Heat Loss Calculation Research Articles

A lumped finite element method for cap rock heat loss calculations

Numerical models of thermal recovery processes arising in petroleum engineering require accurate estimates of the interaction between a reservoir and the surrounding cap and base rock. It is important to obtain an accurate approximation of the energy flux at the interface between the reservoir and the surrounding rock, and the distribution of the temperature in the surrounding rock is of only secondary importance. A flux calculation procedure implemented as a post-processing algorithm based upon a finite element method is used to calculate an accurate approximation to the energy losses. Oscillatory behavior is observed in the computed temperature distribution using a standard computational scheme. If the time derivatives are lumped, the oscillatory behavior is avoided. Computational experiments performed on sample test cases possessing analytical solutions indicate an excellent agreement between the approximations obtained using the lumped procedure and the exact solution.

Why do elephants flap their ears?

The blood flow in the ear of the African elephant Loxodonta africana was measured In anaesthetized animals using the dye dilution technique at the same time as the arterio-venous temperature difference. The calculated heat loss from the ear is shown to be a substantial proportion of the total metabolic heat-loss requirement calculated from body surface area estimations. Reasons are advanced for believing that ear blood flow is controlled in the interests of thermoregulation. Behavioural fanning activity and the large ear surface area and surface to volume ratio suggest that this organ is of major importance in thermoregulation under warm environmental conditions.

Dependence of ground heat loss upon solar pond size and perimeter insulation calculated and experimental results

Ground heat losses from solar ponds are modelled numerically for various perimeter insulation strategies and several solar pond sizes. The numerical simulations are steady state calculations of heat loss from a circular or square pond to a heat sink at the outer boundaries of an earth volume that surrounds the pond on the bottom and sides. Simulation results indicate that insulation on top of the ground around the pond perimeter is rather ineffective in reducing heat loss, and that uninsulated sloping side walls are slightly more effective than insulated vertical side walls, except for very small ponds. The numerical results are used to derive coefficients for a semi-empirical equation describing ground heat loss as a function of pond area, pond perimeter and insulation strategy. Experimental results for ground heat loss and energy balance in the 400 m 2 solar pond at the Ohio State University are reported. Analysis of this data, along with data on solar energy input, heat gain by the pond, heat loss through the gradient zone, and heat extraction from the pond yields a good energy balance. Numerical simulation of ground heat loss from this pond shows good agreement with the results obtained from pond measurements. Loss turns out to be large because of unexpectedly high values of earth thermal conductivity in the region.

A Simplified Predictive Model for Steamdrive Performance

Summary To facilitate screening and evaluation of reservoirs for application of steamdrive as an EOR process, a simplified predictive model for steamdrive performance has been constructed. This model extends existing analytical heat-balance models to include fractional-flow characteristics, vertical and areal sweep effects, steam injectivity, and heat losses in wellbores and surface pipes in a single, easy-to-use computer program. The predictive model assumes that the steamdrive process can be represented by a series of shock fronts created by the injection of steam into a reservoir. The reservoir is divided into six regions: undisturbed zone, cold-liquid zone, hot-liquid zone, steam zone, hot-water drive, and cold-water drive. The size, saturation, and movement of each zone, or bank, is calculated from a fractional-flow characterization of the reservoir and the growth of the steam zone. Vertical and areal sweeps of the steam zone are estimated from empirical relationships, and the sweeps of the other banks are related to their mobilities. The injectivity calculations yield sandface pressure at a specified flow rate or the flow rate at a specified pressure. Wellbore and surface heat-loss calculations give the enthalpy and steam quality at the sandface. An economic package interprets the results of these calculations and provides a cash-flow analysis from which risk and profitability are determined. Introduction The injection of steam into some oil reservoirs has been a successful EOR process for 30 years. Unfortunately, not all reservoirs have responded equally well to steam injection, necessitating decisions from reservoir operators on when, where, and how to inject steam. As only economically successful projects appeal to most operators, reliable methods of predicting the performance and profitability of steamdrive candidates are of benefit. This paper describes a steamflood predictive model (SFPM) that quickly estimates the performance and profitability of the steamdrive process. Such estimations provide operators with information on the costs and rewards of steamflooding a specific reservoir. With this information, an operator may choose to seek another project or to investigate further the potential of the reservoir with more rigorous tools. The basic characterization of steamdrive performance was initially the analytical estimation of steam-zone size.1,2 Many studies refining and redefining the basic equations of steam-zone size enable this quantity to be calculated with relative confidence.3,4 Other facets of steamdrive performance such as surface5 and wellbore6 heat loss, distillation,7 steam overlay,8 and changes in rock properties9 have been studied. Several analytical and numerical models have been written to describe steamflooding behavior more rigorously,10-12 and scaled physical models are able to represent steamflooding characteristics accurately.13 Most of these investigations report remarkably good agreement with measured field performance. This model was written to provide more deterministic predictions of steamflood behavior than did previous analytical models; it incorporates the combined effects of heat and pressure losses, fluid fractional-flow behavior, reservoir sweep effects, and steam injectivity.

