of original gas in place agreed within 10%, which is considered excellent. As a result, proration methods proposed for Rose City are based solely on underlain hydrocarbon pore volume (ASgOeH). This approach is being applied to other multiwell Prairie du Chien fields to ensure equity and improve ultimate recovery.« less

Estimation of Solution GOR of Black Oils

Summary. An empirical equation was developed to estimate stock-tank GOR from field data for black oils. Solution GOR at or above bubblepoint pressure can be obtained as the sum of the estimated stock-tank GOR and the measured separator GOR. The equation was derived with data from two-stage separations of 301 black-oil samples. Introduction Volumetric and material-balance calculations of oil in place require estimates of oil FVF and bubblepoint pressure. Several correlations, the most applicable of which was proposed by Standing, I are available for determining bubblepoint pressure and oil FVF when an estimate of solution GOR is available. Frequently solution GOR, Rsb, is estimated for pressures at or above the bubblepoint by setting its value equal to the initial producing GOR. However, the initial producing GOR often does not include gas vented from the stock tank. This omission can cause the estimate of Rsb to be low by 20 % or more. 2 The inaccurate estimate of Rsb then introduces error into estimates of bubblepoint pressure and FVF, and hence into oil-in-place calculations. This paper presents a method of using readily available field data to obtain an accurate estimate of Rsb. Total producing GOR, R, is equal to the sum of stocktank GOR, Rst, and separator GOR, Rsp.

A SIMPLER METHOD FOR FINDING INDEPENDENT REACTIONS

An improved method of matrix transform is provided for finding independent reactions and independent stoichiometric restrictions of a chemical reaction system. This method can deal with various reaction systems without the difficulties that occurred with the usual methods. Two different restrictive conditions among the components are discussed. It has been emphasized that the concept of extent of independent reaction is not necessary for material balance calculation and may confuse an actual reaction system. Some typical examples illustrate the simplicity and versatility of the new method.

The New Engineer Paradigm and the Emergence of Investigative Engineering

Summary How is engineering practiced in the petroleum practiced in the petroleum engineering discipline? A new engineering paradigm that defines and distinguishes between three overlapping regions-operational, design, and investigative engineering-will help us understand. It introduces the concept of investigative engineering, the key to new engineering breakthroughs and innovations. Here, we investigate the impact of investigative engineering on the petroleum engineering discipline and discuss the roles of the university educator, company organizations and structures, and the individual engineer. Two postulates are proposed. First, most engineers receive inadequate training in investigative engineering at the university level, so that they resist the concept later in their career. Second, most companies are structured to operate in the domain of operational and design engineering, with little or no emphasis on investigative engineering. This paper identifies characteristics necessary to achieve success in the investigative-engineering endeavor and proposes organizational structures that proposes organizational structures that will encourage investigative engineering in the corporate environment. Introduction How can universities and companies revitalize the engineering professional to meet the challenges and changes that will occur during the next decade? Is it possible to make engineers more productive, innovative, and effective in maximizing the company's profits? What tools do engineers need to do profits? What tools do engineers need to do their jobs? How should they be trained and supervised? And finally, what type of organizational structure will optimize engineers' skills? What about the engineers themselves? What should be their roles in the future? Can an engineer build a life-long career path around technical leadership? And what about technical obsolescence-what can be done to keep the 10- and 15-year experienced engineer up to date, motivated, and challenged? To address these questions, one must investigate the way that companies, especially energy companies, use engineers' abilities and practice engineering. This identifies new ways in which engineering can be practiced and defines the characteristics of the engineer of the future. This work is based primarily on my nearly 24 years of experience as a practicing engineer and as a technical supervisor and manager of both operations and research. It also draws from a 6-year in-depth study of engineering practices. My active involvement in SPE, which has provided me with many long and penetrating conversations with other engineers about the practice of engineering and their personal views of themselves as engineers, has strongly influenced this work. The detailed basis and background for all the concepts presented are too lengthy to be explained here. Those readers interested in obtaining more background should explore Refs. 1 through 7. Many of the concepts are completely new and may be provocative, and to that end, I do not expect across-the-board agreement. I do not pretend to have all the answers and to know all the details. I am a student of this technology and can give only my cumulative insights at this point in time. Current Engineering Paradigm First of all, what does "paradigm" mean? This is a relatively new word in engineering that has drawn a great deal of interest and attention, as well as multiple definitions. In my opinion, the best definition comes from Fritjof Capra, a physicist at Lawrence Berkeley Laboratory, and Jay Ogilvy, director of research for the Values and Lifestyles Program at SRI Intl. They define paradigm as "a constellation of concepts, paradigm as "a constellation of concepts, values, perceptions, and practices shared by a community, which forms a particular vision of reality and collective mood that is the basis of the way the community organizes itself." In short, it is a model for describing how a selected group of people work together. In our case, the engineering community in general and the petroleum engineering community in specific are of interest. The community is made up of engineers, supervisors, and managers, including all upper managers who affect engineering practices. Fig. 1 depicts how the community organizes itself. Engineering generally can be divided into three major areas:accounting, administrative, and assembly-line engineering, defined as operational engineering (OE);design engineering (DE); andinvestigative engineering (IE). OE comprises all accounting, administrative, and assembly-line engineering tasks that can be reduced to a step-by-step procedure with known rules, procedures, procedure with known rules, procedures, calculations, reports, and practices. Examples of these tasks are material-balance calculations; decline-curve analyses; many economics calculations; basic pressure-transient analyses; hydraulics pressure-transient analyses; hydraulics calculations; cementing volumetrics; and generation of various intercompany forms, forms for agencies, morning reports, and other periodical reports. DE comprises all engineering tasks that pertain to designing any practice, system, structure, or set of equipment, no matter how complex. JPT P. 788

