Steady-state Radial Flow Research Articles

Effective thermal conductivity of LaNi5 powder beds for hydrogen storage: Measurement and theoretical analysis

Accurately measuring and analyzing the effective thermal conductivity of metal hydride beds is critical to design the structure of solid-state hydrogen storage tanks. On the basis of the steady-state radial heat flow method, a measurement cell of effective thermal conductivity was manufactured. The effective thermal conductivities of nonactivated and activated LaNi5 powder beds were measured in helium, nitrogen, and argon atmospheres with the temperature changing from 20 to 60 °C and pressure from 0.1 to 4.0 MPa. Then, the effective thermal conductivities were further analyzed using the Zehner–Schlünder–Damköhler model. Results show that the effective thermal conductivities can be enhanced by increasing gas thermal conductivity, gas pressure, and bed temperature. In addition, the effective thermal conductivities can be accurately predicted using the modified Zehner–Schlünder–Damköhler model considering the Smoluchowski effect (error < ± 5 %). With the use of the modified Zehner–Schlünder–Damköhler model, the contributions of different heat transfer pathways to the entire heat transfer of LaNi5 powder beds were analyzed. Approximately 70 %–91 % of the effective thermal conductivity of LaNi5 powder beds is contributed by the conduction of the particle–gas–particle pathway.

Measurement of effective thermal conductivity of lithium metatitanate pebble beds by steady-state radial heat flow method

As a functional material of the tritium breeding blankets of the future fusion reactor, different candidates of the lithium-based ceramics have been considered to generate and release tritium. These tritium breeding materials in the form of packed pebble beds of nearly spherical-shaped particles have many advantages over the sintered pellets or blocks. For the design and analysis of the breeding blanket, the effective thermal conductivity (keff) of lithium-based ceramic pebble beds are required to be well characterized under the fusion-relevant conditions. In this study, an experimental setup has been fabricated and installed to estimate the keff of pebble beds as a function of bed temperature and filling gas pressure. The working principle of the experiment is based on the steady-state radial heat flow method. The various experiments have been performed on lithium metatitanate (Li2TiO3) pebbles having a diameter of 1 ± 0.15 mm to measure keff in the temperature range from 400 °C to 800 °C and in the environments of stagnant helium gas. The pressure of helium gas was adjusted from 0.105 MPa to 0.4 MPa (abs.) to account the effect of helium gas pressure. The increase in keff has been found with increasing the bed temperature and also increasing the helium gas pressure. The obtained results have been found comparable with the literature results with minimum difference.

Measurement and analysis of effective thermal conductivity of LaNi5 and its hydride under different gas atmospheres

In this work, an ETC measurement cell based on the steady-state radial heat flow method was fabricated, and its reliability was validated by a commercial instrument. The ETCs of unactuated and activated LaNi5 powder beds were measured under various filling gases in the pressure range from 0.1 to 1.5 MPa. The experimental results show that the ETC of activated LaNi5 powder is much lower than that of the unactuated material due to the pulverization effect. The ETCs of unactuated and activated LaNi5 powder in helium atmosphere lie in the ranges of 1.04–1.63 W m−1 K−1 and 0.49–0.85 W m−1 K−1, respectively. Furthermore, the ETC increases with the increasing pressure and thermal conductivity of filling gas. The effects of hydrogen absorption and desorption on the ETC were investigated by step-by-step reaction, which depend mainly on the hydrogen concentration and expansion/constriction of MH particles.

Hydraulic Conductivity Estimation Using Low-Flow Purging Data Elaboration in Contaminated Sites

Hydrogeological characterization is required when investigating contaminated sites, and hydraulic conductivity is an important parameter that needs to be estimated. Before groundwater sampling, well water level values are measured during low-flow purging to check the correct driving of the activity. However, these data are generally considered only as an indicator of an adequate well purging. In this paper, water levels and purging flow rates were considered to estimate hydraulic conductivity values in an alluvial aquifer, and the obtained results were compared with traditional hydraulic conductivity test results carried on in the same area. To test the applicability of this method, data coming from 59 wells located in the alluvial aquifer of Malagrotta waste disposal site, a large area of 160 ha near Rome, were analyzed and processed. Hydraulic conductivity values were estimated by applying the Dupuit’s hypothesis for steady-state radial flow in an unconfined aquifer, as these are the hydraulic conditions in pumping wells for remediation purposes. This study aims to show that low-flow purging procedures in monitoring wells—carried out before sampling for groundwater characterization—represent an easy and inexpensive method for soil hydraulic conductivity estimation with good feasibility, if correctly carried on.

