Does anyone know about or have used narrow point technology?

1. Principle of narrow-point technology: The most cutting-edge aspect in the field of thermal energy at present is optimization control, which is a type of dynamic optimization problem. Its corresponding mathematical model is a set of differential equations, the objective function is in integral form, and the optimal solution obtained is a function of time. The narrow point analysis method introduced in this paper is a static optimization problem, and its mathematical model consists of a set of algebraic equations; therefore, this method is simpler. The core technology of process system optimization methods is the pinch point technique, which focuses on the overall optimized design of the process system, including the appropriate matching between hot and cold streams, as well as the selection of the type and capacity of hot and cold utility systems ； The appropriate placement of heaters, coolers, and various devices in the system such as separators, evaporators, etc., within the network ； A tripartite trade-off among energy efficiency, investment, and operability. The ultimate optimization goal is to minimize the sum of the total annual operating costs and the initial investment cost. In terms of optimization objectives, narrow-point technology initially aimed to minimize energy consumption as the objective for the system; it later evolved to focus on total cost. Furthermore, non-quantitative process objectives such as the safety and operability of the process system, its adaptability to different operating conditions, and its impact on the environment were also taken into consideration. Therefore, the narrow-point technology can be used not only for the optimized integration of heat recovery heat exchange networks, but also for the proper selection of heat engines and heat pumps, determining the level and quantity of utility services required, eliminating bottlenecks to increase production capacity, integrating various equipment, reducing water usage in production, and minimizing exhaust gas emissions. 2. Steps for applying the narrow-point analysis method: The narrow-point analysis method is a comprehensive analysis technique used to evaluate the IE thermal performance of heat exchangers in process systems and to achieve maximum energy recovery. When using this method to solve problems, whether it is a new project or an existing one, construction projects generally should follow these steps: (1) List the cold and hot flow streams in the project, as well as the utility stream streams. Cold flow streams refer to those streams in the utility systems that need to be heated ； A heat flow stream refers to a stream of material that requires cooling, such as chemical products that need to be kept at a low temperature during storage ； Utility stream refers to the stream used for heating or cooling hot and cold streams when heat exchange between them is uneconomical or not feasible. When distinguishing between cold and hot streams, it should be noted that some streams experience temperature changes, but these changes do not occur through heat exchange; such streams are not considered cold streams. For example: when a gas stream is compressed, its temperature rises, but no heat exchange occurs between the streams, so that stream does not qualify as a stream. (2) To determine the thermodynamic parameters of various flow streams, the parameters that need to be identified include: initial temperature, target temperature, heat capacity flow rate, and heat absorption and release amounts. In each step of this method, the influence of the above parameters should be fully considered. Any error in the parameters will lead to incorrect conclusions. (3) Determine the value of the minimum heat transfer temperature difference DTmin. DTmin represents the smallest heat transfer temperature difference across the entire network; to achieve the energy targets, it is required that the heat transfer temperature difference at the narrow points be equal to DTmin, while those at points farther from the narrow points must not be less than DTmin. When DTmin is equal to zero, it represents the maximum limit for energy recovery from cold and hot streams; at this point, the loads on the cold and hot utility systems are both at their minimum values. The larger DTmin is, and the greater the minimum loads of the cooling and heating utility systems, the less energy recovery there is. At the same time, as DTmin increases, the minimum loads of these utility systems increase, and the amount by which energy recovery decreases is exactly equal to the increase in those minimum loads. Typical empirical values for DTmin can be found in relevant references; Linnoff proposed a set of empirical values for DTmin applicable to shell-and-tube heat exchangers, as shown in Table 1. (4) Plotting the composite curve graph: The so-called composite curve graph refers to the temperature-baking curve graph, which includes the hot composite curve and the cold composite curve. The composite curve visually represents the minimum loads of cold and hot utility systems. In the composite graph, the cold and hot flow streams with constant heat flux are represented by straight lines extending from the initial temperature to the target temperature. The specific drawing method is as follows: Arrange the starting and target temperatures of the heat flow stream in ascending order, calculate the total heat release in each temperature range for the heat flow stream, and apply the same process to the cold flow stream. To prevent errors, it is best to include the calculation data in a table. Then plot the data from the table on a temperature vs. baking time graph. From the composite curve graph, the minimum loads of cold and hot utility systems, as well as the temperature values at the narrow points of the cold and hot streams, can be determined. Figure 1 shows the composite curve for project a at DTmin = 10°C. It can be seen from the figure that the minimum loads of the cooling and heating utility systems are 60 kW and 20 kW respectively, while the temperatures at the narrow points of the cooling and heating streams are 90°C and 80°C respectively. Figure 2 shows the comprehensive curve at DTmin = 20°C. At this temperature, the minimum loads of the cooling and heating utility systems are 105 kW and 65 kW respectively, which are significantly higher than those when the narrow-point