Overall Heat Transfer Coefficient Research Articles

5590706 On-line fouling monitor for service water system heat exchangers

The effects of pre-heat temperature (65–95 °C) and holding time (5 and 25 s) on fouling of reconstituted skim milk at high-heat temperatures of 135–150 °C using a bench-top UHT plant were investigated. Fouling was monitored by observing the variation in overall heat transfer coefficient (OHTC) with time and consisted of an induction phase (non-fouling) and a decline phase (fouling). A significantly shorter run-time was obtained with pre-heating at 65 °C than with pre-heating at 75, 85 and 95 °C. A longer holding time (25 s) in the pre-heating section significantly increased the run-time of the plant compared with 5 s holding. The high-heat temperature also affected the OHTC and run-time; similar run-times were observed at 135, 140, 142 and 145 °C but at 150 °C there was no induction phase and fouling rapidly occurred. Overall, pre-heating at 85 °C or 95 °C for 25 s, combined with a high-heat temperature of 145 °C, and pre-heating at 95 °C for 25 s combined with high-heat temperatures of 142 °C, produced the longest run-times of the bench-top UHT plant.

Studies on the zone cooling system in greenhouse 1. Performance of the system in a model-sized greenhouse.

A zone cooling system employing cool air blowing was tested in a model-sized greenhouse. Cool air was provided by a spot cooler, and blown continuously into the lower layer in the greenhouse. The ratio of spot cooler capacity to floor area was about 0.14 kW⋅m-2. The cooling system was tested under dry and wet soil conditions in combination with shading application. The test began on August 18 and terminated on September 12, 1989. In wet soil condition, the cooling system was capable of reducing air temperature at the lower layer in the greenhouse at noon to about 35°C. The system was capable of maintaining air temperature at the lower layer in the greenhouse under dry soil condition to about 1.0°C lower than outside air temperature only during the nighttime (from 18: 00 to 06: 00 JST) . However, under wet soil condition, decreasing air temperature at the lower layer to about 2.7°C lower than that of the outside air was recorded from 17: 00 to 09: 00 JST. The daytime air temperature at the lower layer was about 1.3°C and 2.4°C lower than that of the middle or upper layer under dry and wet soil conditions, respectively. The overall coefficient of heat transfer (U) through single layer cover of vinyl chloride panel was about 15.7 W⋅m-2⋅°C-1 during the daytime, and about 3.6 W⋅m-2⋅°C-1 during the nighttime.

First industrial application of non-azeotropic mixture

Experiments were carried out on a heat pump which recovers energy from a refrigerating installation and warms water from 58 to 68°C. The aim of our experiment is to compare the COP and the thermal power of the heat pump using non-azeotropic mixture instead of R12. Therefore performances of the heat pump have been determined with R12 to obtain a reference, then R12 was replaced by a ternary mixture. The installation includes 31 sensors connected to a computer. We can evaluate the influence of non-azeotropic mixture on the volumetric and isentropic compression efficiencies and on the overall coefficient of heat transfer of the condenser. Tests with the mixture give the following results compared with R12: + 20% for the thermal power at the condenser; +1.5% for the COP; −2% for the volumetric efficiency; −10% for the overall coefficient of heat transfer at the same heat flux. The influence of refrigerant leakages on the mixture composition was studied. The leakages were simulated during running of the plant. It was noticed that the leakages at the input of the dry expansion evaporator and at the top of the receiver do not modify the concentration of the different components enough to change the working conditions of the heat pump.

Chemical reaction engineering aspects of a rotary reactor for carbothermal synthesis of SiC

Heat transfer in a rotary reactor is described for a reactor consisting of a graphite tube with graphite heating elements, and operating at temperatures between 1773 and 2273 K. Under those conditions heat transfer is very good due to radiation and the high thermal conductivity of graphite. An overall coefficient of heat transfer of at least 400 W/m2K is estimated. As an example of the application of a rotary reactor the carbothermal production of SiC is described. A general conclusion is that rotary reactors are well suited for the endothermal reactions.