An Improved Method for the Determination of the Reservoir-Gas Specific Gravity for Retrograde Gases (includes associated papers 20006 and 20010 )

A method is presented that provides an improved estimate of the reservoir-gas specific gravity for retrograde-gas reservoirs from field production information. This method offers several improvements over previous methods. First, a new term has been introduced into the gas-gravity equation in order to emulate the exact solution of the equation. This term, the additional gas production, G/sub pa/, accounts for the gas production from the low-pressure separator and stock tank. Second, a correlation for the vapor equivalent of the primary-separator liquid, V/sub eq/, has been improved. And third, G/sub pa/ and V/sub eq/ correlations were developed for both two-stage and three-stage separation systems. These correlations were developed with the flash liberation results from 234 laboratory fluid analyses. The models were fit to the data by nonlinear regression. The estimate of the reservoir-gas specific gravity is significantly improved by incorporating the new G/sub pa/ and improved V/sub eq/ correlations into the gas-gravity equation. Also, the improved V/sub eq/ correlation, which accounts for the low-pressure separator gas, stock-tank gas, and rock-tank liquid production, can be used to obtain better estimates of reservoir fluid withdrawal.

Fast pyrolysis of sawdust in an entrained flow reactor

Fast pyrolysis of sawdust was investigated over a temperature range of 1000–1400 °C, a particle residence time of 0.56–1.0 s, and particle size fractions ranging from 250 to 630 μm. A medium-c.v. gas was produced throughout the course of the investigation. For most experiments, material balance calculations showed that more than 87 % of the sawdust fed into the system was accounted for in the product streams. With the exception of the lowest temperature and shortest residence time, the calculated cold gas efficiency was over 70% for all the experiments, with an average of ≈79%. At higher temperatures no tar was observed.

Evaluation of direct methane conversion to higher hydrocarbons and oxygenates

This report describes evaluation studies on processes that directly convert methane to higher hydrocarbons and oxygenates. The detailed evaluation includes designs of base and sensitivity cases, heat and material balance calculations of the thermal and carbon efficiencies, and the process duties.

Reliability of material balance calculations a sensitivity approach

Material balance packages are used to estimate unmeasured variables and upgrade the measured ones in mineral processing plants. The reliability of such estimates strongly depends on the data structure. Their variance-covariance matrix is here derived to evaluate the reliability of estimated flowrates, dilutions, particle size distributions and chemical assays. A relationship is shown to relate estimates reliability to the degree of redundancy of data. An illustration is given for a flotation plant.