How to calculate heat losses through open doors

How to calculate heat losses through open doors

Development of Insulation in Neonatal Cotton Rats (Sigmodon hispidus)

Data on environmental temperatures, skin temperature, animal size, the depth of fur, density of hairs in fur, hair length, and diameter of hair shafts were used to calculate fur thermal conductivity and heat loss, using a porous medium model modified from that of Kowalski and Mitchell. The total thermal conductivity of fur changed little with respect to the age of the animal, but calculated heat loss per unit area decreased because of a decrease in the thermal gradient across the fur caused by an increase in fur depth. A sensitivity analysis of the model showed that skin, air, and radiant environmental temperatures were most important in determining heat loss in all sizes of animals. Fur depth is the only important property of fur determining heat loss in nestling rats, but in adults, all the properties of fur exert significant effects on heat loss. The diameter of animals is a significant variable in all sizes of rats.

Efficiency of fresnel lenses with respect to thermal losses

Experimental observations and heat loss calculations for a Fresnel lens under forced and natural convection have both been obtained. A lens with a 2·0 mm step width and 325·99 cm 2 area when exposed to solar radiation and kept normal to solar radiation with an intensity of 43·116 cal/cm 2/h has given a steady-state temperature of 187·5°C at its focus.

How to calculate heat losses through open doors

When an outside door is opened the wind blows into a building, the rate at which air enters is limited by the fact that it has to leave again as part of the exfiltration. This simple truth is the basis of a method of calculating the rate at which air enters the building, and how long it takes to reach a steady state, given the area of the door, the volume of the building, and the air change rate caused by infiltration, when the door is shut. Resulting heat losses are unacceptably high, but not as high as claimed by door manufacturers.

Determination of heat losses in biogas installations

SYNOPSIS During the winter 1979/80 a biogas plant located on an average sized dairy farm was monitored with respect to its heat requirements. The results showed that the energy consumption was higher than the energy content of the biogas produced. A comparison of the data collected with the calculated heat losses indicated strongly that substantial amounts of heat were lost through heat bridges. These losses could be visualised with thermography. Additional thermography determinations at other biogas plants showed that the most critical area of insulation was the overflow from the digester to the storage tank. The conclusions for an improved insulation are: 1. The insulation material should be at least 12 cm thick.2. The insulation material should fulfil the required criteria, e.g. withstand mechanical forces, be protected against humidity, etc.3. The insulation should include in- and outflows of the digester as well as heating pipes.4. To minimize temperature differences between the digester and the environment, the former should be built in the earth if possible.

Downhole measurements and fluid chemistry of a castle rock steam well, the Geysers, Lake County, California

Wellbore and reservoir processes in a steam well in the Castle Rock field of The Geysers have been studied by means of down-hole pressure and temperature measurements and analyses of ejected water and steam produced under bleed and full flow. Down-hole measurements show that below a vapor zone there is liquid water in the well in pressure equilibrium with reservoir steam at a depth of 2290 m. The progressive decreases, from 1973 to 1977, of pressure and temperature in the vapor zone indicate that wellbore heat loss is high enough to condense a large fraction of the steam inflow. The chemical composition of water ejected from the well is consistent with an origin from wellbore condensation of steam. Calculations using the differences in gas and isotopic compositions between bleed and full-flow steam show that about half of the full-flow steam originated as liquid water in the reservoir and that about 30% of the steam entering the well under bleed was condensed in the wellbore and drained downward. Heat loss calculations are also consistent with this amount of condensation.