A Study Of The Fouling Characteristics Of Prairie Geothermal Waters

Abstract The aim of this paper is to assess the importance of fouling of heat exchanger surfaces in the recovery of heat from low-temperature geothermal brines. Samples of brines associated with four western Canadian gas and oil well operations were re-circulated through a test heat exchanger loop over periods of 11 to 30 days. Over-all heat transfer coefficient, pressure drop and brine composition were continuously monitored. The decrease in heat transfer coefficient and the increase in pressure drop which occurred during this time indicated fouling of the heat exchange surface. Typically, the over-all heat transfer coefficient decreased by 2% to 9% over 15 days; however, for one brine sample the drop was as high as 34%. Analyses of deposits found on the heat exchanger tube indicated that corrosion was playing an important role in the fouling process. Introduction Geothermal brines from the Canadian prairies are potential sources of low-grade energy, obtainable as they are at well-head temperatures which are typically in the vicinity of 60 °C. However, the brine produced in geothermal wells is usually very saline with dissolved solids concentrations up to 30%. The heat recovery from such brines is often adversely affected by the scale deposited on the heat transfer surfaces. Deposits may originate as soluble species in the geothermal water, in which case they are usually composed of CaCO3 ? silica or CaSO4, that precipitate due to local supersaturation. Cooling and de-pressurization of the brines will promote deposition of normal solubility salts and carbonates respectively. Alternately deposits may be associated with corrosion processes in the piping system, in which case they may consist largely of iron oxides, silicates and sulphates, or copper or nickel compounds. Thus, the nature of the brine, and its temperature and pressure, as well as the piping materials, will influence the mechanisms of deposit formation and the deposit composition. The work of Bott and Gudmundsson(1,2) deals with deposition from Icelandic brines entering the heat exchanger at about 80 °C to 90 °C and where silica is the primary species in the deposit. Chan and co-workers(3,4) have carried out higher temperature tests using artificial brines with inlet temperatures of about 165 °C, again with silica as the predominant species in the deposit. Lombard(5) studied fouling of California brines at a heat exchanger inlet temperature of about 177 °C, and found deposits which were mainly compounds of iron, sodium, copper and silicon. Presumably, corrosion processes were involved. Materials selection and treatment methods to minimize corrosion and scaling of some U.S. geothermal brines have been described(6). The geothermal brines of interest in the Canadian prairies have been described by Vigrass, Vandenberghe and Postlethwaitea(7,8). Those brines contain roughly 60 000 mg CI/I and are relatively low in silica. Some corrosion testing has been done(9), but no heat exchanger fouling studies have been reported. There is a need for such data because fouling will impact\ on the economics of the heat recovery process through its effects on heat transfer and pressure drop.

Measurement of the overall volumetric coefficient of heat transfer of a shaking flask

The overall volumetric coefficient of heat transfer ( Ua) of a shaking flask was measured under various shaking conditions using three types of flask. Ua was significantly affected by flask weight ( W F), which could be attributed to the thickness of the flask wall, the rotational speed of the shaker ( N), wind velocity ( V W), and the liquid volume in the flask ( V L). The limiting step of heat transfer seemed to be the heat radiation process from the surface of the flask to the surroundings. To predict the value of Ua, the following empirical equations were obtained for each type of flask by the least squares method: 1. (1) for deformed creased flask (M-type flask), Ua=17.4 W F −0.43 V L −0.61 N 0.12 V W 0.36 2. (2) for creased flask (N-type flask), Ua=9.2 W F −0.36 V L −0.57 N 0.17 V W 0.27 3. (3) for smooth flask (S-type flask), Ua=5.3 W F −0.26 V L −0.62 N 0.19 V W 0.25.