Use of liquid phase tracers in material balance calculations

A relatively inexpensive and reliable method of using liquid phase tracers to aid in the solution of material balance problems is introduced. The method is of value in situations where one is required to calculate a material balance around a process that has the operating appearance of a “blender” or “splitter” with respect to the available slurry sample data. The paper briefly reviews material balance development and tracer applications in mineral processing, introduces the problem to be addressed, and provides both theoretical and industrial evidence establishing the potential of the method.

Extreme hydrogen, oxygen and carbon isotope anomalies in the pore waters and carbonates of the sediments and basalts from the Norwegian Sea: Methane and hydrogen from the mantle?

Abstract D H ratios in the pore waters of the sediments from the Norwegian Sea decrease as a function of depth to values as low as −14%. Oxygen isotope ratios in the pore waters and carbon and oxygen isotope ratios in carbonates both in the sediments and basalts are low. Extensive alteration of basalt has been given as the explanation for the low oxygen isotope ratios. Material balance calculations suggest that alteration of volcanic material and oxidation of organic matter cannot explain the hydrogen and carbon isotope anomalies. Arguments are presented suggesting that methane and hydrogen from the mantle are oxidized to carbon dioxide and water by sulfate and ferric iron in the basaltic crust to yield the low hydrogen and carbon isotope ratios.

Drainage Performance and Capillary- Pressure Curves With a New Centrifuge

Summary A new centrifuge has been used to measure the drainage performance and the drainage capillary-pressure function, P, of various rock samples. The permeabilities of the rocks used for this study range from 0.1 to 700 md. A unique feature of the apparatus is that the rock sample is always in contact with the wetting phase at the outlet face so that the saturation boundary condition is known at this end. The drainage performance and P data for a variety of reservoir rock samples reported in this paper are expected to provide the basis for added insight into the drainage of oil from porous media. Introduction Gravity drainage is believed to be one of the most effective processes of producing oil reservoirs. In some of Iran's giant fractured processes of producing oil reservoirs. In some of Iran's giant fractured reservoirs where oil has been produced for several decades and the reservoir has been subject to both waterdrive from the bottom region and gravity-drainage mechanism from the top region, material-balance calculations indicate higher oil recoveries in the gravity- drainage areas than the water-displacement regions. As an example, one particular reservoir has a bottomwater-drive oil recovery efficiency of about 30%, whereas the top gravity-drainage-zone efficiency is some 45 % (these reservoirs have low matrix permeabilities on the order of 1 md and oil columns ranging from 1,000 to several thousand feet thick). Many papers have been published that describe high recovery efficiencies where gravity effects influence the production mechanism. In an early paper, Katz reported recoveries of more than 90% from a completely drained portion of the Oklahoma City Wilcox sand. Haldorsen et al. recently revealed recoveries on the order of 60% for the gravity-drainage areas of the Prudhoe Bay field. The understanding of the gravity-drainage mechanism is not as complete as that of other production processes. Relative permeability and capillary pressure are believed to be the two major permeability and capillary pressure are believed to be the two major parameters that determine the recovery performance of a porous parameters that determine the recovery performance of a porous medium for this process. Data in the form of drainage capillary pressure and drainage performance of various rock samples will pressure and drainage performance of various rock samples will provide the basis for added insight into the oil drainage from porous provide the basis for added insight into the oil drainage from porous media. Dykstra reviewed the limited experimental data on drainage performance of unconsolidated sand columns in his examination of the theory of gravity drainage. He commented that the data lacked some required information (i.e., permeability, fluid properties). Dykstra further suggested a more thorough research effort to obtain all required information. For consolidated porous media and for permeabilities less than 100 to 500 md, the gravity-drainage data are basically measured from centrifuge runs. Marx used a centrifuge to establish the gravity-drainage performance of a Torpedo sandstone of 1.15-in. [2.92-cm] length. He also measured the drainage performance of the same rock with a length of 60.63 in. [154 cm] in the normal gravity field. Marx's experiments showed that recovery data from the centrifuge and normal gravity environment compare well when the time is scaled. He did not report pertinent fluid and rock data. Hagoort reported the pertinent fluid and rock data. Hagoort reported the gravity-drainage performance of nine core samples with permeabilities ranging from 40 to 2,400 md when a centrifuge was used. Capillary-pressure curves were not measured for these core samples. The purpose of this research project is to provide experimental data on the gravity-drainage performance and drainage capillary pressure of a variety of sandstone, limestone, and dolomite reservoir pressure of a variety of sandstone, limestone, and dolomite reservoir rock samples by use of a new centrifuge. Two of the core samples have been selected to examine the effect of capillary pressure on wetting- and nonwetting-phase relative permeabilities. The result of this study are presented elsewhere.