Grid convergence for numerical solutions of stochastic moment equations of groundwater flow

We provide qualitative and quantitative assessment of the results of a grid convergence study in terms of (a) the rate/order of convergence and (b) the grid convergence index, GCI, associated with the numerical solutions of moment equations (MEs) of steady-state groundwater flow. The latter are approximated at second order (in terms of the standard deviation of the natural logarithm, Y, of hydraulic conductivity). We consider (1) the analytical solutions of Riva et al. (Transp Porous Med 45(1):139–193, 2001) for steady-state radial flow in a randomly heterogeneous conductivity field, which we take as references; and (2) the numerical solutions of the MEs satisfied by the (ensemble) mean and (co)variance of hydraulic head and fluxes. Based on 45 numerical grids associated with differing degrees of discretization, we find a supra-linear rate of convergence for the mean and (co)variance of hydraulic head and for the variance of the transverse component of fluxes, the variance of radial fluxes being characterized by a sub-linear convergence rate. Our estimated values of GCI suggest that an accurate computation of mean and (co)variance of head and fluxes requires a space discretization comprising at least 8 grid elements per correlation length of Y, an even finer discretization being required for an accurate representation of the second-order component of mean heads.

Steady-State Radial Flow Modeling through the Production Well in the Confined Aquifer of Monzoungoudo, Benin

This study aims to develop a mathematical analysis for one-dimensional modeling of a radial flow through a production well drilled in a confined aquifer, in the case of steady-state flow conditions. An analytical solution has derived from that expression for estimation of drawdowns according to different flowrates. Through that process, the evaluation of static pressure, the calculation of hydraulic charge due to the waterflow through the well is evaluated, the drawdowns curves are drawn and at last, the obtained curves are analyzed. The curves obtained for the different flow rates have an asymptotic direction, the axis of the hydraulic charges. The variation of the hydraulic charge depends on the radial distance for different flow rates. The P point, is a common point of all curves obtained for different production flowrates in the well. This point is where the well production flowrate is optimum for the optimal hydraulic charge.

Steady State Radial Flow in Anisotropic and Homogenous in Confined Aquifers

The purpose of this paper is to introduce the analysis of steady-state radial flow in an anisotropic and homogenous hydraulic property and discuss who we can estimate aquifer parameters from field pumping tests.

Direct estimation of hydraulic parameters relating to steady state groundwater flow

Groundwater as an important, life-sustaining resource for humankind is being threatened by massive over-extraction and wide-spread contamination. Wise development and protection of this crucial resource requires a thorough understanding of groundwater flow in the subsurface. This paper presents a novel direct method to estimate important hydraulic parameters characterizing steady state groundwater flows for confined and unconfined isotropic aquifers. The method is appropriate for application in aquifers where horizontal flow dominates. The governing equations for the direct estimation method are superposed extensions of the well-known Thiem equation governing steady-state radial flow toward a pumping well under confined and unconfined conditions. This new approach has the following advantages over conventional methods: (1) simultaneously provides estimates of both hydraulic conductivity and hydraulic gradient, (2) can be applied using historical data without the need to conduct a pumping test, and (3) is a simple analytical method that can be applied easily. Verification of the direct estimation method is achieved by applying it to hypothetical homogeneous and heterogeneous aquifers simulated by three-dimensional finite element models. The usefulness of the method is also demonstrated with data from an actual field site.

Inflow Performance of a Cyclic-Steam-Stimulated Horizontal Well Under the Influence of Gravity Drainage