Prediction of Bottom-hole Conditions For Wet Steam Injection Wells

Abstract The design of steam injection projects requires a knowledge of the quality and pressure of steam at the sandface before it enters the formation. In order to make such predictions, the multiphase flow and energy balance equations must be solved simultaneously. There are very few multiphase correlations in the literature that could be applied to the down flow of steam. A mathematical model was developed for multiphase, non-isothermal down flow of steam in pipes. Several correlations were tested against limited experimental data. A method was also developed to adjust one of the correlations to fit available experimental data. The results of this investigation indicate the limitations of existing correlations and show the need for more experimental data. Introduction Wellbore heat loss and pressure drop for steam injection wells are often ignored and most thermal reservoir simulators as· same the sandface condition of the steam to be the same as that at the surface. This may be a good approximation for shallow wells, but for deep steam injection wells wellbore heat loss is often substantial. One of the first workers to consider this problem was Ramey(l). He was primarily concerned with wellbore heat loss during the injection of hot water. Ramey developed a model with the following assumptions:The physical properties of the fluid and the formation are independent of depth and temperature.Heat transfer in the wellbore rapidly reaches steady state, while heat transfer to the formation occurs under transient conditions.The over-all heat transfer coefficient, U, is independent of depth.The frictional losses and kinetic energy effects are negligible. Satter(2) improved Ramey's analytical model by making the over-all heat transfer coefficient, U, dependent on depth and the fluid properties a function of temperature. Holst and Flock(3) further improved the models proposed by Ramey and Satter to include friction losses and kinetic energy effects. Pacheco and Farouq Ali(4), as well as Herrera et al(5), presented comprehensive models, but only considered single-phase fluid flow in the tubing. In this paper, a mathematical model is presented that also accounts for two-phase flow in the tubing. Our objective is to see if available two-phase flow correlations, possibly with some minor modifications, are applicable to the down flow of wet steam. Mathematical Model Assuming constant rate of injection (flow rate in the tubing), the conservation of mass, the conservation of energy and the mechanical energy balance equations may be combined to yield the following two simultaneous ordinary differential equations(4.6). (Equation in full paper) Method of Solution The method of solution chosen to simultaneously solve equations 1 and 2 is the Fourth Order Runge Kutta Method(l3). The convergence of the method was tested to obtain the maximum ∆z that could be used without incurring appreciable truncation error. A ∆z of 100 ft was found to be adequate. The computer model consists of a main program and six subroutines. A flow chart of the main program is shown in Table 1.

Study on a Heat Pipe Heat Exchanger

In this paper, the results of the performance tests of the air to air heat exchanger and the heat pipe used in the unit are presented. The heat exchanger is consisted of 28water-copper grooved type heat pipes with 9.74mm diameter. The number of rows of heat pipes is 8 rows with plate Al fins. Face area is 0.01852m2.As the results of the tests, it can be concluded that(1) the experimental values of the over-all heat transfer coefficients are nearly equal to the values calculated by equation being based on over-all thermal resistance of the heat pipe.(2) the experimental values of outside heat transfer film coefficient including fin effi-ciency and contact resistance between fin and heat pipe are lower than the values obtained by using Vampola's equation by 10 percent.(3) the heat transfer rate of the heat pipe exchanger can be obtained diagrammatical on the curve of the evaporator zone surface temperature vs condenser zone surface temperature under a constant heat input.(4) the pressure drop across a heat pipe bunk is higher than the calculated values, but there is not a big difference between the experimental values and the calculated values.

Functions and structure of the Karlsruhe subassembly monitoring system KASUMOS

The KArlsruhe SUbassembly MOnitoring System KASUMOS is a mini-computer based signal processor for individual surveillance of fast reactor fuel elements in real-time. The tasks performed by the system for each subassembly are • - sensitive monitoring with respect to loss of cooling • - measurement of absolute coolant flow rate • - measuring the power generated in the fuel • - monitoring of over-all heat transfer coefficients between fuel and coolant Newly developed methods based on noise analysis techniques are used for this purpose. The common principle behind these methods is comparing measured fuel element outlet temperatures with the outputs of individual fuel element simulators which model the thermal hydraulic performance of the fuel elements. Input to the fuel element simulators are a neutron detector signal and an inlet temperature signal. Into addition, KASUMOS also discontineously measures noise characteristics, e.g. power spectral densities, coherences, correlation functions, rms values, of various plant signals in order to collect early indications of developing malfunctions other than local loss of cooling. KASUMOS is used on-line at the sodium cooled 58 MW th research reactor KNK-II for testing of early failure detection methods. It shall provide the knowledge and experience necessary for developing a reliable surveillance system for improving safety and availability of fast breeder reactors.

