Influence Of Groundwater Flow Research Articles

Design and optimization of the U-shaped well geothermal systems for heat production performance: A case study from Huangling, China

U-shaped well geothermal systems have obvious advantages in deep geothermal development due to the long heat exchange distance and no fluid leakage. Well layout is a primary optimization target to enhance the heat production performance. However, there is a lack of studies for well location selection and installation configuration considering regional groundwater flow. In this study, a coupled thermo-hydro model considering 1D U-shaped well and 3D reservoirs groundwater flow is proposed for the optimization of U-well geothermal systems. The proposed model is calibrated by the field test of U-shaped well in Huangling, China. First, the U-shaped well geothermal system with multiple injection wells is designed. The feasibility is comprehensively evaluated from the aspects of heat production performance and levelized cost of electricity. Subsequently, the influence of groundwater flow on heat production performance is analyzed in detail, including flow velocity, porosity, aquifer thickness and flow direction. Finally, sensitivity studies of thermal conductivity of cement, wellbore diameter, and injection flow rate are investigated to provide reference for production operations. The results show that the heat production performance of the U-shaped well geothermal system with multiple injection wells are significantly better than the single U-shaped well. And the levelized cost of energy can be reduced by 0.0288 $/kWh compared to the average industrial electricity price in China. The groundwater flow velocity remarkably affects the heat production performance. The large aquifer thickness and porosity contribute to the improvement of the heat production performance of the U-shaped well geothermal system. The U-shaped well with injection wells located in the lower reaches of groundwater flow field has better heat production performance. The research results can provide references for design and optimization of the U-shaped well geothermal systems.

Dissolved carbon dynamics and exchange in a high permeability beach aquifer

The biogeochemical transformation of dissolved carbon in tidal beaches affects the coastal carbon cycle and budget. Yet, the influence of groundwater flow on the behavior of dissolved carbon and CO2 flux across the different interfaces in these dynamic beach systems remains poorly understood, especially in deep beach aquifers. In this study, we investigated the biogeochemical reactions and origins of dissolved carbon and quantitatively evaluated CO2 outgassing driven by submarine groundwater discharge (SGD) in a high permeability beach aquifer (9–13 m depth) located in the South China Sea shelf. Results revealed that both dissolved inorganic carbon (DIC) and total alkalinity (TA) exhibited non-conservative additions across the salinity gradient. The excess DIC and TA most likely resulted from organic carbon decomposition in the brackish and saline zones. Aerobic respiration (upper saline plume zone), anaerobic reactions, and tidal mixing were identified as the dominant processes controlling DIC and TA dynamics. The mean CO2 outgassing flux across the beach sediment-air interface was estimated to be 1.05 g m−2 d−1, significantly higher than the CO2 flux across the sea-air interface. The outgassing pattern of groundwater CO2 from beach aquifer appeared to be driven by tidal pumping. Considering the combined effects of SGD-derived dissolved carbon and nutrients, we suggest that SGD yielded a net CO2 flux, contributing to 45 % of the CO2 flux across the sea-air interface. SGD directly and indirectly delivered substantial CO2 from the beach aquifer to the atmosphere, approximately (4.89–9.21) × 103 tons of CO2 per year along the 76.2 km long sandy coast. These findings demonstrate that intertidal beach aquifers, as active biogeochemical reactors have the strong potential to intensify CO2 emissions to the atmosphere through both beach sediment-air and sea-air interfaces. This study provides a better understanding of the links between carbon biogeochemical cycles and hydrologic processes in the coastal zones.

Study on configurational operation strategy of ground heat exchangers under the effect of groundwater flow

In large-scale ground source heat pump (GSHP) systems, the accumulation of thermal energy resulting from seasonal load imbalances has emerged as a significant impediment. The implementation of a rational operation strategy can effectively mitigate heat accumulation in soil. This study investigates the impact of the configurational operation strategy for large-scale vertical ground heat exchanger (GHE) on the spatial distribution of ground temperature under the influence of groundwater flow. The internal heat source model is proposed to describe heat transfer process of GHE. Sandbox experiment is conducted to verify the model with maximum deviation of 3 %. The validated model is then utilized to simulate soil temperature profile in the large-scale GHE field over a 10-year operational period, considering a matrix of three configuration strategies and three operation strategies. The results shows that trapezoidal configurations combined with operation Strategy 3 has a minimal temperature increment of 2.9 °C in soil temperature. The contribution of this study lies in provision of a methodology for mitigating thermal accumulation in large-scale GHE field.