Summary In this paper, we present a new, semianalytical gravity-drainage model to predict the oil production of a cyclic-steam-stimulated horizontal well. The underlying assumption is that the cyclic steam injection creates a cylindrical steam chamber in the upper area of the well. Condensed water and heated oil in the chamber are driven by gravity and pressure drawdown toward the well. The heat loss during the soak period and during oil production is estimated under the assumption of vertical and radial conduction. The average temperature change in the chamber during the cycle is calculated using a semianalytical expression. Nonlinear, second-order ordinary differential equations are derived to describe the pressure distribution caused by the two-phase flow in the wellbore. A simple iteration scheme is proposed to solve these equations. The influx of heated oil and condensed water into the horizontal wellbore is calculated under the assumption of steady-state radial flow. The solution from the semianalytical formulation is compared against the results from a commercial thermal simulator for an example problem. It is shown that the model results are in good agreement with those obtained from reservoir simulation. Sensitivity studies for optimization of wellbore length, gravity drainage, bottomhole pressure, and steam-injection rate are conducted with the model. Results indicate that the proposed model can be used in the optimization of individual-well performance in cyclic-steam-injection heavy-oil development. The semianalytical thermal model presented in this work can offer an attractive alternative to numerical simulation for planning heavy-oil field development.

Intercomparison of Insulation Thermal Conductivities Measured by Various Methods

In the present contribution, systematic effective thermal-conductivity measurements with different methods are reported for various materials. One of the materials studied, calcium silicate, is isotropic; the other two, alumino-silicate and alumina fiber mats, are non-isotropic. The measurements were carried out with two different steady-state panel test apparatus (according to ASTM C201, designed and constructed by authors), two guarded hot-plate apparatus (ISO 8302, with either one or two samples), one steady-state radial heat flow apparatus (designed by authors), and one transient hot-wire instrument (DIN EN 993-14). These apparatus are operated at ambient pressure and atmosphere (air) between 20 and 1,650°C, and are briefly described in the article. The results show the well-known increase of effective conductivity with temperature, mainly due to radiation heat transfer. For the case of the isotropic calcium silicate material (bulk density of 220 kg m−3), no significant differences between the various methods have been found and the results can easily be correlated within ± 10%. The fiber-mat results, however, show additional effects of the density (between 103 and 170 kg m−3) and the fiber orientation. Large differences exceeding 30% are found between plate and hot-wire results.

Pressure Transient Analysis in SAGD

Abstract Steam Assisted Gravity Drainage (SAGD) is an in situ thermal recovery technique used at Petro-Canada's MacKay River Project. The objective of this study is to develop an analytical well test method that would allow a measure of steam chamber volume and potentially the timing and location of steam chamber coalescence. This well test method would also prove useful in determining an analytical solution for near wellbore characteristics and reservoir boundaries. A pseudo-compositional thermal simulator was used to generate reservoir pressure responses by shutting off an injector at different periods of time and monitoring the pressure fall-off while continuing with production. Confined, unconfined, and coalesced 2-dimensional sink-source well pair models, based upon the geology and drilling pattern at Petro-Canada's MacKay River Project, were used in the study. The effect of the magnitude of the vertical permeability and the vertical to horizontal permeability ratio on the shut-in pressure response was also studied so that this method could be applied to other reservoirs of differing geology. Pressure response type curves were generated and the relationships between pressure drop at the injector, shut-in time, and steam chamber volume were determined. We show that the pressure response type curves are unique for different types of SAGD wells and levels of steam chamber development. This information will aid in determining the timing of operational conversions and determining recovery factors and possibly locations of reservoir boundaries, as well as steam chamber coalescence. Introduction In a commercial SAGD project, it can be expected that as the steam chambers mature and sweep through the reservoir, the well pairs will begin to interact with each other and the steam chambers will coalesce(1). Coalescence is defined as the point at which separate adjacent steam chambers merge to form one large steam chamber. Coalescence is used for timing operational conversions to secondary recovery schemes, such as solvent injection. As a result of the planning that is required for the operational conversion, a method of measuring the volume of the steam chamber would prove useful in estimating the timing of coalescence and the subsequent operational conversions. Considering there are 25 well pairs at MacKay River, it is also necessary to know which well pairs have coalesced so as to know the well pairs in which to institute operational conversions. For this reason, a well test method for determining which well pairs have coalesced is also required. The distance to and orientation of boundaries, flow regime, near wellbore characteristics (such as skin factor), and reservoir characteristics (such as effective permeability) can be determined through conventional pressure transient analysis. Conventional horizontal well testing has four different flow regimes that can be observed in the pressure response: early time radial flow, early time linear flow, pseudo steady state radial flow, and late time linear flow(2). The analytical solution is then applied in segments to the well test based upon the flow regime indicated by the pressure response. This segmental analysis can then be used to determine the reservoir characteristics.

