Annular Fluid Research Articles

Experimental evaluation of surge/swab pressure in varying annular eccentricities using non-Newtonian fluid under Couette-Poiseuille flow for drilling applications

Global energy demand is rapidly increasing at a rate of 8% between 2004 and 2019, and conventional energy sources are unable to meet this requirement. Therefore, the oil and gas energy industry is working continuously to produce unconventional energy sources such as deepwater oil and gas reservoirs, gas hydrates, and geothermal energy using drilling operations. In the drilled borehole, the stability and integrity issues are encountered that are related to pressure differential generated by the Couette-Poiseuille (CP) fluid flow phenomenon occurred during pipe tripping operation. There is a lack of experimental data to comprehend the impact of CP flow on pressure differential using non-Newtonian fluid in concentric and eccentric annuli, especially in petroleum exploration. Hence, an experimental investigation is performed to replicate the tripping operations during oil and gas well drilling. The investigation provides an extensive understanding of the physical and mechanical characteristics of non-Newtonian fluids under CP flow at varying inner pipe tripping speeds (0.030481–0.21336 m/s), rheological properties, and geometrical dimensions. The results indicate that surge/swab pressure gradient tends to decrease with increasing eccentricity (ε) and increase with increasing diameter ratio (δ) and pipe tripping speed (Vp). Furthermore, the pressure differential rate is considerably high at low tripping speed but reduces at high pipe tripping speed due to the shear-thinning behavior of YPL fluid. The study also reveals that gel strength increases the surge/swab pressure gradient by approximately 18%. A multi-variable correlation is developed to predict surge/swab pressure gradient, exhibiting an excellent agreement with experimental data and existing theoretical models.

Convective heat transfer and friction factor characteristics of helical strip inserted annuli at turbulent flow

Helical baffles, wire coils, and rectangular ribs are used to improve the annular fluid flow turbulence and heat transfer performance. Among the different insert types, loose-fitted helical baffles or strips are of major interest because of their better performance. Tight-fitted helical strips can show better performance in the annular flow because they can act as a fin besides acting as a swirl generator compared to loose-fitted ones. For that reason, a three-dimensional (3D) computational fluid dynamics (CFD) study is performed to investigate the heat transfer and pressure drop characteristics of turbulent flow (4000 ≤ Re ≤ 10000) at annuli with and without tight-fitted helical strip inserts. Annuli with 0.6, 0.7, and 0.8 annuli diameter ratio (ADR) are studied for plain and helical strip inserts with pitch ratios (PRs) of 1, 2, and 3. Result showed that higher heat transfer coefficient (HTC) and friction factor were found for insert-fitted annuli compared to those of plain annuli. HTC increased with increase in Re and ADR and decrease in insert PR. The best performance was for 0.8-ADR insert-fitted annuli: 171%–207% (1 PR), 82%–105% (2 PR), and 56%–75% (3 PR) compared to 0.8-ADR plain annuli. Although HTC increased with increase in ADR, the Nusselt number (Nu) decreased because of the smaller hydraulic diameter. Nu increased with increase in Re but decreased with higher ADR and insert PR. The friction factor increased with decrease in insert PR and ADR and decreased with increase in Re. A figure of merit (FoM) was used to combine the benefit of heat transfer enhancement and the drawback of higher pressure drop. The FoM ranged from 0.9 to 1.3, 0.94 to 1.22, and 0.92 to 1.24 for ADR values of 0.6, 0.7, and 0.8, respectively, for a specific Re range. The heat transfer performance obtained was in the order of 3 PR < 2 PR < 1 PR for insert-fitted annuli, but the FoM followed 1 PR < 2 PR < 3 PR because of a much higher pressure drop for lower PR. This study confirms that inserts improve heat transfer, which is better at lower Re.

A new linearly unstable mode in the core-annular flow of two immiscible fluids

Abstract

Convective boundary layer flow and heat transfer of polar fluid in vertical concentric annuli with thermal slip

This study deals with natural convective flow of a polar fluid between two concentric open-ended cylinders when the inner surface temperature is higher than the outer or at a constant heat flux. Due to rotation of inner cylinder with angular velocity proportional to gradient of radial/linear velocity with thermal slip at the inner cylinder, a sheared flow is generated. The flow sets in due to momentum as well as thermal energy transport within the annular region. The equations for the velocity, microrotation and temperature fields are solved analytically. There exists a limit to the gap between the cylinders to augment linear velocity as well as microrotation and also a limit to the ratio of vortex viscosity to the dynamic viscosity to override the effects of surface thermal conditions. The thermal slip has an adverse effect on destabilising properties of polar fluid flow.