Condensation Heat Transfer within a Circular Tube under Centrifugal Acceleration Field

Experimental and analytical investigation has been carried out to determine the effect of centrifugal acceleration on the condensation heat transfer within a circular tube. The experiments were conducted by condensing steam on the inside of a vertical tube rotating about an axis parallel to its own. A physical model was proposed consisting of a laminar filmwise condensation region and a bottom condensate flow region. The results of the present study indicate that the overall coefficient of heat transfer increases substantially with increasing centrifugal acceleration and it is slightly lower than the value for the case of condensation on the outside of circular tube under the same acceleration field.

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

Calculation of Pressure And Temperature Profiles In Multiphase Pipelines And Simpne Pipeline Networks

Abstract The structure and related theory for a computer program to perform detailed design calculations for pipelines and simple pipeline networks are presented and discussed. The sensitivity to calculated pressures, temperatures and total liquid holdups of parameters such as pipe-to-ground heat transfer coefficient, ground temperatures, pipeline orientation (horizontal, uphill and downhill) and total flow rate are examined and discussed in detail for a typical natural gas - condensate system. Some characteristics of several different design calculation procedures are noted. Introduction Multiphase flow in wells and gathering systems is of considerable interest to petroleum engineers as well as many working in other branches of engineering. Petroleum engineers arc particularly interested in the prediction of flow pattern, holdup and pressure drop in well tubings and gathering lines or networks. These calculations areusually rather involved and the problem is further complicated because:no single design method is "best" under all conditions:several design methods must be tried to get some appreciation for the possible range of answer andwhere reliable fluid property or other data are not available, sensitivity of results to variations of these data must be investigated. This makes hand calculations impractical. The calculations are, however, particularly amenable to computer programs and one such program is discussed in this paper. Applications of a previous version of the program are discussed elsewhere.(1,2) Program Structure For calculation purposes, the actual pipeline elevation profile is approximated by choosing a series of modal points on the profile for which x and z coordinates are available. The pipeline is assumed to have a constant slope, mass flow rate and diameter between nodal points; however, any or all of these parameters may change at the nodes. In the program, the distance between nodes is divided into a specified number of segments and, starting with the end where the pressure and temperature are known calculations are performed in a sequential fashion for one segment at a time until calculations are completed for the entire system. The segment size is selected so that the variation of fluid properties over its length is small and differential forms of the flow and energy equations can be used. The flow equation may be written as follows: There are many methods available in the literature for calculating the various terms in Equation (1). These are discussed in detail by Govier and Aziz(3) and compared with experimental data in a series of papers by the authors and Mandhane(4,3,6). In most cases of practical interest, ~PKE is negligible with respect to ΔPHH + ΔPr and can be neglected without significant error. The program contains fouf flow pattern prediction method(4), ten different holdup calculation methods(5) and fourteen different pressure- drop calculation methods(6). The energy equation is discussed in different forms in several references(7,8,9). In the energy equation the heat transfer term q may be estimated from (Equation Available In Full Paper) Estimation of the over-all heat transfer coefficient, U, is possible by a number of available method (10,11,12).

Research and development of multi-effect horizontal tube film evaporator

MEHF (Multi-Effect Horizontal Tube Film Evaporator) was established by the series of R & D since 1972. As the following results of them, we successfully established more economical evaporator than the existing distillation plant in view of evaporator cost, power and chemical consumption and required plot area; 1. By the experimental study on heat transfer characteristics of film evaporation, the over-all heat transfer coefficient is in range of 4500 to 6500 kcal/m 2h°C at the corresponding evaporation temperature of 60 to 100°C under non-foul conditions. 2. The over-all heat transfer coefficient is greatly influenced by evaporation temperature, however, less susceptible to heat flux, seawater sprayed flow rate and tube diameter from the same study as item (1). 3. According to the process and shell construction studies, each effect chamber must be vertically arranged in main combined with supplemental horizontal arrangement to achieve a compact and integrated shell construction and to circulate the brine once-through from the first to the last effect tube bundle with mutual pressure difference and gravity for minimization of power consumption and tube surface scale formation. 4. As for scaling prevention, according to the results from the test operation of a single effect apparatus and the practical plant of 150 m 3/d (3-effect), the pretreatment of make-up seawater by the pH control method usually employed on the MSF is sufficiently effective, and the chemical addition method employing inhibitor “X” can be also applicable to MEHF.