Effect of Thermal Conductivity Mismatch on the Thermal Stresses in a Dispersed Phase-Continuous Matrix Composite Material Undergoing Steady-State Heat Flow

Under conditions of heat flow a mismatch in the thermal conductivity of the components in a composite material gives rise to localized stresses and displacements not present under isothermal conditions. These localized displacements result in additional bending displacements (i.e., additional curvature) at the continuum level. When such curvature is constrained, additional thermal stresses will arise which are superposed on those based on conventional thermoelastic theory and the isothermal properties of the composite material. This phenomenon is referred to as the “thermal conductivity mismatch effect.” For any given composite material, this effect can be analyzed by numerical means. It is the purpose of this study to present an analytical approach to this problem based on an approximate analytical expression for the effective coefficient of thermal expansion in thermal bending under conditions of steady-state heat flow. The specific geometry selected for this analysis consisted of a short ring subjected to steady-state radial heat flow. The approach taken was to first calculate the thermal stresses based on isothermal thermal properties and then superpose the stresses resulting from the change in the coefficient of thermal expansion in thermal bending due to the presence of heat flow. Numerical examples for an aluminum oxide-aluminum composite material indicated that the thermal conductivity mismatch effect can play a significant role in the magnitude of the thermal stresses and can be positive or negative depending on the direction of mismatch. This latter finding suggests a solution for materials selection for engineering design involving high magnitudes of thermal stress.

Time-related capture zones for radial flow in two dimensional randomly heterogeneous media

We consider the effect of randomly heterogeneous hydraulic conductivity on the spatial location of time-related capture zones (isochrones) for a non-reactive tracer in the steady-state radial flow field due to a pumping well in a confined aquifer. A Monte Carlo (MC) procedure is used in conjunction with FFT-based spectral methods. The log hydraulic conductivity field is assumed to be Gaussian and stationary, with isotropic exponential correlation. Various degrees of domain heterogeneity are considered and stability and accuracy of the MC procedure is examined. The location of an isochrone becomes uncertain due to heterogeneity, and it is strongly influenced by hydraulic conductivity variance. The probability that a particle released at a point in the aquifer is pumped by the well within a given time is identified. We propose a new expression for the probabilistic spatial distribution of isochrones, which is formally similar to the analytical solution for a uniform medium and takes into account the effects of heterogeneity.

The Combined Effect of Near-Critical Relative Permeability and Non-Darcy Flow on Well Impairment by Condensate Drop Out

SummaryWe present a comprehensive numerical method to calculate well impairment based on steady-state radial flow. The method incorporates near-critical relative permeability and saturation-dependent inertial resistance.Example calculations show that near-critical relative permeability, which depends on the capillary number, and non-Darcy flow are strongly coupled. Inertial resistance gives rise to a higher capillary number. In its turn, the improved mobility of the gas phase caused by a higher capillary number enhances the importance of the inertial resistance.The effect of non-Darcy flow is much more pronounced in gas condensate reservoirs than in dry gas reservoirs. Well impairment may be grossly overestimated if the dependence of relative permeability on the capillary number is ignored.