A Simple Method For Predicting Cap And Base Rock Heat Losses In' Thermal Reservoir Simulators

Abstract A fast simple method is given for calculating heat losses to cap and base rock in thermal reservoir simulators. The method can handle backflow of heat and cyclic temperature variations. Test comparisons against analytic results are given. The method gives remarkably accurate results on the test problems, considering its simplicity. Introduction In thermal reservoir simulations, it is necessary to calculate the heat loss from the reservoir to the surrounding environment, usually to the cap and base rock. A finite-difference calculation can become expensive, especially on computer storage, as the temperature profile can extend large distances into the overburden and underburden, requiring large numbers of grid blocks for its description. However, high accuracy in the solution of the heat loss calculations is not usually required in reservoir simulators owing to the uncertainty in cap and base rock thermal parameters. This paper describes an efficient semi-analytical method for the case where the one-dimensional linear heat conduction equation is adequate for the heat loss calculations. Semi-analytical methods have been used previously (1,2,3), and a study of the results given in these papers leads us to the following tentative conclusions:Conduction within the cap rock rapidly wipes out any sharp differences in temperature. Thus, the temperature in the cap rock varies smoothly, even for rather erratic changes at the interface.Longitudinal heat conduction in the cap rock can usually be neglected, because the Peclet number is normally high for reservoir floods(2).The most important physical features of the heat loss process are good descriptions of the boundary conditions at the interface and conservation of cap rock energy. The tail of the temperature distribution contains little energy and is relatively unimportant. These points suggest that the temperature profile into the cap or base rock can be adequately approximated by any reasonably flexible function containing a few parameters. If such a function could be made to fit the thermal diffusivity equation with appropriate boundary conditions, and the calculation of the parameters could be done in a simple fast fashion, the method would become extremely attractive further justification for such an approach is that high accuracy is not required, as the coefficient of thermal conduction of the cap and base rock is rarely known precisely. The Method We choose as the fitting function for the temperature profile into the cap or base rock: (Equation Available In Full Paper) θ is the temperature at the interface between the reservoir and the cap or base rock (the zero level has been defined at the initial interface temperature); p and q are the fitting parameters yet to be determined; d may be interpreted as the diffusion length and should be of order √kt where t is the time measured from the instant at which the interface temperature first begins to change. The deepest penetrating term in (1) is z2e−z/d, which has its maximum at z = 2d. Hence we choose for the diffusion length:

The food requirements of whales in the southern hemisphere

Feeding data for small and medium sized cetaceans parallel the basal metabolism predicted for mammals. Heat loss calculations, a consideration of feeding volumes, and the feeding data indicate the energy requirements of the large whales can be expressed as 1.5 times the calculated basal metabolism. Comparing the energy requirement calculated for fin whales to the energy available from storage indicates that fin whales must feed, though at a reduced level, while away from the Antarctic. A summation of the food requirements for both the initial and recent populations of whales in the southern hemisphere indicate that whales are major oceanic consumers. The reduction in their numbers through hunting has reduced their food requirements by about 50% in the open ocean and by 75% in the Antarctic, leaving approximately 96 × 10 6 tons per year of ‘unconsumed’ food.