Heat transfer under solidification of liquid on agitated vessel wall.

The heat transfer under solidification of lauric and capric acids on the cooling wall of an agitated vessel is studied, and the over-all and convective heat transfer coefficients, respectively, are measured and correlated with the impeller Reynolds number. The over-all heat transfer coefficient decreases sharply as depositing solid layer forms, but the convective heat transfer coefficient is well correlated by the already reported correlation equation independently of existence of solid layer. That is, the convective heat transfer coefficient in the vessel with solid layer coincides with that in the vessel without solid layer.

A Study on Non-Steady Combustion : 1st Report, On the Fluctuation of the Entropy Mode

In the flow field accompanying combustion, there exist three kinds of fluctuating modes such as pressure, entropy and vorticity types. Then, it can be regarded that the self driving sources of combustion oscillation originate from the mutual transforming rate and the mutual coupling processes among these three modes. However, if we restrict the oscillations to axial types only, the vorticity mode can be excluded. Among the former two modes, this report deals with the fluctuations which belong to the entropy mode. In the first place, experimental equations of steady heat release rate and temperature state are proposed. In the second place, expressions of non-steady state concentration, heat release rate and temperature are derived theoretically. As a separate subject, it was examined how and to what degree the decreasing process of entropy mode would be affected by frequency, heat conductivity, over-all heat transfer coefficient and flow velocity. The obtained results show that the temperature oscillations decrease slowly, which has been considered to be dissipated immediately behind the heat source.

Some Results of Actual Observations of Soil Heat Transfer in Heated Greenhouses

The formula for calculating the heat requirements in greenhouses is represented by the following equation:Q=Aw(K+hven)(Ti-To)+AfBswhere Q=heat requirements, Kcal hr-1K=over-all coefficient of heat transfer, Kcal m-2 hr-1°C-1hven=ventilating heat transfer coefficient, Kcal m-2 hr-1°C-1Bs=soil heat transfer, Kcal m-2 hr-1Ti, To=inside air temperature and outside air temperature, °CAf, Aw=floor area and exposed surface area, m-2From the above equation, the heating load coefficient of greenhouses is represented by the following expression:K=k+hven+βBs/Ti-Towhere K=heating load coefficient, Kcal m-2 hr-1°C-1β=Af and Aw ratioIn order to evaluate the heating load coefficient, the magnitude and the direction of soil heat transfer are required to be decided clearly.The middle house of the three similar type plastic greenhouses (Fig 1-A) not planted to any crops and the two similar type plastic greehouses (Fig. 1-B) planted to tomatoes were used as sample houses for the tests. Each of the greenhouses shown in Fig 1-A was covered with a clear vinyl chloride film of 0.1mm in thickness. And the middle house was lined inside with single or double clear vinyl chloride film of 0.075mm in thickness, respectively, leaving a 15-cm air space between the two film covers. The houses were heated by electrical heating cables or by electrical hot air heaters. The output capacity of these heating systems is variable from 0.6kW to 12kW.The greenhouses shown in Fig. 1-B were covered with clear vinyl chloride films of 0.1mm each in thickness. One house was heated by electrical hot air heaters and another was heated by electrical heating cables. The total calorific values generated by these heating systems was estimated at 5160 Kcal per hour.The observed values of temperature and soil heat transfer and the calculated values of heating Fig. load coefficient and overall coefficient of heat transfer are as given in Table 1. From Table 1. and 2, it was proved that the heat transfer from the soil in the triple-covered house heated by a 0.6kW electrical hot air heater accounted for about 50% of the total heat supply.Therefore, it was concluded that the difference between the heating load coefficient and the over-all coefficient of heat transfer in the double- or triple-covered air- tight house is due to a great quantity of soil heat transfer, as compared with the total heat supply.From Fig. 5, the heating load coefficient was calculated at 3.7Kcal m-2 hr-1 °C-1 in the house heated by electrical heating cables and at 3.2 Kcal m-2 hr-1°C-1 in the house heated by electrical hot air heaters. However, judging from the growth of tomatoes, the soil temperature and the vertical distribution curve of air temperatures, it might safely be concluded that the heating system by means of electrical heating cables in the greenhouse is more suitable than the heating system by means of electrical hot air heaters.