Reservoir Inflow While Underbalanced Drilling-A Qualitative Perspective

Abstract This paper discusses the importance of inflow in underbalanced drilling. The various inflow models are mentioned. A link between dynamic inflow performance model and hydraulic model is emphasized. The potential quantification of inflow on bottomhole pressure changes due to injected blend ratios during underbalanced drilling is highlighted. Using the relationship between inflow and bottomhole pressure changes, optimum wellbore lengths as well as reservoir evaluation could be achieved during underbalanced drilling. Introduction The application of underbalanced drilling is gaining momentum as a new technology capable of providing economic benefit to projects where formation damage and/or problematic drilling events have frequently affected project viability and economics. An unexplored and poorly understood benefit of underbalanced drilling is the ability to quantify reservoir inflow in real time while drilling. Reservoir engineers have not previously been given the opportunity to directly relate inflow to decreased damage due to the underbalanced drilling process. Reservoir modelling and calibration has typical been based on history matching of wells that were drilled "conventionally." In spite of extensive production data and years of knowledge applied in the field, experience has shown that predictions of formation inflow rates for underbalanced wells can be underestimated by as much as 200 to 300%. The methodology used to calculate inflow as applied to wells drilled underbalanced must be revised. Many reservoir inflow computer models exist and are available to the reservoir engineer. Internal calculation engines typically rely on the conservation of mass and/or heat. Basically, these models predict inflow of a fixed well geometry over a specific sandface drawdown in a specified time. Radial, spherical and linear flow regimes ranging from pseudo-steady-state through to steady-state flow conditions are investigated, ultimately providing data regarding total flow to surface. What is not commercially and readily available, is a reservoir model that predicts inflow in a dynamic elemental sense. Simulation of petroleum reservoir performance refers to the construction and operation of a model whose behaviour assumes the appearance of actual reservoir behaviour(1). The model itself is either physical (for example, a laboratory sandpack) or mathematical. A mathematical model is simply a set of equations that, subject to certain assumptions, describes the physical processes active in the reservoir. In calculating the productivity of wells, the common assumption is that inflow into the well is directly proportional to the pressure differential between the reservoir and the wellbore. The proportionality constant PI, is derived from Darcy's law for steadystate radial flow for a single, incompressible fluid. In instances where this relationship holds, a plot of production versus bottomhole pressure yields a straight line. Muskat(2) pointed out that when two-phase (liquid and gas) flow exists in the reservoir, this relationship may not hold; and went on to present theoretical calculations to show that graphs of producing rates versus bottomhole pressures for two-phase flow resulted in curved rather than straight lines. With the existence of a curvature, a well cannot be said to have a single PI, since the value of the slope varies continuously with changes in the drawdown.

On Optimizing an Acid Treatment

Abstract A theoretical approach has been used to develop a method for optimizing an acid treatment of a formation. The technique is based on an experimental determination of the permeability increase with porosity due to reaction with the acid. The calculation applies mostly to matrix acidizing and is more uncertain when wormholes are present Introduction In view of recent studies in the theory and practice of acidizing a formation matrix to increase reservoir production(1,2,3,4,5), it seems useful to outline an approximate theoretical approach which optimizes the effect of acid on the rock by determining a preferred distribution of permeability. That a suitable choice of radius of penetration and permeability around the wellbore may give favorable results was suggested by Rowan(6) a number of years ago. The approach in this Note determines the permeability distribution around the well likely to yield the maximum improvement in productivity for a given amount of acid injected into a uniform formation. The method considers the idealized case in which some definable relationship between the permeability and rock porosity attained during acidizing can be obtained experimentally. This is possible in those cases where acid penetrates the Rock matrix in a relatively uniform manner. These would include sandstones and sometimes carbonates under carefully controlled conditions(7). For carbonates, however, the tendency to develop wormholes during acid injection makes such a relationship more uncertain(7). However, in such cases, if a relation between permeability and porosity can be obtained the following analysis would apply. The mathematical technique which permits specifying the manner of distribution of the porosity and, hence, of the acid depends on the Calculus of Variation(8). Throughout the Note it is recognized that the theory is idealized and would ultimately depend on the development of practical field techniques for its application. Theory It is sufficient for present purposes to consider the simple ease of steady-state radial flow of a single phase incompressible fluid and a permeability which varies radially but not vertically. For this case Darcy's law may be applied to radial flow to give the following for the overall pressure drop: Equation (1) (Available in full paper) The permeability k(r) is allowed to vary with radial distance from the wellbore and is determined by the local porosity. The productivity index is given by Equation (2) (Available in full paper) Define dimensionless variables Equation (3a,b,c) (Available in full paper) Equation (3d,e,f) (Available in full paper) where t = treated radius and substitute into Equation (2) obtaining Equation (4) (Available in full paper) We assume that the productivity JD will have its maximum value when kD(rD) is chosen to make the integral in Equation (4) a minimum. A constraint on the choice of kD(rD) is provided by the requirement that a given amount of acid will react with a fixed amount of rock. The local value for permeability will then be determined by the local porosity, i.e., kD = kD [ΦD(rD)]. This method depends upon the possibility of obtaining a relationship of permeability to porosity by laboratory tests on the rock of interest.