Wellbore Heat Loss in Production and Injection Wells

JPT Forum Articles are limited to 1,500 words including 250 words for each table and figure, or a maximum of two pages in JPT. A Forum article may present preliminary results or conclusions of an investigation that the present preliminary results or conclusions of an investigation that the author wishes to publish before completing a full study; it may impart general technical information that does not warrant publication as a full-length paper. All Forum articles are subject to approval by an editorial committee. Letters to the editor are published under Dialogue, and may cover technical or nontechnical topics. SPE-AIME reserves the right to edit letters for style and content. Introduction The classic work by Ramey on wellbore heat transmission derived the temperature distribution in a well used for injecting hot fluid. Ramey later expanded on this to give the rate of heat loss from the well to the formation. However, by assuming that the fluid remains at its inflow temperature, Ramey's analysis effectively gave the heat loss at infinite fluid flow rate - in other words, the maximum possible heat-loss rate. This paper reexamines this problem for finite fluid flow rate and determines the heat-loss rate as a function of fluid properties and fluid flow rate. Because this analysis is valuable when considering geothermal wells, results will be presented for producing and injection wells. This paper presented for producing and injection wells. This paper considers only single-phase fluids flowing in the well. Satter suggested a method for estimating wellbore heat loss when considering condensing steam flow and presented a sample procedure for a given set of reservoir presented a sample procedure for a given set of reservoir properties. His analysis also may be extended to properties. His analysis also may be extended to production wells to obtain heat-flow estimates with two-phase production wells to obtain heat-flow estimates with two-phase flow. For single-phase flow, the formulation permits direct calculation of wellbore heat loss with various production and injection conditions. production and injection conditions. Injection Using Ramey's analysis and notation, consider a heat balance in the radial direction on a section of a well with height dz, losing heat at rate dq from the casing to the formation. Then, ...............(1) where T1 is the temperature of the fluid in the tubing, Te is the temperature of the formation, k is the earth thermal conductivity, r, is the inside radius of the tubing, U is the over-all heat-transfer coefficient between the inside of the tubing and the outside of the casing (see Willhite), and f(t) is a dimensionless time function described by Ramey. For long times, f(t) can be approximated as ......................(2) where r2 is the outside radius of the casing in meters, a is the thermal diffusivity of the earth in square meters per second, and t is the production time in seconds.Performing an over-all heat balance on the well and considering the changing temperature of the fluid as it flows in the tubing, T, can be evaluated as ..................(3) where az + b is Te, the formation temperature (assuming linear geothermal gradient), b is the surface temperature, and z is measured downward. T0 is the injection temperature. A is a group of variables defined as ..................(4) where w is the fluid flow rate and c is the specific heat of the fluid.Integrating Eq. 1 (with respect to depth z) and substituting T1 = T0, Ramey obtained .............(5) JPT P. 116

A human calorimeter for the direct and indirect measurement of 24 h energy expenditure.

1. A calorimeter for the continuous measurement of heat production and heat loss in the human subject, for at least 24 h, is described. The calorimeter operated on the heat-sink principle for direct calorimetry and an open-circuit system for indirect calorimetry. 2. Sensible heat loss was measured using a water-cooled heat exchanger, and the temperature of water entering the heat exchanger was controlled to maintain a mean temperature gradient of zero across the chamber walls. 3. Evaporative heat loss was determined from ingoing and outgoing wet-and-dry bulb temperatures and air flow-rates. 4. Problems associated with the calculation of evapoative heat loss and the estimation of the volume of incoming air in open-circuit systems are considered. 5. The calibration, limits of accuracy, sources of error and experiments with subjects are discussed.

Radiation heat losses in solar collectors with plastic covers

The use of plastic covers instead of glass covers in solar collectors requires a modification of the calculation of radiation heat loss, because plastics are, in contrast to glass, partly transparent for thermal radiation. This article describes a simple method which enables calculation of radiation heat loss in collectors equipped with plastic covers. Comparison of this method with an incorrect method used by some authors shows that the latter leads to large errors in some cases. The results of the correct method indicate that in some situations the glass covers can be replaced by much cheaper plastic covers with a negligible increase in collector heat loss.

Respiratory water loss: A predictive model

A steady-state model, based on a combination of empirical and mechanistic relationships, is developed to predict respiratory water loss from terrestrial vertebrates. Model parameters are evaluated from published data for the banner-tail kangaroo rat ( Dipodomys spectabilis). A three-dimensional representation of model behavior is presented, emphasizing the interaction of organismal and environmental variables. The model makes possible the calculation of respiratory water and heat losses for animals in both artificial and natural environments.