The coupled model of wellbore temperature and pressure for variable gradient drilling in deep water based on dynamic mass flow

Variable gradient drilling in deep water is a new drilling method of using separators to separate hollow glass spheres (Referred to as HGS, it is the glass microbeads with low density less than 1.0 kg/m3, and the worse thermal conductivity) from the drill string directly into the annulus, which can form multiple gradients of drilling fluid density in annulus. This method can better deal with the problem of narrow pressure window in deep water drilling. At present, there are few studies on the wellbore temperature and pressure distribution of this technology, and the separation efficiency of the existing separator is too low to achieve variable gradient. The purpose of this paper is to develop a new separator to improve the separation efficiency, and to study the coupled wellbore temperature and pressure field of variable gradient drilling based on dynamic mass flow. Firstly, indoor simulated experiments were used to study the separation efficiency of the newly developed filter separator, and based on the separation efficiency, wellbore flow theory and the first law of thermodynamics, the dynamic mass flow at the location of the separator were fully considered. Considering the influence of wellbore temperature and pressure on thermophysical parameters, a coupled model of wellbore temperature and pressure was established based on dynamic mass flow. Then the model was discretized and solved by finite difference method and cyclic iterative algorithm. Further, this model was verified based on the existing models and drilling site data. Finally, the effects of key parameters in variable gradient drilling on the annulus temperature, pressure and fluid density were studied. The results show that the filter separator has high feasibility, and the separation efficiency can reach 95%–98.5%. Compared with conventional drilling, distribution curve of the temperature, pressure and the mixture density in annulus of the filter separator section has obvious inflection points in variable gradient drilling, and the number of inflection points is equal to the number of separators. What's more, the number and location of separators, the HGS volume fraction, pump flow rate, and the HGS density have significant effects on the annulus temperature and pressure. This research can significantly improve the feasibility of variable gradient drilling in deep water and provide a theoretical reference for further research in this direction.

Investigation on fluid field characteristics and cinders transport laws in the annulus of grooved drill pipe based on two-phase flow model

Despite the grooved drill pipe (GDP) has been applied in the soft coal seam in recent years, it remains unclear of the cinders transport mechanism in the annulus of GDP. In this study, the cinders transport model of GDP was developed based on an improved method, combining the kinetic theory of granular flow and Eulerian-Eulerian two-phase flow model. The annular fluid field characteristics and cinders transport laws of GDP were studied in this model by considering drag force, lift force, and virtual mass force. Finally, the precision of this model was verified via the experimental data. The results show that the annular velocity and cinders distribution present periodic variations with the drill pipe pitch. A role of guiding and tangential force on fluid field by the helix grooves is found. The volume fraction of residual cinders is dramatically reduced from 0.144 to 0.085 as the inlet velocity increases from 0.6 m/s to 1.2 m/s. This indicates the performance of cinders transport can be improved by increasing inlet velocity of drilling fluid.

Application of soft computing techniques to optimize thermal parameters in a double heat exchanger with cylindrical turbulators

AbstractIn the present study, the dimensions of the cylindrical turbulators have been optimized to achieve the highest thermal performance. A double pipe heat exchanger with cylindrical turbulators placed in the annulus side is modeled and a numerical simulation is carried out for different operating conditions. The simulation is conducted for different diameters of the turbulators for various Re for the annulus fluid. The Nusselt number (Nu), friction factor (f), and thermohydraulic performance index (THPI) are the responses simulated for the above different cases of input conditions. Response surface methodology has been used to study the influence of operating parameters on the responses. It is observed that Nu, f, and THPI increased as the Re and turbulator diameter increased. Response optimizer is used to optimize the turbulator diameter to obtain the highest thermal performance in terms of highest Nu and THPI and lowest f. The results indicated that maximum performance was obtained for a diameter of 4.45 mm and for a Re of 5530. The Nu and THPI corresponding to the above combinations are 68.4 and 2, respectively.