PVT Correlations for Middle East Crude Oils

Summary. Empirical equations for estimating bubblepoint pressure, oil FVF at bubblepoint pressure, and total FVF for Middle East crude oils were derived as a function of reservoir temperature, total surface gas relative density, solution GOR, and stock-tank oil relative density. These empirical equations should he valid for all types of oil and gas mixtures with properties falling within the range of the data used in this study. properties falling within the range of the data used in this study. Introduction PVT correlations are important tools in reservoir-performance PVT correlations are important tools in reservoir-performance calculations. The major use of PVT data is in carrying out material-balance calculations. In 1947, Standing published correlations for determining the bubblepoint pressure and FVF from known values of temperature, solution GOR, gas relative density, and oil API gravity. A total of 105 experimentally determined data points on 22 different crude oil and gas mixtures from California were used in deriving the correlations. Standing reported an average relative error of 4.8% for the bubblepoint pressure correlation and an average relative error of 1.17% for the FVF correlation. In 1980, Glaso presented correlations for calculating bubblepoint pressure, oil FVF, and total FVF from known values of temperature, solution GOR, gas relative density, and oil API gravity. A total of 45 oil samples, mostly from the North Sea region, were used in obtaining the correlations. Glaso reported average relative errors of 1.28%, -0.43%, and -4.56% for the bubble point pressure, the bubblepoint oil FVF, and the total FVF correlations, pressure, the bubblepoint oil FVF, and the total FVF correlations, respectively. Reviews of other empirical PVT correlations were presented by Sutton and Farshad in 1984. Standing used a graphic method and Glass used both a graphic method and linear regression analysis in the development of their PVT correlations. The graphic estimation and curve-fitting, PVT correlations. The graphic estimation and curve-fitting, however, do not lead to the best estimate. Therefore, this study developed the correlations using only linear and nonlinear multiple regression analyses to obtain the highest accuracy. This paper deals with PVT correlations exclusively for samples of Middle East crude oils. However, they should he valid for all types of gas/oil mixtures with properties falling within the range of data used in this study. Moreover, this study evaluates the accuracy of Standing's and Glass PVT correlations, which are shown in Table 1. Error analyses were done for this study and also for Standing's and Glass correlations to compare their degree of accuracy. Finally, nomographs for bubblepoint pressure, bubblepoint oil FVF, and two-phase total FVF were constructed on the basis of the developed empirical correlations. PVT Data PVT Data The PVT analyses of 69 bottomhole fluid samples from 69 Middle East oil reservoirs were made available for this study. The experimentally obtained data points were 160 each for the bubblepoint pressure, Pb, and bubblepoint oil FVF, Bob, correlations, and pressure, Pb, and bubblepoint oil FVF, Bob, correlations, and 1,556 for the total FVF, Bt, correlation. The ranges of the data used are shown in Table 2. PVT Correlations PVT Correlations The correlations for bubblepoint pressure, bubblepoint oil FVF, and two-phase total FVF were developed by use of the linear and nonlinear multiple regression analyses shown in the Appendix. Bubblepoint Pressure. The following general relation of bubblepoint pressure of an oil and gas mixture with its fluid and reservoir properties was assumed: (1) Table 3 shows the 160 experimentally determined bubblepoint pressures obtained from PVT analyses of 69 different Middle East pressures obtained from PVT analyses of 69 different Middle East oil/gas mixtures. The nonlinear multiple regression analysis was used to develop the following relation: (2) wherePb = bubblepoint pressure, Rs = solution GOR, gammag = dissolved gas relative density (air = 1), gammag = stock-tank oil relative density (water = 1), and T = absolute temperature. Bubblepoint Oil FVF. Oil FVF at bubblepoint pressure can he derived as a function of solution GOR, average gas relative density, oil relative density, and temperature as fellows: (3) The following empirical equation was developed by use of the nonlinear multiple regression analysis and a trial-and error method based on the 160 experimentally obtained data points shown in Table 3: (4) where B is an intermediate oil FVF value. The bubblepoint oil FVF correlation (Eq. 4) was further refined by applying the linear regression analysis on the same data. P. 650