Wellbore Heat Losses and Pressure Drop In Steam Injection

This mathematical model of the mechanics of flow of wet and saturated steam down the wellbore during steam injection takes into account the variation of steam temperature and pressure due to friction, as well as heat losses by radiation, conduction, and convection. It consists of two coupled nonlinear equations that are solved iteratively. Introduction Chekalyuk et al., Moss and White, and Fokeev and Kepyrin, investigated wellbore heat losses during injection of a hot or cold fluid down the casing. Ramey made a comprehensive study of the injection of liquids and gases down casing or tubing. Squier et al. presented a complete analytical treatment of hot water injection down the wellbore. Satter extended Ramey's treatment to the case of steam injection. Huygen and Huitt, presented results of a theoretical and experimental treatment of wellbore heat losses during steam injection, and pointed out the importance of the radiation heat loss. Holst and Flock as well as Earlougher extended the above treatments by including, steam pressure calculations. Eickmeier et al. considered the early transient performance, using a finite-difference model. performance, using a finite-difference model. Apart from these studies, Leutwyler gave a comprehensive treatment of casing temperature behavior, and Willhite presented a complete calculation of the over-all heat presented a complete calculation of the over-all heat transfer coefficients. The chief objective of our work was to formulate a comprehensive mathematical model of steam injection into a reservoir to include simultaneous calculation of steam pressure and quality. The model took into account the variation of steam temperature and pressure due to friction, as well as heat losses by pressure due to friction, as well as heat losses by radiation, conduction, and convection, and consisted of two coupled nonlinear differential equations that were solved iteratively. The model results were compared with those predicted by several of the above-mentioned approaches. Formulation of the Model Steam at a constant injection pressure, constant mass flow rate, and constant quality (at the surface) is injected through the tubing into the wellbore. The complete system consists of the fluid, the tubing, the annular space containing low-pressure air, the casing, the cement, and the formation. We propose to compute the pressure and the quality of steam as functions of depth and time. An energy balance and a momentum balance can be written for the flowing fluid as follows: Energy balance ..........(1) Momentum balance ..............................(2) The term dQ is given by,...................(3) where the rate of heat transfer to the formation is (4) dq = , JPT P. 139

Experimental Determination of Greenhouse Heating Load Coefficient

In order to calculate the heat requirement per unit floor area for greenhouse heating design, a simple equation has been derived (eq. 1), and its constant has been defined as heating load coefficient(K). Suppose that r% of the total heat loss from the greenhouse is transferred into the soil, the heating load coefficient results in 100kt/(100-r) and the total heat requirement is given by eq. 6, where Kt is the sum of thee overall heat transfer coefficient of the greenhouse wall (k) and the heat transfer coefficient due to ventilation (hven). These coefficients, the over-all heat transfer coefficient of the greenhouse wall and the heat transfer coefficient due to ventilation are expressed by eqs. 3 and 4, respectively.In the present field experiment, two identical greenhouses, one is east-west oriented and the other is north-south have been used. Both of them were heated by circulating hot water.The heat balance analysis of the greenhouses shows that 50% of the total heat loss from the greenhouse is due to radiation, 20% due to convection from the outside surface to the outside air, 20% due to ven tilation, and 10% due to conduction into the soil in approximate values. It is also shown that the over-all heat transfer coefficient of the greenhouse wall is constant (k=4.8) and would not be affected by the fluctuation of the outside weatherconditions, and the heat transfer coefficient due to ventilation is a linear function of the outside wind speed(eq. 7).The ratio of the heat loss into the soil to the total heat loss of the greenhouse given as percentage is presented in Fig. 5. In order to evaluate the heating load coefficient, the value of r must be determined. In the present study, the value of 10 is adopted for fail safe. Consequently, the heating load coefficient of the greenhouse is determined as a linear function of outside wind speed, i. e., eq. 10. Using eqs.1 and 10, the stochastic evaluation of the heat requirement of the greenhouse is demonstrated in relation to outside wind speed and daily minimum temperature in Figs. 6a and b. In the same figure, the heat requirement lines are indicated by the group of hyperbolic curves.

