Respiration rate equations

Equation (5.12) shows a linear dependency in the DO concentration that is not in agreement with the results shown in Figure 5.6. Matos (1992) also found a discrepancy between Equation (5.12) and experimental results and substituted the expression 5.3 S0 in Equation (5.12) with a constant equal to 10.9. This constant depends on biofilm and wastewater characteristics and should be determined from local measurements. In addition to the information given by Bjerre et al. (1998b) in Example 5.2, values of respiration rate measurements for sewer biofilms are shown in Table 5.5. 

In the model, the internal structure of the root is described as three concentric cylinders corresponding to the central stele, the cortex and the wall layers. Diffu-sivities and respiration rates differ in the different tissues. The model allows for the axial diffusion of O2 through the cortical gas spaces, radial diffusion into the root tissues, and simultaneous consumption in respiration and loss to the soil. A steady state is assumed, in which the flux of O2 across the root base equals the net consumption in root respiration and loss to the soil. This is realistic because root elongation is in general slow compared with gas transport. The basic equation is... 

As noted earlier, air-velocity profiles during inhalation and exhalation are approximately uniform and partially developed or fully developed, depending on the airway generation, tidal volume, and respiration rate. Similarly, the concentration profiles of the pollutant in the airway lumen may be approximated by uniform partially developed or fully developed concentration profiles in rigid cylindrical tubes. In each airway, the simultaneous action of convection, axial diffusion, and radial diffusion determines a differential mass-balance equation. The gas-concentration profiles are obtained from this equation with appropriate boundary conditions. The flux or transfer rate of the gas to the mucus boundary and axially down the airway can be calculated from these concentration gradients. In a simpler approach, fixed velocity and concentration profiles are assumed, and separate mass balances can be written directly for convection, axial diffusion, and radial diffusion. The latter technique was applied by McJilton et al. 

Temperature is recognised as having an effect on the growth yield, the endogenous respiration rate and the Monod kinetic parameters Ks and pm. Within the temperature range of 25 to 40°C these have been shown to have dependencies which could be accounted for by Arrhenius-type exponential equations (Topiwala and Sin-CLAIR<52)). If the temperature-dependent nature of the constants has to be taken into account, equation 5.70 must be written as ... 

However, inspection of Fig. 5.57 suggests that the operation of a chemostat at dilution rates other than those approaching washout conditions results in growth at low values of substrate concentration S. For this condition the endogenous respiration rate becomes significant and Ya Yx/S, as indicated in equation 5.54. It therefore becomes more realistic to express the specific growth rate p as ... 

An additional advantage of this DO control system is the possibility of having a real-time estimation of the cells respiration rate. As can be observed in Equation 1, if C is constant, the term of the transfer kLa.(Cs-C) is equivalent to the consumption Q02 X. With the actuation value of the controller, the transfer rate can be calculated, and also the consumption at each moment (Kamen et al., 1996). There are several reports in the literature dealing with the use of respiration measurements to estimate cell concentration online, based on the assumption that, during the growth phase, each cell consumes a constant amount of oxygen (Yoon and Konstantinov, 1994 Ruffieux et al., 1998 Jorjani and Ozturk, 1999). 

Both equations have been taken from ISO 1334431 and use LC50 values for lethality to provide reference data for the individual gases to calculate toxic potency, based on rats exposed for 30 min. The N-Gas model in Equation 17.1 assumes that only the effect of the main toxicant CO is enhanced by the increase in respiration rate caused by high C02 concentrations (expressed as a step function with one value of m and b for C02 concentrations below and another for those above 5%). 

From this equation, KiCi may be calculated, which can then be corrected to obtain using the temperature relation. (KiO)2o is one of the factors needed to calculate a. The organisms in wastewater respire, so oxygen utilization must be incorporated. Calling the respiration rate by f, Equation (9.11) is modified to... 

By analogy with Equation (9.35), the respiration rate due to NBOD, (f) , may be obtained from... 

Body size (weight) Excretion (or respiration) rate (T) can be related to body weight (W) according to the allometric equation ... 

Figure 16 Calculated soil CO2 concentrations versus depth for three contrasting ecosystems using Equation (13) and the following data total soil respiration rates (tundra = 60 g C m yr , grassland = 442 g C m yr, and tropical forest = 1,260 g C m yr ), Ds = 0.021 crn s , atmospheric CO2 = 350 ppm, and L = 100 cm (respiration data from Raich and Schlesinger, 1992).

Figure 17 Measured (points) and modeled (curves) soil carbonate values for three soils along an elevation (climate) gradient in the Mojave desert/Great Basin of California and Nevada. Modeled carbonate values based on Equation (14) plus the fractionation between CO2 and carbonate ( 10%o). The elevations (and modeled soil respiration rates that drive the curve Ht) are (a) 330 m (0.18 mmol C02m h ) (b) 1,550 m (0.4 mmol CO2 h ) and (c) 1,900 m (1.3 mmol CO2 m h ). The value of soil organic matter (CO2 source) was about — 21%o at all sites. Note that depth of atmospheric CO2 isotopic signal decreases with increasing elevation and biological CO2 production (Quade et al, 1989a) (reproduced by permission of Geological Society of America from...