Use of SiO2 Nanoparticles in Water-Based Drilling Fluids for Improved Energy Consumption and Rheology: A Laboratory Study

Summary In wellbore drilling, it is appreciable to devise methods to study the rheology of high-speed annulus fluid flows. In this paper, a high-speed Taylor-Couette system (TCS) was devised to explore non-Newtonian fluid flow behavior appraised by SiO2 nanoparticles toward friction reduction, power saving, and rheology modeling of nanofluids. Water-based mud (WBM) as an environmentally friendly drilling fluid is investigated by adding SiO2 nanoparticles at four low-volume concentrations of 0.05, 0.1, 0.5, and 1% at speeds from 0 to 1,600 rev/min with 200 rev/min intervals in the TCS. Five rheology models based on the Herschel-Bulkley-Extended (HBE) model and a generalized Reynolds number were optimized to fit with the experimental data. All models except the Newtonian model have fitted all nanofluids with high accuracy, especially Bingham and HBE models. Negative deviation from Darcy friction was avoided for power-law (PL) and Herschel-Bulkley (HB) models using the modification to the generalized Reynolds number. Higher energy saving and enhanced rheology is reported particularly at lower volume concentrations of SiO2 WBM nanofluids. The Darcy friction factor deviated from laminar flow at the generalized Reynolds number beyond 2,000 into turbulent, which is a good indicator for the flow condition of complex non-Newtonian nanofluids in real-life application.

Research and application of logging technology for annulus fluid production profile in highly deviated wells

In view of the low success rate of logging in annulus fluid production profile in domestic oil fields, the relationship between instrument string and well deviation is carried out Requirements of downhole instruments for annular testing construction in highly deviated wells; The lifting and lowering technology of well entry instruments in highly deviated wells has been systematically studied. After field application, the logging technology has been updated and improved. By using large diameter cable, flexibly connecting and splitting instruments, reducing the outer diameter of instruments, configuring automatic direction finder, enhancing the umbrella collecting strength and other improvements in technology and construction methods, the problem of difficulty in measuring the logging data of liquid production profile in the annulus of highly inclined pumping wells is well solved, and the demand of dynamic monitoring of highly inclined wells in oil fields is met.

Size-dependent stability analysis of a functionally graded cylindrical shell subjected to swirling annular flow including the fluid viscosity

In this paper, the stability and dynamics of a functionally graded materials (FGMs) cylindrical micro-shell subjected to swirling annular fluid through the annulus between the inner shell and the outer shell are firstly investigated. The fluid perturbation pressure related to the shell vibration is determined by the potential flow theory. The steady viscous forces are derived based on the fully developed turbulent flow. The shell motion equations are established on the basis of the Hamilton's principle along with the Donnell shell theory. To capture the size effect of micro-shell, the zero-level contour method is adopted to obtain the solutions of shell motion equations. First, the system subjected to an ideal annular flow is studied. The results show effects of the fluid rotation, material length-scale parameter, and material properties on the fluid-micro-shell system stability. Furthermore, the coupling effect of the fluid rotation and the material length-scale parameter on the dynamical stability of the system is evaluated. Second, the system subjected to a viscous annular flow is further studied. A more impressive result is observed that the fluid viscosity effect renders the system subjected to an annular flow more unstable, and the physical explanation for the phenomenon is presented.

Non-uniform magnetic field impact on thermomagnetic convection of paramagnetic air in a permanent magnet-inserted horizontal annulus

Heat transfer enhancement using an external magnetic field with a high level of energy economy is a promising subject. The permanent magnets with no additional electrical power consumption are adopted to produce the applied magnetic fields. The effects of the magnet assembly and magnet strength on the thermomagnetic convection of paramagnetic fluid in a horizontal annulus are studied numerically by a finite volume method. The variations of the flow pattern, thermal structure and convective heat transfer characteristics are investigated to clarify the heat transfer rate characteristics of thermomagnetic convection of paramagnetic air induced by both magnetic and gravitational buoyant forces for cases of moderate- and large-gap annuli. The results showed that the thermomagnetic convection is significantly affected by the gap width of the annulus and the magnetic field gradient induced by the permanent magnet. The average heat transfer increases more than 150% when one magnet is placed. It can be attributed to the more efficient disturbance in the boundary layer and improves heat transfer greatly. A stronger magnetic field induced better mixing in the flow which increase the Nusselt number. In addition, reducing the gap width of the annulus can effectively enhance heat transfer.