Modeling nutrient behavior in Wetlands

A simple mathematical model os developed which permites dynamic simulation of wetland hydrology and of nutrient-driven interactions between wastewater and the wetland ecosystem. Spatial variations due to surface water flow are described, and material balance calculations carried out for phosphorus, nitrogen, and chloride. A hydrology model, described elsewhere, predicts overland flow. Ecosystem phenomena are represented, using a one-dimensional, spatially distributed compartmental model. Compartments representing active parts of the ecosystem include soil, surface water, interstitial soil water, and various types of live biomass, standing dead and litter. Solutions to the partial differential equations which comprise these spatial models are demostrated using finite-difference methods. Computer simulations are compared with operating data from the Porter Ranch wastewater treatment facility at Houghton Lake, Michigan. They accurately predict solute concentrations in surface water, biomass growth patters, changes in the litter pool, and soil accretion rates.

Uranium-thorium series radionuclides in brines and reservoir rocks from two deep geothermal boreholes in the Salton Sea Geothermal Field, southeastern California

Naturally occurring U and Th series radionuclides have been analyzed in high temperature brines (~300°C, 25 wt% dissolved solids) and associated rocks from two deep geothermal wells located on the northeastern margin of the Salton Sea Geothermal Field (SSGF). These data are part of a study of the SSGF as a natural analog of possible radionuclide behavior near a nuclear waste repository constructed in salt beds, and permit evaluation of some characteristics of water-rock interaction in the SSGF. Rock/Brine concentration ratios ( R c = (dpm/ g) rock /(dpm/ g) brine ) were found to vary from near unity for isotopes of Ra, Pb and Rn to about 5 × 10 5 for 232Th. The high sorptivity of 232Th is closely followed by that of 238U and 234U ( R c ~ 5 × 10 4), suggesting that U is retained in the +4 oxidation state by the reducing conditions in the brines. The relatively high solubility of 210Pb and 212Pb is attributed to formation of chloride complexes, while the high Ra solubility is attributed to chloride complexing, a lack of suitable adsorption sites due to the high brine salinity and temperature, and the reducing conditions that prevent MnO 2 and RaSO 4 from forming. The 228Ra 226Ra ratios in the brines are approximately equal to those of their parents ( 232Th 230Th ) in associated rocks, indicating that Ra equilibration in the brine-rock system is achieved within the mean life of 228Ra (8.3 years). The 224Ra 228Ra ratios in these brines are about 0.7, indicating that either (1) brine composition is not homogeneous and 224Ra decays in fracture zones deficient in Ra and Th as the brine travels to the wellhead or (2) Ra equilibration in the brine-host rock system is not complete within the mean life of 224Ra (5.2 days) because the desorption of 224Ra from the solid phase is impeded. The 228Ac 228Ra activity ratio in the SSGF brines studied is <0.1, and from this ratio the residence time of 228Ac in the brine before sorption onto solid surfaces is estimated to be <70 minutes, indicating the potential for rapid removal of reactive isotopes fom brines. The brine is greatly enriched in 226Ra (2–3 dpm/g, about 10 4–10 5 times that of its parent 230Th), while reservoir rocks are about 10% deficient in 226Ra relative to 230Th. Material balance calculations for 2 226Ra and 18O suggest that brines reside in the reservoir for 10 2–10 3 years, that the SSGF formed 10,000–40,000 years B.P., and that porosity cannot be more than 20%.