The atypical Mathew solar house at Coos Bay, Oregon

The Mathew solar house in Coos Bay, Oregon is an atypical solar house in several respects: Its location on the cloudy winter Oregon coast. Its combination of near-vertical collector and near-horizontal reflector. Its unusually large 8,000 gallon storage tank. Its combination of near-identical collectors; one on the house, the other freestanding. This paper assesses the contributions made by solar energy in space heating. The apparent solar contribution is approached from two directions: 1. (1) Calculation of “Assumed Solar” Energy— House heat loss is calculated and known heat contributed by electricity, people and direct solar gain through windows is subtracted; remainder is assumed stored solar energy. 2. (2) Calculation of “Measured Solar” Energy— Stored solar energy utilized is calculated by measuring the energy provided by the collectors, then adjusting for energy deposited or withdrawn from storage during each month, and for losses to ground from storage. The monthly “assumed solar” is compared to the monthly “measured solar”, and reasons for differences are discussed. The distribution of the complete energy needs of the house (24,230 kWh for the season) is: 52%: Stored solar energy. 22%: Direct solar gain through windows. 13%: Electric appliances and lights. 9%: Electric space heating. 4%: Heat from occupants' metabolism. When the net heating requirement is considered (24,230 kWh less the direct solar gain through windows, lights and appliances, and people) this requirement is 14,802 kWh, and is termed the “space heating” requirement. This is distributed: 85% Stored solar energy. 15% Electric resistance units. Calculation of measured solar collector/storage tank contributions, when compared with those assumed from the heat loss calculation, indicate close agreement over the 8-month heating season, but wide variations in some months. Some of the variation can be attributed to uncertainties in measurements; but it does indicate a large storage role for the earth facing the uninsulated storage tank.

Estimating water temperatures and time of ice formation on the Saint Lawrence River

Monthly mean heat losses from the surface of the St. Lawrence River during the fall‐winter cooling period were determined by an empirical heat budget which incorporated the processes of radiation, conduction, convection, and precipitation. Calculations indicate that the heat loss can be reasonably represented by a simple linear relation with air‐water temperature differential. It is suggested however, that the coefficient of proportionality changes with variations in the ratio of radiation to evaporation. An equation was evaluated which relates surface heat loss to temperature decline along the international section of the river. Within the limits of accuracy of the heat loss calculations, the equation provides adequate estimates of water temperature changes for the period of study. The water temperature decline equation was used as the basis for developing a prediction technique which enables river freeze‐up estimates to be made as early as 1 October. When observed freeze‐up dates were used, predictions for a 6‐year period (1965–1970) yielded standard deviations of 4.7, 3.3, and 3.5 days for predictions starting at the beginning of October, November, and December. Observed freeze‐up occurred within 2 days of the predicted date in 4 of the 6 years examined. Experimental predictions for two additional years yielded similar results.

The Thermal Conductivity and Diffusivity Of Green River Oil Shales

Thermal conductivities of Green River oil shales vary fourfold, decreasing with increasing oil yield and temperature. Values also decrease as the kerogen decomposes, but these changes are small after about 9 hours. Mineral composition, geographic location, depth of burial, axial stress, and pressure have no significant erect. The thermal properties, which are transversely isotropic, are applicable to the calculation of heat losses from in-situ recovery operations. Introduction Thermal decomposition of the essentially insoluble organic matter in oil shales is the easiest way to obtain shale oil. Proper planning of both surface and sub-surface thermal oil-shale recovery operations requires values of the thermal conductivity and diffusivity of oil shales.There are few publications reporting thermal conductivities of oil shale from the Green River formation. Gavin and Sharp reported three values for the thermal conductivity of an oil-shale sample assaying 42.7 gal/ton. Their reported values were obtained over the temperature range from 77 degrees to 167 degrees F, but the direction with respect to the bedding plane in which the measurements were taken was not indicated. Thomas presented thermal conductivity data of an oil shale assaying 30 gal/ ton and at a mean temperature of 104 degrees F, finding values parallel to the bedding plane to be 30 percent higher than those normal to it and finding essentially no effect of stress levels of 1,000 psi and above.Tihen et al. report on the thermal conductivity and diffusivity at room temperature of unconfined raw, retorted, and burned oil shales assaying from 8.6 to 58.6 gal/ton. Correlations for thermal conductivity are given for temperatures as high as 1,100 degrees F while considering the anisotropic character of the oil shales. Though bolted, samples developed cracks during heating, suggesting those results may be more applicable to rubbled pieces in subsurface cavities or large surface retorts than to the calculation of heat losses from a process zone in subsurface thermal operations.This report presents thermal conductivity data of confined Green River oil shales over a wide range of temperature, fluid pressure, axial stress, and kerogen content. The bulk of our measurements were carried out on oil shales as they are found in nature; that is, they were not previously retorted. At the higher temperatures, however, our reported values include the effects of at least some decomposition of the organic matter. Thermal conductivities of burned (organic-free) oil shales were measured on only two samples.The effects of kerogen content, fluid pressure, axial stress, temperature, orientation, heating time, and mineral composition on the thermal conductivities of oil shales were investigated. These basic results were then used together with specific gravity and a correlation of specific heat with oil yield by Fischer assay and temperature to obtain calculated thermal diffusivities for each sample. Instrumentation The transient line heat-source (probe) method, whose application is not particularly complicated by the addition of means for stressing the sample, was used in our investigation. JPT P. 97

