Balance calculations for

Gas reservoirs are produced by expansion of the gas contained in the reservoir. The high compressibility of the gas relative to the water in the reservoir (either connate water or underlying aquifer) make the gas expansion the dominant drive mechanism. Relative to oil reservoirs, the material balance calculation for gas reservoirs is rather simple. A major challenge in gas field development is to ensure a long sustainable plateau (typically 10 years) to attain a good sales price for the gas the customer usually requires a reliable supply of gas at an agreed rate over many years. The recovery factor for gas reservoirs depends upon how low the abandonment pressure can be reduced, which is why compression facilities are often provided on surface. Typical recovery factors are In the range 50 to 80 percent. 

The primary drive mechanism for gas field production is the expansion of the gas contained in the reservoir. Relative to oil reservoirs, the material balance calculations for gas reservoirs is rather simple the recovery factor is linked to the drop in reservoir pressure in an almost linear manner. The non-linearity is due to the changing z-factor (introduced in Section 5.2.4) as the pressure drops. A plot of (P/ z) against the recovery factor is linear if aquifer influx and pore compaction are negligible. The material balance may therefore be represented by the following plot (often called the P over z plot). 

Performs preliminary design of MliA, DliA, and MDEA plants through mass and energy balance calculations for all major equipment involved. 

Table 10-13 Mass balance calculation for removal of river-derived constituents from the ocean (all units in lO mmol)...

A very approximate mass balance calculation for the whole range of employed SO2 concentrations based on known amount of SO2... 

Dawn M. Bernard , "Water-Balance Calculations for Solid-Polymer-Electrolyte Fuel Cells," Journal of Electrochemical Society, Vol. 137, No. 11, November 1990. 

Table 21.11 Mass Balance Calculation for the Removal of River-Derived Constituents from the Ocean. ... 

The results of the mass balance calculations for eight major elements and 22 minor elements for run 9 are given in Tables II and III, together with the corresponding concentrations in the coal, precipitator inlet and outlet fly ash, and in the slag tank solids. Complete tabulation of results for all three runs and some data for 57 elements is given in a project progress report (4). 

Mass-balance calculations for the first 3 years of acid additions indicate that the principal IAG processes are sulfate reduction and cation production. Specifically, one-third of the total sulfate input (added acid and deposition) was neutralized by in-lake processes. Increased sulfate reduction consumed slightly more than one-sixth and production of cations neutralized somewhat less than one-sixth of the acid added. Of the remaining sulfate, one-third was lost by outflow, and one-third decreased lake alkalinity. Laboratory determinations suggest that sediment-exchange processes occurring in only the top 2 cm of surficial sediments can account for the observed increase in water-column cations. Acidification of the near-surface sediments (with partial loss of exchangeable cations) will slow recovery because of the need to exchange the sediment-bound H+ and neutralize it by other processes. Reactor-based models that include the primary IAG processes predict that... 

Table IV. Mass Balance Calculations for Sulfur Isotope and Total Sulfur Data. Yields are normalized to 1 g starting kerogen for both types of pyrolysis.

SimpleBox is a multimedia mass balance model of the so-called Mackay type. It represents the environment as a series of well-mixed boxes of air, water, sediment, soil, and vegetation (compartments). Calculations start with user-specified emission fluxes into the compartments. Intermedia mass transfer fluxes and degradation fluxes are calculated by the model on the basis of user-specified mass transfer coefficients and degradation rate constants. The model performs a simultaneous mass balance calculation for all the compartments, and produces steady-state concentrations in... 

MATERIAL-BALANCE CALCULATIONS FOR CLOSED-CIRCUIT GRINDING 13.6... 

These data are almost identical to those calculated above for normal corpses131 and confirm the accuracy of our heat balance calculations for both the triple- and the eight-muffle ovens. 

Mass balance calculations for the Amazon shelf seabed provide important insights into N cycling in the study area. If all of the riverine particulate N regeneration is assumed to take place in the water column, the total supply of N to the seabed (including marine PON deposition and the diffusive flux across the sediment-water interface) equals 5 7 x 10 mol d . This value is 4.4 x 10 mol d i greater than the burial term for N on the Amazon shelf (1.3 x 10 mol d O. Based on the observation of denitrification reactions in the seabed (Aller et al. 1986,... 

Part 1 of the next example presents a detailed material balance calculation for a separation process that involves recycle. Part 2 of the problem shows what would happen if the recycle were omitted and, in doing so, illustrates one of the reasons for recycling. 