Tidal Pumping Controls Dissolved Organic Matter Properties and Outwelling From Mangrove Groundwater to Coastal Water

AbstractDissolved organic matter (DOM) in highly productive intertidal mangroves is an important carbon and nutrient source to the coastal ocean. In highly dynamic mangrove intertidal systems, both tidal pumping or geochemical factors can control DOM characteristics. The influence of groundwater flow on DOM properties and fluxes remains poorly understood. Here, we compared the concentrations, sources, and spectroscopic characteristics of DOM across a recharge‐discharge gradient. We used a three‐dimensional array sampling strategy to reduce spatial biases, groundwater monitoring to quantify tidally driven exchange, and spectrofluoroscopy to quantify DOM fluorescent components. The results showed that tidal hydrology played the key role driving groundwater DOM properties in both horizontal (i.e., from the mangrove to the sea) and vertical directions. Due to the high spatial heterogeneity of dissolved inorganic (DIC) and organic (DOC) carbon concentrations in mangrove groundwater, carbon outwelling showed a high degree of variability at the intertidal scale (54.8–234.8 μmol m−2 d−1 for DIC and 2.5–12.4 μmol m−2 d−1 for DOC). The contribution of terrestrial DOM gradually decreased toward the ocean, but the microbial contributions for recently produced autochthonous DOM increased. Deep groundwater received less terrestrial DOM and experienced anaerobic microbial mineralization, resulting in lower organic carbon than shallow groundwater. Greater variations in spectroscopic characteristics were found in shallow groundwater than in deep groundwater. Overall, tidally driven surface water‐groundwater interactions control the variability in DOM properties and how DOM contributes to carbon budgets and sequestration in mangrove groundwater.

Experimental Study on the Influence of Hydromechanical Boundary Conditions on Shear-Flow Coupling Characteristics of Granite Joints

The instability of jointed rock mass is usually the shear process of the rock mass along discontinuities under the influence of groundwater flow. By conducting laboratory tests and numerical experiments on the shear-flow coupling of rock joints under constant normal stiffness (CNS) and constant normal stress (CNL) boundary conditions, the influence of normal boundary conditions and seepage pressure on the shear mechanical and flow characteristics of joints were investigated. The test results were as follows: The joint shear stiffness, peak, and residual shear strength under the CNS boundary condition were predominantly larger than those under the CNL boundary condition. Overall, these parameters were positively correlated with the initial normal stress σ n 0 . When σ n 0 > 2 MPa, the postpeak shear stress of the CNS boundary condition showed a sharp decrease, whereas that of the CNL boundary condition changed from a slowly decreasing type ( σ n 0 = 4 MPa, 6 MPa) to a sharply decreasing type at σ n 0 = 8 MPa. The peak dilation rate under the CNS boundary condition at all levels of normal stress was lower than that of CNL, and the strain softening in postpeak of the latter was more remarkable. In the process of joint shear, the hydraulic aperture displayed a four-stage variation law of “steady-sudden increase-slow increase-basically stable.” Moreover, the hydraulic aperture under the CNS boundary condition was always lower than that under the CNL boundary condition. The seepage pressure increased from 0.5 MPa to 1.5 MPa, and the average hydraulic aperture in the stable stage under normal stress at all levels increased from 0.146 mm to 0.187 mm. In addition, the average peak shear stress and average shear stiffness decreased by 0.9 MPa and 0.83 GPa/m, respectively. We also established a numerical model of a real rough three-dimensional joint, compiled a calculation program for the shear-flow process of a joint under CNS boundary conditions, and visualized the flow channel inside the joint. The seepage flow bypassed the area where the joints contacted each other, forming obvious flow channels. The flow rate increased at the intersection of the flow channels.