The Influence of temperature to pressure and flow performance in production well

Fluid temperature and pressure distribution along the borehole play a vital role in completion design, well performance, and flow assurance of the flowing fluids. Quantitative knowledge of wellbore heat transmission and pressure drop correlation is very crucial as it helps improve the accuracy of the temperature and pressure computation. It should be noted that the surrounding wellbore’s components (e.g., casing, annulus fluid, cement sheath, and formation) can directly affect the fluid temperature profile due to the thermal interactions. Therefore, in this study, the primary objective is to determine the best-fit temperature model for an offshore well associated with complex borehole structures. There are three selected temperature models including Sagar et al., Alves et al., and Hasan and Kabir. In line with that, for the pressure drop model, the modified Hagedorn and Brown, which is one of the most widely used method, is also applied to the calculation process. The validity of the models has been verified by field production temperature and pressure data from the oil well SXX-P in S oil field, Cuu Long basin, Vietnam. Apart from that, sensitivity studies were also carried out to evaluate the effect of different parameters (e.g., tubing size, injection rate, and production rate) on the fluid’s temperature which in turn impacts the fluid’s pressure. As a result, the Hasan and Kabir appears to be the most suitable model for the temperature profile of oil well SXX-P with an average difference of 0.38%. Meanwhile, Alves et al. and Sagar et al. approaches yield a larger difference of 12% and 1.26% on average, respectively. In terms of pressure prediction, the result shows an insignificant difference which is approximately 3% with the field data by the modified Hagedorn and Brown correlation.

Laminar natural convection of non-Newtonian power-law fluid in an eccentric annulus

This work is about studying the natural convection of two-dimensional steady state non-Newtonian power law fluid numerically. The inner cylinder was put eccentrically into the outer one. The cylinders are held at constant temperatures with the inner one heated isothermally at temperature Th and the outer one cooled isothermally at temperature Tc (Th&gt;Tc). The simulations have been taken for the parameters 103?Ra?105, 10?Pr?103, 0.6?n?1.4, 0???0.9 and an inclination angle ? from 0? up to 90?. The average Nusselt numbers for the previous parameters are obtained and discussed numerically. The results revealed that the average Nusselt number has the highest values when n=0.6, Ra=105 at ?=0 which is a signal for the large transfer herein and has the lowest values for n=1.4, Ra=103 at ?=90? which is a signal that the transfer is by conduction more than convection. Furthermore, the increasing of eccentricity causes an increase in the Nusselt number for all the cases. Finally, the best case where we can get the best heat transfer is at ? = 0, ?=0.9 among them all. The results have compared with some precedent works and showed good agreement.

Using Shale as a Barrier Simplifies Well Abandonment

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 199654, “Simplifying Well Abandonments Using Shale as a Barrier,” by Eric van Oort, SPE, and Maria Juenger, The University of Texas at Austin, and Munir Aldin, SPE, Metarock Laboratories, et al., prepared for the 2020 IADC/SPE International Drilling Conference and Exhibition, Galveston, Texas, 3-5 March. The paper has not been peer reviewed. The complete paper presents the results of an investigation into the creep behavior of North Sea shales and their ability to form effective annular barriers. The large-scale laboratory results show that Lark-Horda shales will form competent low-permeability annular barriers when left uncemented, as confirmed using pressure-pulse-decay measurements. Experimental conditions were found to influence the rate of barrier formation. Higher effective stress, higher temperature, and beneficial manipulation of annular fluid chemistry all have a significant effect. Introduction An alternative to traditional plug-and-abandonment techniques presented it-self more than a decade ago, with observations that formations such as mobile salts and shales could creep into uncemented annular spaces and form competent annular barriers that could be identified on sonic and ultrasonic bond logs and verified using pressure testing. Shale particularly has the necessary characteristics that several guidelines require of a good barrier, being largely impermeable, nonshrinking, ductile, and resistant to chemicals and substances, all of which help provide long-term integrity. Shales that appeared to be particularly well-suited to beneficial annular creep behavior were characterized by low strength and high ductility, high clay content with relatively high smectite content, low levels of quartz and carbonate cementation, relatively high porosity and low compressional wave velocity, and a tendency to yield wellbore instability problems while being drilled. Mechanisms other than creep were considered for the annular blockage behavior observed, but the mounting body of evidence indicates that the predominant mechanism is indeed creep (i.e., the viscoplastic behavior of argillaceous rocks). In the laboratory and field work published to date, stimulation of shale barriers through accelerated creep by pressure and temperature manipulation has received the most attention. The authors investigate barrier activation not only by temperature and pressure activation but also by chemical activation, because it offers practical advantages and reduces risks associated with temperature and pressure activation. Temperature has a significant effect on the viscoplastic behavior of shale, but heating a long shale section (with a minimum barrier length of 50 m) through casing with an effective downhole heater presents considerable practical challenges. Pressure reduction in the annulus through reduction of the hydrostatic head in the wellbore brings with it well-control concerns, particularly when no functional annular barrier is in place. By contrast, circulating a chemical solution in place in an annular space through casing perforations with a workstring and packer arrangement is relatively straightforward and is routine when practicing the perforate, wash, and cement technique in the field.