Permafrost Thawing Around Producing Oil Wells

Abstract A mathematical thermal model for predicting the time dependent temperature distribution surrounding a production well is described. The model provides for two-dimensional radially symmetrical and vertical heat conduction in the surrounding earth. Heat transfer from the produced fluids to the earth by conduction, convection and radiation is accounted for through an over-all heat transfer coefficient. The latent heat of fusion of water is included in the Model. The boundary of the melted zone at any time corresponds to the location of the 32 °F isotherm at that time. This boundary can be determined for various well completions either with or without insulation protection. Thus, the need for insulation can be determined as well as the effectiveness of various insulation schemes. Typical calculated results are presented for a well completed through 1,400 feet of permafrost with the top 700 feet of tubing insulated. INTRODUCTION THE DISCOVERY OF OIL IN ARCTIC REGIONS has introduced many new and unique problems which must be dealt with successfully before that oil can be brought to market. One anticipated difficulty is the thawing of the permafrost around the producing oil wells in these regions. This thawing is caused by the production of large volumes of hot fluids (possibly at 200 °F bottom-hole temperature) for extended periods of time. Any thawing that occurs at the cement-permafrost interface will destroy the cement bond. Thawing of the permafrost in the layers near the surface will result in sloughing of the soil around the wellbore. The ensuing mechanical stresses imposed on the casing could result in irreparable damage and necessitate premature abandonment of the well. In view of the tremendous drilling and completion expenses encountered in the Arctic, this is obviously undesirable. There are two possible approaches to solving this problem. One is to prevent thawing of the permafrost through a section thick enough to maintain a competent well completion. The other is to allow permafrost thawing and design a well completion which will be compatible with the adverse conditions resulting there from(1). For the first of these solutions there are again two possible means for accomplishing this goal. One method is to adequately insulate the production string through some portion of the permafrost zone. The second method is to refrigerate the casing string through some portion of the permafrost zone. In order to evaluate the alternatives of insulating the production string, a mathematical model giving a detailed description of the heat flow in and around the producing well is required. Previous models of wellbore heat flow(2,3) have neglected vertical heat flow in the earth surrounding the well, and the latent heat of fusion was not included in their energy balance. The use of these older models must be considered as only approximate solutions for the thawing problems treated here. A mathematical model has been developed which can predict the extent to which thawing will occur in unprotected wells and can evaluate the effectiveness of various schemes of insulating the production string.

A Note on the Theory of Temperature Logging

Interest in temperature logs has been renewed recently. One of the main problems of temperature logs in injection wells is that of determining the zones that are taking fluids. A great step toward solving this problem has been reported in a recent paper. paper. The purpose of this paper is to point out another aim of temperature logging namely, that of relating the flow rate in water injection wells to some characteristics of the temperature logs. It has been stated that a factor of 6:1 gives approximate values in converting into B/D. The factor F, which has been found empirically, may be explained from theoretical considerations and because of this, it may be estimated more accurately. It has been shown that, for flow of a liquid ,............................(1) where .......................(2) a quantity that is different from zero. Eq. 1 can be written as ,..................................(3) which shows that, as is defined in Ref. 2, is identical to A. For injection down casing, the over-all heat transfer coefficient, U, may be considered infinite. Therefore, ...................................(4) Considering the wellbore as a linear point source, ....................(5) or, if ........................................(6) .......................(7) It has been observed that surprisingly good results are obtained by using the values k = 33.6 Btu/day-ft-F and a = 0.96 sq ft/day for different locations. Taking the values p = 350 lb/bbl, c = 1 Btu/lb-F, one obtains: ........................(8) It should be noted that the lower curve of Fig. 1 of Ref. 3 does not agree, for low values of t, with the solution .........................(9) corresponding to the constant heat flux line source and for this reason the graph should be used with caution. Eq. 8 has been plotted in Fig. 1 for three values of the external radius r'. It may be used to estimate the rate of water injection down casing from the shape of the injecting temperature log above the zone of entry of fluids. P. 375