Numerical study on the heat performance of enhanced coaxial borehole heat exchanger and double U borehole heat exchanger

• The BHEs model considering the multilayer properties and groundwater flow. • An enhanced coaxial model with intermittently laid spiral ring fins was proposed. • The heat transfer performance of the vertical BHEs was evaluated. • The influence level of different factors on heat transfer performance was analyzed. • The influence of groundwater flow on the ground temperature field was analyzed. Borehole heat exchangers (BHEs) are widely used in various building air conditioning and heating systems. It has always been the unremitting pursuit of researchers to provide solutions for energy conservation by improving the heat transfer efficiency of BHE. In this work, comprehensively considering groundwater seepage in the surrounding rock and soil and the difference of heat transfer performance between various layers of rock and soil, three-dimensional geometric models of double-U BHE and enhanced coaxial BHE with intermittently laid spiral ring fins were established. The established model was verified by the drilling, geothermal, thermal response data collected through filed tests and the actual operating data of the system. The heat transfer performance and influencing factors of the two BHEs models under different working conditions were simulated by improving and replacing the double-U BHE model by means of equivalent buried pipe cross-sectional area. The results showed that the linear meter heat transfer of the enhanced coaxial BHE was significantly better than the linear meter heat transfer of the equivalent U BHE. The average linear meter heat transfer of the enhanced coaxial BHE can reach 1.46 times and 1.45 times of the equivalent U BHE under winter and summer working conditions, respectively. Finally, the results of the sensitivity analysis of single factor showed that the inlet temperature/inlet fluid heating power is the most significant impact on the heat transfer performance, followed by the inlet flow rate, and the hydraulic gradient of groundwater seepage has the least impact. The results obtained can provide a new type of the buried pipe structure that can be used as a reference for improving the heat transfer performance of BHEs in the simulation and experiment conditions.

Influence of groundwater flow on the ground heat exchanger performance and ground temperature distributions: A comprehensive review of analytical, numerical and experimental studies

The performance of the ground heat exchanger (GHE) possesses a pivotal role in the geothermal exploitation. In recent years, a growing body of literature that recognizes the importance of groundwater flow has been presented. This article reviewed the literature dealing with the impact of groundwater flow on the GHE performance and ground temperature distribution, which were classified by analytical, numerical and experimental approaches. The characteristics of the three approaches were summarized respectively. Various GHE configurations, including U-tube, double U-tube, spiral tube, tunnel lining, horizontal spiral GHEs and GHE groups, were involved in the discussion. It was found that the groundwater flow is beneficial to the ground temperature recovery and improves the GHE heat exchange rate. The effective thermal conductivities of rocks and soils, and borehole resistances, are also affected by groundwater flow. The impact extent depends mainly on the thickness, depth and flow rate of the aquifer layer. The discussion on the collected literature demonstrated that ignoring the groundwater flow would cause non-negligible prediction errors in the evaluation of GHEs. Based on the analysis of the characteristics and applicabilities of the discussed models and methods, this review is expected to provide a more comprehensive reference for promoting the utilization of geothermal energy by GHEs.

Model test and numerical simulation on the development of artificially freezing wall in sandy layers considering water seepage

Abstract The influence of seepage on the development of the frozen wall must be considered when artificial ground freezing (AGF) is applied to the coarse-grained soil layers. In this paper, the influence of groundwater flow in a sandy layer on the temperature field during artificial freezing is studied. Model tests were carried out with different seepage velocity, and the temperature field changes of upstream and downstream as well as the development of the frozen wall were obtained. The experiment was numerically simulated using a finite element platform, COMSOL Multiphysics. The test showed that the frozen wall was symmetrical when there was no seepage, which was approximately elliptical. Under the seepage condition, the upstream and downstream frozen walls were asymmetrical, approximately heart-shaped. The asymmetry increased with the increase of seepage velocity and pipe spacing. When the seepage velocity increased, the closure time of frozen wall increased. The numerical simulation results and the experimental results were basically consistent. The asymmetry of the frozen wall under the seepage condition was quantitatively analyzed based on numerical simulations.