Novel Geophone Array Measures Exact Location of Fluid Movement Behind Casing

This article, written by JPT Technology Editor Judy Feder, contains highlights of paper SPE 197560, “Enhanced Well Remedial Decisions From Exact Location of Fluid Movement Behind Casing Identification,” by Marcel Croon, SPE, Perry Huber, SPE, and Jacob Wright, SPE, Weatherford, SPE, prepared for the 2019 Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, 11-14 November. The paper has not been peer reviewed. Historically, acoustic wellbore monitoring is among the primary methods of detecting fluid movement behind the casing. However, analysis of the complex acoustic environment in the wellbore can be challenging. A standard hydrophone noise tool is unable to measure flow directions (vertical and horizontal) and cannot detect low flow, low-pressure sporadic events, or multiple sources. The complete paper discusses a geophone array, including four, three-component geophones deployed by wireline, that provides a solution for this problem by creating a 3D map of the acoustic environment. Introduction Well-integrity issues such as a poor cement bond can lead to undesirable fluid movements behind the casing, which could have negative effects with regard to health, safety, and the environment. A detailed understanding of annular fluid movement is critical in identifying potential source locations for wells with surface-casing vent-flow (SCVF) issues. Applicable scenarios include the following: Planned well-intervention activities for wells with multiple-source vent/flow situations Confirming the presence of flow (gas/oil/water) behind the casing Identifying areas with suspected crossflow between zones Integrity confirmation for gas storage caverns or zones Identifying unwanted flow for well-abandonment activities Well abandonment is bound by stringent regulations in some countries where the testing and repair of SCVF and gas-migration (GM) issues before final abandonment are required. An ex-ample is western Canada, where surface casing vents must be tested through a bubble test at minimum. This involves connecting a small container with 2.54 cm of water using fittings to the surface casing vent and monitoring for gas bubbles for 10 minutes. Often the flow rates are very low (less than 35 cu ft/d) with minimal pressure buildup. If bubbles are detected during the monitoring period, the well is deemed to have a positive vent flow. Consequently, the source of the vent flow must be identified by a survey as approved by the energy regulator, which could be conducted by means of acoustic logs, temperature logs, or gas- isotope analysis. Additionally, GM measurements must be conducted before final abandonment in specific areas within western Canada but are recommended for all wells. The complete paper details this process.

A two-dimensional asymptotic model for capillary collapse

Abstract

Restoration of annular zonal isolation using localized casing expansion (LCE) technology: A proof of concept based on laboratory studies and field trial results

Sustained casing pressure (SCP), surface casing vent flow (SCVF) and other expressions of annular fluid migration are widely encountered zonal isolation issues. Conventional solutions for SCP/SCVF include perforate and squeeze cementing, or section milling and recementing. Regrettably, the former approach shows only limited success rates, while the latter involves time and cost intensive operations that require a drilling rig. We will show that localized casing expansion (LCE) technologies offer promising alternatives, enabling rigless remediation of annular fluid migration. The LCE concept involves imposing permanent deformation on the casing pipe to locally enlarge its diameter. The associated annular volume reduction causes closure of defects such as micro-annuli and cement fractures, plus potentially even larger voids, and results in an overall densification of the cement microstructure. The Shell-developed Local Expander tool is e-line deployable and imposes the required casing deformation in a mechanical, fully controlled manner. Tailored-shaped energetic charges offer valuable supplementary means for achieving expansion. We will demonstrate the sealing effectiveness of LCE in both laboratory experiments and field trials, describe how the radial deformation impacts the casing and cement, and generally discuss the current state of knowledge, capabilities and limitations of LCE with respect to SCP/SCVF remediation.