In the sections that follow, we introduce terminology commonly used in the analysis of combustion reactors and discuss material balance calculations for such reactors. Methods of determining the energy that can be obtained from combustion reactions are given in Chapter 9. 

Use the heat of solution data in Table B.IO and solution heat capacity data to (a) calculate the enthalpy of a hydrochloric acid, sulfuric acid, or sodium hydroxide solution of a known composition (solute mole fraction) relative to the pure solute and water at 25 C (b) calculate the required rate of heat transfer to or from a process in which an aqueous solution of HCl, H2SO4, or NaOH is formed, diluted, or combined with another solution of the same species and (c) calculate the final temperature if an aqueous solution of HCl, H2SO4, or NaOH is formed, diluted, or combined with another solution of the same species adiabatically. Perform material and energy balance calculations for a process that involves solutions for which enthalpy-concentration charts are available. 

Energy balance calculations for a system (a process unit or combination of units) are conveniently organized through the construction of an inlet-outlet internal energy table (or enthalpy table). The table lists n (or h) and U (or ft) for each species at each state (phase, temperature, pressure) in which the species is found in process streams. Once all of these variable values have been determined and inserted in the table, the subsequent evaluation of AC,. AH. or AH is straightforward. 

Two methods are commonly used to choose reference states for enthalpy calculations and to calculate specific enthalpies and AW. We outline the two approaches below, using a propane combustion process to illustrate them. For simplicity, the material balance calculations for the illustrative process have been performed and the results incorporated into the flowchart. 

Set up a spreadsheet to perform material and energy balance calculations for single-unit and multiple-unit processes. 

Calculated Material Balances. Material balances calculated for selected elements are shown graphically in Figures 4 and 5 for the Livermore 125-kg retort and the SRC pilot plant. The mass flow balances... 

Although the continental crust constitutes only 0.6% by mass of the silicate Earth, it contains a very large proportion of incompatible elements (20-70%, depending on element and model considered Rudnick and Fountain (1995)), which include the heat-producing elements and members of a number of radiogenic-isotope systems (Rb-Sr, U-Pb, Sm-Nd, Lu-Hf). Thus the continental crust factors prominently in any mass-balance calculation for the Earth as a whole and in estimates of the thermal structure of the Earth (Sclater et al., 1980). 

The crust is the Earth s major repository of incompatible elements and thus factors prominently into geochemical mass-balance calculations for the whole Earth. For this reason, and to understand the processes by which it formed, determining the composition of the continental crust has been a popular pursuit of geochemists from the time the first rocks were analyzed. 

Pearcy L. G., DeBari S. M., and Sleep N. H. (1990) Mass balance calculations for two sections of island arc crust and implications for the formation of continents. Earth Planet. Sci. Lett. 96, 427-442. 

Mass-balance studies are widely considered to be the most reliable means of making quanta-tive determinations of elemental transfer rates in natural systems. Garrels (1967) and Garrels and Mackenzie (1967) pioneered the use of mass-balance calculations for mineral weathering in their classic study of Sierra Nevada springwaters. These waters were chosen because a careful set of water analyses and associated primary igneous rock minerals and the soil mineral alteration products were known. Since the actual compositions of the minerals were not known, Garrels and Mackenzie used the theoretical formulas for the minerals. 

Table 3 Summary of mass-balance calculations for the stratified drift and bedrock aquifers of Connecticut.

A process analysis conqiuter software, AspenPlus , was used as the basic framework to perform material and energy balance calculations for the process cases. Aspen is a steady-state process analysis program extensively employed in chemical engineering process modelling. 

Table HI Results from the mass and energy balance calculations for each flow of the... 

As with all other treatment technologies, considerable attention has been paid to the pollutant degradation reactions and the extent to which it proceeds to complete mineralization. This is extremely important, especially when one considers the possibility of generating intermediates that may be more toxic than the starting material. Consequently, care has been taken to identify intermediates and do proper mass-balance calculations for the reaction. Hybrid approaches should also be considered, for example, combining the AOTs discussed earlier with more standard treatments such as GAC adsorption in a pre-or poststage. In the end, economic considerations will determine the approach that is used. The reader is referred to Chapter 8 of Ref. 112 for a detailed evaluation of the economics of the various treatments discussed earlier. 

The charge-balance calculation for the zero plane ignores species A and in the beta plane and considers only the zero plane species to which these ions are adsorbed, plus unfilled adsorption sites (SO" sites) and sites occupied by specifically adsorbed protons (SOHJ sites). With A and assigned to the beta plane, the net charge of that plane is given by... 

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