Water flow, oil biodegradation, and hydrodynamic traps in the Llanos Basin, Colombia

In this study, we provide new data to understand the groundwater flow patterns in the Llanos Basin and their impact on oil biodegradation and the geothermal regimes as well as how the structural styles and anthropogenic activities impact these patterns. Previous studies suggest an active flow of groundwater and variable salinities whose spatial pattern is apparently unrelated to topographically driven groundwater flow. These observations have led to different hypotheses regarding the influence of groundwater flow on Llanos Basin geothermal gradients and oil biodegradation. In this contribution, we present data regarding the hydraulic heads, salinities, geothermal gradients, and structural styles of the Llanos Basin to propose hypotheses explaining these observations. Structural cross sections and subsurface stratigraphic correlations allow us to suggest that the pattern of flow is best explained by a correlation between groundwater flow and structural styles. A basement map of the Llanos Basin confirms that the most important factor controlling geothermal gradients is the type of basement, whereas the factor of groundwater flow appears to be of secondary importance. The evolution of the basin and the frequent absence of correlation between fresh water and the more biodegraded oils support the interpretation that biodegradation is controlled by an older flow of water that started as early as the Oligocene. Finally, mass balances suggest that the temporal scales and volumes of groundwater flow are much larger than the scales observed during the development of the oil fields.

Influence of groundwater flow on cost minimization of ground coupled heat pump systems

This paper introduces a new sizing methodology for ground coupled heat pump (GCHP) systems which takes into account groundwater flow (by using G-functions based on analytical models) in order to achieve an economic optimization of the total cost of the project. The procedure includes the calculation of the initial and the annual operational costs. Optimal design variables (boreholes depth, distance between consecutive boreholes, etc.) and borefield layouts (number of boreholes in the x-direction) are presented for different values of the thermal conductivity of the ground. In addition, a parametric study is done to measure the impact of the groundwater flow velocity and angle with respect to the borefield on the economics of the project. It is shown that the effects of the groundwater flow velocity on total cost become apparent only for high velocities, i.e., Pe>∼10−2. On the other hand, the groundwater flow angle is less impactful regardless of the groundwater flow velocity, i.e., the net economic gain that can be obtained by choosing the optimal orientation is much smaller compared to total cost of the system (less than 2%). A simultaneous comparison of the initial and operational costs shows that for all Pe values, higher initial costs usually result in lower operational costs. Finally, optimized designs are tested under off-design operating conditions. It can be observed that the economic consequences of operating under off-design conditions are far worst if the groundwater flow velocity is overestimated, which can lead to an increase of the operational costs of as high as 5.8%. A wrong estimation of the flow angle in the design phase, however, only leads to an increase of the operational costs of at most 2.4% for the cases considered in this paper.

A Numerical Study on the Impact of Grouting Material on Borehole Heat Exchangers Performance in Aquifers

U-pipes for ground source heat pump (GSHP) installations are generally inserted in vertical boreholes back-filled with pumpable grouts. Grout thermal conductivity is a crucial parameter, dominating the borehole thermal resistance and impacting the heat exchanger efficiency. In order to seal the borehole and prevent leakages of the heat carrier fluid, grouting materials are also hydraulically impermeable, so that groundwater flow inside the borehole is inhibited. The influence of groundwater flow on the borehole heat exchangers (BHE) performance has recently been highlighted by several authors. However groundwater impact and grouting materials influence are usually evaluated separately, disregarding any combined effect. Therefore simulation is used to investigate the role of the thermal and hydraulic conductivities of the grout when the BHE operates in an aquifer with a relevant groundwater flow. Here 3 main cases for a single U-pipe in a sandy aquifer are compared. In Case 1 the borehole is back-filled with the surrounding soil formation, while a thermally enhanced grout and a low thermal conductivity grout are considered in Case 2 and Case 3 respectively. Simulations are carried out maintaining the inlet temperature constant in order to reproduce the yearly operation of the GSHP system. For each of the 3 cases three different groundwater flow velocities are considered. The results show that a high thermal conductivity grout further enhances the effects of a significant groundwater flow. The conditions when neglecting the grout material in the numerical model does not lead to relevant errors are also identified.

Borehole thermal energy storage systems under the influence of groundwater flow and time-varying surface temperature

A 3D finite element model of circular borehole cluster connected in series is used as a response model to generate normalized transfer functions of a borehole thermal energy storage system under the influence of ground surface temperature variations and groundwater flow. Two response functions are obtained by convolving transfer functions of the system's outlet fluid temperature with two incremental input functions describing the temperature variation of the inlet and outlet fluid and variations of the ground surface temperature. Superposition is applied to obtain the resulting fluid temperature with respect to thermal inputs at the inlet fluid and the ground surface over the course of ten years and results are compared for various groundwater velocities. This work demonstrates that the combined effect of groundwater flow and ambient air temperature variations can significantly decrease the performance of a BTES system. The methodology used can be extended to simulate complex system.