Spatial averaging of hydraulic conductivity under radial flow conditions

Steady-state radial flow in three-dimensional heterogeneous media is investigated using a geostatistical approach. The goal of the study is to develop a model of the relationship between corescale hydraulic conductivities measured at the wellbore and the conductivity of the surrounding drainage region as measured by a larger scale flow experiment such as a pump test. Conductivity at the point or core-scale is modeled as a stationary and multivariate lognormal spatial random function. Conductivity of the drainage region is obtained by a weighted nonlinear spatial average over the point-scale values within. This empirical spatial averaging process is shown to yield excellent approximations of true effective drainage region conductivities calculated using a numerical flow model. The geostatistical model for point-scale conductivity and the spatial averaging process are used to determine the first and second order ensemble moments of drainage region conductivity. In particular, an expression is derived for the conditional expectation of drainage region conductivity given point-scale values measured at the wellbore. The results are illustrated in a case study of a well from a sandstone oil reservoir where both core and transient-test conductivity data from the same interval are available for comparison.

Pumping test data interpretation and drift inflow assessment by finite-difference radial modelling

A digital radial (r-z-t) finite-difference model for the simulation of constant-discharge pumping-tests in multilayered ground is described. The model is particularly useful for the interpretation of multiport piezometer data since the drawdown at each port can be independently simulated on the r-z-t grid. Unlike conventional methods of pumping-test interpretation, where flow and ground properties are usually averaged over one or two layers, the radial (r-z-t) model allows a detailed approximation of the vertical variation in ground hydraulic properties. A case study is described in which the radial (r-z-t) model is applied to the interpretation of multiport piezometer data from two pumping-tests carried out in a site investigation for a proposed new surface drift. The resulting permeability distribution is then used as input data to model inflows to the proposed drift under construction. Three-dimensional inflows to a short length of unlined drift open section are approximated using steady-state radial (r-z) flow models. Use of the numerical modelling techniques result in a better understanding of the groundwater system than that obtained from conventional analytical techniques.

Production-Systems Analysis for Fractured Wells

Summary Production-systems analysis has been in use for many years to design completion configurations on the basis of an expected reservoir capacity. The most common equations used for the reservoir calculations are for steady-state radial flow. Most hydraulically fractured wells require the use of an unsteady-state production simulator to predict the higher flow rates associated with the stimulated well. These high flow rates may present problems with excessive pressure drops through production tubing designed for radial-flow production. Therefore, the unsteady-state nature of fractured-well production precludes the use of steady-state radial-flow inflow performance relationships (IPR’s) to calculate reservoir performance. An accurate prediction of fractured-well production must be made to design the most economically efficient production configuration. It has been suggested in the literature that a normalized reference curve can be used to generate the IPR’s necessary for production-systems analysis. However, this work shows that the reference curve for fractured-well response becomes time-dependent when reservoir boundaries are considered. A general approach for constructing IPR curves is presented, and the use of an unsteady-state fractured-well-production simulator coupled with the production-systems-analysis approach is described. A field case demonstrates the application of this method to fractured wells.

Finite-element simulation of low-temperature, heat-pump-coupled, aquifer thermal energy storage

A two-dimensional, Galerkin finite-element, transport model was applied to a feasibility study of low temperature, heat pump coupled, aquifer thermal energy storage in a confined sandstone aquifer in northeastern Ohio. Simulations were run to determine the relative sensitivity of the model to transient versus steady-state radial flow, grid size, time-step lengths, and injection temperatures. In order to determine the effects of uncertainties in the values of aquifer and aquitard parameters, energy recovery factors and recovery temperatures were calculated for worst-case, best-case, and best-estimate simulations. Aquifer and aquitard parameters were either measured directly or were estimated based on previous hydrogeologic investigations. All simulations were performed assuming a 150 d injection phase with a pumping rate of 15 m 3h −1, a 35 d storage phase, and a 150 d production phase, also with a pumping rate of 15 m 3h −1. The worst-case simulation for an injection temperature of 23.9°C produced an energy recovery factor of 0.43 and a final production temperature of 14.6°C. The best-case simulation resulted in an energy recovery factor of 0.69 and a final production temperature of 16.2°C. The best-estimate simulation predicted an energy recovery factor of 0.50 and a final production temperature of 15.0°C. Both the energy recovery factor and the recovery temperature were most affected by the uncertainty in the storage formation longitudinal dispersivity. Using the best-estimate parameter values, an injection temperature of 18.0°C resulted in a final production temperature of 13.2°C and an energy recovery factor of 0.50. The best-estimate parameter values used with an injection temperature of 27.0°C yielded a final production temperature of 15.9°C and an energy recovery factor of 0.50.