Application of Variational Principles to Cap and Base Rock Heat Losses

Abstract Variational principles stated by, Biot have been applied to obtain a two-parameter (approximation for heat losses to cap and base rock from a reservoir undergoing thermal recovery. The approximation predicts heat losses to within a few percent of the predicts heat losses to within a few percent of the exact value when the beat losses result from one-dimensional conduction into cap and base rock in the direction normal to the reservoir boundary surfaces. Conduction in the longitudinal direction is neglected. Therefore, the approximate temperature distribution is valid only when the temperature gradient in this direction is small. But because the Peclet number (ratio of convective to conductive heat transport) is high in most reservoir thermal processes, the horizontal temperature gradient will processes, the horizontal temperature gradient will be small everywhere except in the vicinity of a thermal front, and the approximation will be valid. Comparison with a finite-difference solution in cap and base rock shows that reasonable accuracy is obtained when the Peclet number is 100 or greater. The variation solution has been incorporated into our thermal simulator and yields a considerable sailings in core storage. It is no longer necessary to store grid-block temperatures for cap and base rock nor to solve the finite-difference form of the energy balance in this region. Instead a system of two nonlinear ordinary differential equations must be solved for each grid block at the interface of the reservoir and the cap rock. In addition to savings in core storage, a reduction in computation time is achieved because fewer finite-difference grid blocks are needed. Introduction Heat losses to cap and base rock must be considered in modeling thermal processes in petroleum reservoirs. Since there is no mass petroleum reservoirs. Since there is no mass transport in the cap and base rock, the only mechanism for heat transfer is conduction. One of the most obvious ways of determining heat losses from the reservoir is to solve the energy equation in the cap- and base-rock region by finite differences. To do this, the reservoir finite-difference grid must be extended into the cap- and base-rock region. This can consume a good deal of computer core storage - at a time when all available core storage is needed to adequately model mass and energy transport in the reservoir region. Furthermore, since there is no mass transport in the cap and base rock, one would like to eliminate having to solve the conservation-of-mass equations in this region, but to do so requires a special computer code. Hence, a finite-difference solution can be costly. It does, however, have the advantage of generality in that a minimum of assumptions is involved in formulating the conservation equations. There are ways of calculating heat losses to cap and base rock other than by finite differences. However, for a method to be competitive with the finite-difference method, it must offer some advantage such as accuracy, reduced computer core storage, or lower computation time. One alternative to finite differences is the use of superposition to couple an analytic solution for the cap and base-rock temperature distribution with the finite-difference solution of the reservoir energy balance. But, during the course of the simulation, the superposition principle would necessitate having temperature data for all previous time steps for each grid block adjacent to the cap and base rock. This requires an appreciable amount of computer core storage, perhaps even more than would be required for a complete finite-difference solution. Hence, this method does not seem attractive. The use of variational principles appeared to offer the advantages of both reduced core storage and lower computation time and was therefore considered as a means of treating heat losses to cap and base rock. The advantage of the variational method is that a priori knowledge of the approximate shape of the temperature profile can be used to choose the functional form of the temperature distribution. The chosen functional form will contain several free parameters. SPEJ P. 200