Analysis of the influence of different groundwater flow conditions on the thermal response test in Tangshan

Comprehensive thermal conductivity of the rock and soil is generally measured by thermal response test ignoring the effect on groundwater flow. However, the influence of the groundwater flow on thermal conductivity is drastic, so the design of ground heat exchangers with no consideration of groundwater flow is inaccurate. Tangshan is distributed in the river alluvial–proluvial fan of Luanhe River system and groundwater flow rapidly. Hence, analysis of thermal conductivity with thinking about groundwater flow is necessary. In this paper, the comprehensive thermal conductivity within depth of 100 m in Tangshan is measured by two methods: thermal response test and laboratory experiment. Pumping test and tracer test are implemented to simulate of groundwater flow field with different flow conditions. Test results show that: (1) Laboratory experiment results cannot truly represent the comprehensive thermal conductivity of layers. The average thermal conductivity of natural flow field is 23% higher than the laboratory experiment weighted results. (2) The comprehensive thermal conductivity increased 23% with the groundwater flow from the 1.026 to 4.176 m/d. Acceleration of groundwater flow is propitious to improve the thermal conductivity. (3) With the increase in groundwater flow, the initial temperature of ground decreases about 2.3 °C, the results of the stable thermal flow test and the stable operation condition test gradually rise slightly. So acceleration of groundwater flow is conducive to heat exchange. It is proved that the influence of groundwater flow cannot be ignored.

Analysis of Geo-Temperature Restoration Performance under Intermittent Operation of Borehole Heat Exchanger Fields

Intermittent operation can improve the coefficient of performance (COP) of a ground source heat pump (GSHP) system. In this paper, an analytical solution to analyze the geo-temperature restoration performance under intermittent operation of borehole heat exchanger (BHE) fields is established. For this purpose, the moving finite line source model is combined with the g-function and the superposition principle. The model takes into account the heat transfer along the borehole, thermal interference between BHEs, and the influence of groundwater flow. The accuracy of the model is validated through comparison with an experiment carried out under intermittent operation. The model makes it possible to analyze the geo-temperature restoration performance and its influencing factors, such as BHE spacing, heat flow rate, operation mode, and groundwater flow. The main conclusions of this work are as follows. The heat transfer along the borehole should be considered when analyzing the geo-temperature restoration performance. When the BHE spacing increases, the soil temperature change decreases and the heat recovery improves. Therefore, adequate borehole separation distance is essential in the case of a multiple BHE system with unbalanced load. The presence of groundwater flow is associated with interference between the BHEs, which should not be ignored. In the case of long-term operation, the groundwater flow is beneficial to the geo-temperature recovery process, even for downstream BHEs. Finally, a greater groundwater flux leads to a better geo-temperature recovery.

Chromium(VI) transport and fate in unsaturated zone and aquifer: 3D Sandbox results

The simulation of Cr(VI) behavior in an unsaturated zone and aquifer, using a 3D experimental set-up were performed to illustrate the distribution, transport and transformation of Cr(VI), and further to reveal the potential harm of Cr(VI) after entering the groundwater. The result indicated that chromium(VI) was transported in the vertical direction, meanwhile, was transported in the horizontal direction under the influence of groundwater flow. The direction and distance away from the pollution source zone had great effect on the chromium(VI) concentration. At the sampling sites near the pollution source zone, there was a sudden increase of chromium(VI) concentration. The concentration of chromium(III) concentration in some random effluent samples was not detected. Chromium had not only transported but also had fraction and specie transformation in the unsaturated zone and aquifer. The relative concentration of residue fraction chromium was decreased with time. The content of Fe–Mn oxide fraction chromium was increased with time. The relative content of exchangeable and carbonate-bound fraction chromium was lower and the content variations were not obvious. Chromium(VI) (91–98%) was first reduced to chromium(III) rapidly. The oxidation reaction occurred later and the relative content of chromium(VI) was increased again. The presence of manganese oxides under favorable soil conditions can promote the reoxidation of Cr(III) to Cr(VI).