Although photosynthesis is the ultimate source of O2 to the atmosphere, in reality photosynthesis and aerobic respiration rates are very closely coupled. If they were not, major imbalances in atmospheric CO2, O2, and carbon isotopes would result. Only a small fraction of primary production (from photosynthesis) escapes respiration in the water column or sediment to become buried in deep sediments and ultimately sedimentary rocks. This flux of buried organic matter is in elfect net photosynthesis , or total photosynthesis minus respiration. Thus, while over timescales of days to months, dissolved and atmospheric O2 may respond to relative rates of photosynthesis or respiration, on longer timescales it is burial of organic matter in sediments (the net photosynthesis ) that matters. Averaged over hundreds of years or longer, burial of organic matter equates to release of O2 into the atmosphere - - ocean system ... 

It is clear from these measurements that the respiration rate of zooplankters is temperature-dependent. It is also dependent on the weight of the zooplankter in question and its life cycle stage (59). As a first approximation, a straight line dependence is adequate, and the endogeneous respiration rate is given by the equation respiration rate = K3T where K3 = 0.2 =t 0.1 (day °C) 1. The conversion from the reported units to a death rate is made by assuming that 50% of the zooplankton... 

Respiration rates are calculated by dividing each term in Equation (9.17) by the 14C ages. The calculated respiration rates for terminal electron acceptors O2, MnC>2, Fe3+, and SC>4 are 10-6, 10-8, 10-4, and 10-6 per liter per year, respectively. These rates are again much lower than those estimated from biological methods such as adding substrate or electron acceptors, and are lower than the near-surface sediments. 

Karel and Go (20) also investigated the effect of temperature on the rate of respiration and assumed Equation 7 to be R0 = f(c(02), T). They found that at a given oxygen concentration level, temperature dependence of respiration rate conformed to the Arrhenius type equation. 

Veeraju and Karel (21) followed up on an earlier work of (12) and tried to use two films of different permeabilities for controlling oxygen and carbon dioxide levels in a package and met with reasonable success. They worked with apples and focussed on steady-state concentration values. They simultaneously solved the following two equations, while using the respiration rates, as needed, from the experimental curves for R0 and Rc ... 

Deily and Rizvi (24) derived analytical solutions, similar to (21), solutions of Equations 9 and 10 to optimize packaging parameters or to estimate transient and equilibrium gas concentrations in polymeric packages containing peaches. The respiration rate functions based on experimental data were of the following form, which were used in obtaining the analytical solutions ... 

Nole. Patch- (grass and various woody communities) and soil-specific SR rates measured monthly over an annual cycle at La Copita (McCulley, 1998) were multiplied by the area of respective commrmity types (Scanhui a]id Archer, 1991). Effects of mean annual temperature change (MAT, "C) on SR were estimated from (A) equations in Raich and Schlesinger (1992) for La Copita (MAT - 22.4°C and MAP - 720 mm) a. 0 and 6°C increase in MAT would produce a 3.9 and 7.8% increase, respectively, in soil respiration and (B) Q,o values of in sitti, community-specific soil respiration from McCulley (1998). Estimates are probably conservative, as respiration rates used in computations w ere measured during a below-normal rainfall year. 

The therapist entry for pressure-controlled ventilation is shown in Figure 18.8 (lower left-hand side). In contrast to the volume-controlled ventilation, where Qj(t) was computed directly from operators entry (Equations 18.1 through 18.3), the total desired flow is generated by the closed-loop airway pressure controller shown in Figure 18.8. This controller uses the therapist-selected inspiratory pressure, respiration rate, and the 1 E ratio to compute the desired inspiratory pressure trajectory. The trajectory serves as the controller reference input. The controller then computes the flow necessary to make the actual airway pressure track the reference input. Assuming a proportional-plus-integral controller, the governing equations are... 

The coupling equation above is stiU strongly linked to the radiation field, including the respiration term. At obscurity (anywhere in the photobioreactor) or at a very low value of, 4(x), the maximal respiration rate must be considered constant and can be measured in independent experiments. In this case, the value of the new parameter K, is not independent because it can be deduced directly from the data on the specific photon absorption rate at the compensation point Ac (the other parameters known in our knowledge model) ... 

Table A smnmary of the photosynthetic and respiratory O2 exchange of leaves grown at different canopy positions. Data points were en from a combination of four separate hght curves per canopy level. Light saturation points were estimated visually, and maximum net photosynthesis values are Wed on rates at 1800 /iEi m s PAR. Apparent quantum yields, hght compensation points, and dark respiration rates were determined by a linear equation fitted to hght intensity points ranging from 0 to 102 /iEi m s (r > 0.9 in ah cases). Absorbed photon yields can be estimated by dividing apparent quantum yields by the average leaf absorbancy.

In this equation, the values of the numerator are determined by metabolic activities and renal excretion. The values in the denominator are determined by the respiration rate. 

In the above equation. Area is the area of the silicone membrane (m ), RR is respiration rate of the product stored under MA condition (liter of CO kg" day ), M is mass of stored produce (kg), is permeability of the silicone membrane to CO (liter day m atm ), and CO is desired CO partial pressure difference across the membrane (atm). 

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