Evaluation of Annulus Pressure Buildup During Injection Operations

Abstract More than 300 million barrels of saltwater is produced everyday from oil and gas production wells. Most of this volume is injected through either saltwater disposal wells or used for water flooding and enhanced recovery purposes. Usually, the regulations require the injection to be conducted through the injector well tubing that is isolated from the well annulus to protect the underground source of drinking water (USDW) by preventing any possible leak through the well casing. Monitoring of the annulus pressure during injection ensures the well integrity. The annulus pressure changes can occur by one of the following mechanisms: thermal expansion of the annulus fluid; ballooning of the injection tubing; communication between the tubing and the annulus; or fluid migration behind the casing. Determining the communication mechanism can be a complex process and a need may arise to run several testing procedures and inspect all the wellbore components. Successful evaluation of the annulus pressure values and trends can directly identify the root cause of the annulus pressure buildup and simultaneously save time and reduce the cost associated with the workover operations. The seven case studies presented in this paper focus on the details pertaining to the annulus pressure buildup under different well conditions and purposes the interpretation technique for each case.

Characteristics of sustained annular pressure and fluid distribution in high pressure and high temperature gas wells considering multiple leakage of tubing string

Tubing leakage is one of the main reasons to cause annular pressure in HPHT gas wells. This kind of annular pressure is called “sustained” because it is long-lasting and can not be eliminated by releasing. Sustained annular pressure is adverse to well barrier reliability, gas well management and repair. Even fire hazard and tubing fracture may happen. Therefore, it is necessary to study related characteristics of sustained annular pressure and fluid distribution, thus reducing potential risk. However, nearly all available research concentrates on cement integrity failure. So this paper develops a model of sustained annular pressure caused by multiple tubing leakage points. The wellbore temperature and pressure are calculated first as the gas leakage power, which considers the impact of pressure and temperature on gas properties. And then, tubing leakage point is classified as gas-leak and gas-liquid-leak. Fluid Leakage rate is calculated. Finally an equation is proposed to calculate the annular fluid distribution and annular pressure. To solve this model, the coupling relationship between leakage rate, sustained annular pressure and fluid distribution is analyzed. And then the well space and leakage time are divided into short segment. Two typical situations are selected as example. One is multiple gas leakage points. The other is combination of gas-leak and gas-liquid-leak points. By the proposed model, characteristics are analyzed, including annular pressure, pressure balance position, annular gas volume and liquid level. Also, sensitivity of factors is evaluated, including leakage point position, size, production rate and bottom pressure. The results indicate that rising process of sustained annular pressure can be divided into three zones (a, b, c). Annular pressure should be released to zone c when acoustic log is applied to locate leakage points. Method based on U-principle is not suitable to locate multiple tubing leakage points. Both pressure and liquid level should be monitored to evaluate tubing integrity. For multiple gas-leak points, position and size of leakage point have impact on maximum annular pressure and final liquid level. When gas-liquid-leak point exists, sustained annular pressure and liquid level continue changing, so annular fluid distribution and its change law can help to judge the existence of gas-liquid-leak points. Increase of production rate and decrease of bottom pressure can be considered as potential measures to reduce the rising rate and maximum sustained annular pressure under both two situations. This paper can help to diagnose tubing integrity by the characteristics of annular pressure and fluid distribution. Acoustic log is recommended to locate tubing leakage point. Potential measures are discussed to reduce maximum annular pressure. The proposed model can also be applied to calculate maximum annular gas volume and gas leakage rate when parameters of tubing leakage points are known, thus helping to assess potential risk.

Investigation on optimal shell-to-tube radius ratio of a vertical shell-and-tube latent heat energy storage system

This study aims to investigate the optimal shell-to-tube radius ratio in a vertical shell-and-tube latent heat thermal energy storage system with phase change material packed in the annulus and heat transfer fluid circulating in the central tube. A conjugate thermodynamic model is developed and validated, and then applied to investigate two series of system configurations: varying the phase change material shell radius at a fixed heat transfer fluid tube radius and varying the heat transfer fluid tube radius at a fixed shell radius. The numerical investigation compares and evaluates energy storage/retrieval density, energy storage/retrieval rate, and total stored/retrieved energy capacity under different shell-to-tube radius ratios. The results show that the thermal behaviour in both series of units is very similar. The optimal radius ratio slightly increases as the total charging/discharging time increases. The unit height has a gentle effect on the optimal radius ratio in the charging process and a negligible influence in the discharging process. By balancing the energy storage/retrieval density, energy storage/retrieval rate, and storage/retrieval capacity in both charging and discharging processes, the optimal shell-to-tube radius ratio is found to be around 5 for both series of configurations at the studied total charging/discharging times.