Indication of deep groundwater flow through the crystalline rocks of southern Norway

We assess the major aspects of the subsurface thermal regime within crystalline rocks of southern Norway. Results of two-dimensional modeling of coupled groundwater flow and heat transfer demonstrate that advective cooling due to groundwater flow is an important factor for the reduction of subsurface temperatures in southwestern Norway (the Bergen and Stavanger areas) where the normal annual precipitation is high on the western (windward) side of the Scandes mountains. On the other hand, the influence of groundwater flow on subsurface temperatures is most likely relatively low in southeastern Norway (the Moss area), which represents the rain-shadow area with light precipitation and is characterized by smoothed landforms. Therefore, where the reduced subsurface temperatures are associated with high atmospheric precipitation and complex surrounding topography, deep groundwater flow is most likely present within crystalline rocks. In this case, the observed low values of the thermal gradient within crystalline rocks can be used as groundwater flow tracers.

Heat Transfer Analysis of Groundwater Flow for Ground Heat Exchangers in the Multi-Borehole Field of Ground Source Heat Pump under the Intermittent Operation

In order to analyze the influence of groundwater flow on ground heat exchangers with different arrangements, with a project in Nanjing the access temperature field in the multi-borehole field was simulated after the ground source heat pump system had been performed for a year. Simulation results show that the access temperature is higher in the ground surrounding the borehole than the center of the corresponding borehole, thus forming a thermal barrier surrounding the borehole. Groundwater flow helps relieve temperature imbalance owing to the imbalance of heating and cooling load. The performance of the ground heat exchangers is better in staggered arrangement than in aligned arrangement. In the borehole field, the boreholes upstream have thermal interference on those downstream. And the extent of thermal interference depends on the direction of the groundwater flow when the locations of the boreholes are fixed in the borehole field.

Numerically simulating the thermal behaviors in groundwater wells of groundwater heat pump

In the geothermal energy utilization of a closed loop groundwater system of a GWHP (groundwater heat pump) and an ATES (aquifer thermal energy storage), thermal breakthrough is a very important aspect in the design of these systems. It can cause a gradual variation in the temperature of the pumping water and impact the efficiency of the GWHP. For pumping and injecting well groups, the influence of groundwater flow on the heat transfer is particularly important, especially for the aquifers with high porosity and hydraulic conductivity, the direction and velocity of groundwater directly affects the underground temperature field evolution. In this research, heat-water transfer numerical simulation and experiment has been conducted to study the evolution rule between aquifer temperature field and groundwater flow field. Simulation results were compared with the experimental results, and the validity of the simulation model was confirmed. Furthermore, the effects of groundwater flow on pumping average temperature and thermal breakthrough have been estimated by the numerical analysis, which will serve as a basis for the engineering design and further study of GWHP system.

Derivation of an approximate analytical solution for understanding the response characteristics of the EBS

ABSTRACTTo perform a safety assessment for the geological disposal of radioactive waste, it is important to understand the response characteristics of the disposal system. In this study, approximate analytical solutions for steady-state nuclide releases from the engineered barrier system (EBS) of a repository were derived for an orthogonal one-dimensional diffusion model. In these approximate analytical solutions, inventory depletion, decay during migration and the influence of groundwater flow in the excavation damaged zone (EDZ) were considered. These solutions were simplified by the Taylor theorem in order to clearly represent the response characteristics of the EBS. The validity of these solutions was shown by comparison with numerical solutions. The response characteristics of the EBS are useful for identifying target values for important parameters that would have the effect of improving the robustness of system safety. The robustness of the geological disposal system and the reliability of the safety assessment can thus potentially be improved using the approximate analytical solutions.

A moving finite line source model to simulate borehole heat exchangers with groundwater advection

Available analytical models for the thermal analysis of ground source heat pumps (GSHPs) either neglect groundwater flow or axial effects. In the present study a new analytical approach which considers both effects is developed. Comparison with existing analytical solutions based on the finite and infinite line source theory is carried out. This study shows that in general the heat transfer at the borehole heat exchanger (BHE) is affected by groundwater flow and axial effects. The latter is even more important for long simulation times and short borehole lengths. At the borehole wall the influence of the axial effect is restricted to Peclet numbers lower than 10, assuming the BHE length as characteristic length. Moreover, the influence of groundwater flow is negligible for Peclet numbers lower than 1.2. As a result for Peclet numbers between 1.2 and 10 the combined effect of groundwater flow and axial effects has to be accounted for when evaluating the temperature response of a BHE at the borehole wall and thus the use of the moving finite line source model is required.