temperature is 10°C. An increase in the narrow-point temperature leads to an increase in the minimum heat transfer temperature difference, thereby reducing the amount of energy that can be recovered. As a result, more energy must be supplied to the system from outside to meet the requirements, which causes the minimum loads of both the cooling and heating utility systems to increase. As can be seen from the composite curve graph, the narrow point divides the entire process into two independent subsystems. Above the narrow point, heat only needs to be absorbed from the thermal utility system, while below the narrow point, heat only needs to be released to the cooling utility system. Therefore, no utility cooling units should be installed above the narrow point, and no utility heating units should be installed below it, in order to avoid heat exchange across the narrow point. The so-called heat exchange across a narrow point refers to the heat exchange between the hot fluid above the narrow point and the cold fluid below it; if the amount of heat crossing the narrow point is α, it will result in an increase of α in both the load on the cold and hot utility systems. (5) Generation of the initial network: In the preliminary network diagram, cold and hot flow streams are represented by horizontal lines; the initial temperature and target temperature are marked at both ends of the line, while the vertical line in the middle indicates the temperature at the narrow point. The circles in the diagram are used to represent heat exchangers, while the unconnected circles denote heat exchange devices that exchange heat with utility streams. The initial network of Project A is shown in Figure 3. When establishing the initial network, logistics matching is carried out separately for the upper and lower parts at the narrow point; meanwhile, the following points should be noted: ① Matching should first take place at the narrow point, and then gradually move away from it. At the narrow point, the constraints of the W criterion must be followed, that is: above the narrow point, the heat capacity flow rate of the hot stream should not be greater than that of the cold stream ； Below the narrow point, the heat capacity flow rate of the hot stream should be no less than that of the cold stream to maintain a temperature difference for heat transfer within the network. The matching away from the narrow point is not constrained by the W criterion, but it still must satisfy that the minimum heat transfer temperature difference is greater than or equal to DTmin. ②Try to maximize the heat load of the heat exchanger in order to reduce the number of heat exchange units. ③Note that hot utility systems should be installed only above the narrow section, and cold utility systems only below it. ④Logistics diversion technology is employed. Since coolers are not allowed above the narrow point, the number of cold flow streams above the narrow point must be greater than (or equal to) the number of hot flow streams; conversely, below the narrow point, the number of hot flow streams must be greater than (or equal to) the number of cold flow streams. When the requirement is not met, shunting technology should be employed; similarly, when the number of flow streams meets the requirement but does not satisfy the W criterion, shunting technology must also be used. (6) Further optimization and integration of the network: The initial network that meets the energy consumption targets is not optimal; it merely ensures that the operating costs are minimized under a given DTmin, whereas the initial investment cost is not necessarily minimized. Therefore, a trade-off must be made between energy consumption and initial investment. When performing network integration, three rules need to be followed in sequence: ① Perform energy relaxation along paths and loops to reduce network fluctuations. The specific approach is to first conduct an energy target analysis, and then remove heaters and coolers whose load exceeds the minimum requirements for cold and hot utility systems, as well as heat exchangers with low loads that exceed the minimum number required. The so-called path refers to a continuous channel formed through logistics and heat exchangers between thermal utility systems or between cold utility systems, as well as between cold and thermal utility systems. A loop refers to a system of closed pathways formed between different heat exchange devices within a heat exchange network. ②When changing the location of cold and hot utility systems, the cooler is always moved to the cooler area, and the heater is moved to the hotter area ； When two heaters (coolers) on two streams are combined into one larger heater (cooler) on a single stream, the resulting heater (cooler) should have a higher (lower) average stream temperature. In some cases, the number of heat exchange units can be reduced by diverting flow and then recombining it; in other cases, the number of such units can be decreased by combining flow again or by using bypass systems. Overall, this method can be divided into three stages: goal analysis, corresponding to steps (1) to (4) ； Generate the initial network, i.e., step (5) ； The final stage is the further optimization and integration of the network. 5 Applications of narrow-beam technology: Narrow-beam technology is suitable for the design of process systems and energy-saving upgrades. Process industries are those sectors whose purpose is to handle energy flows, such as the chemical industry, metallurgy, oil refining, papermaking, cement production, food processing, pharmaceuticals, and the power industry. In the production systems of the process industry, throughout the entire production process from raw materials to finished products, there are always aspects such as energy supply, conversion, utilization, recovery, generation, and disposal. For example, the feed material needs to be heated, while the product needs to be cooled. The heat exchange between cold and hot fluids constitutes a heat recovery system; in cases where heating is insufficient, fuel or steam provided by thermal utility systems must be used, and when cooling is insufficient, cooling water, cooling air, or cooling capacity provided by cooling utility systems must be utilized ； The operation of pumps and compressors requires electricity or can be driven directly by steam turbines, etc. Over the past 20 years, the narrow point analysis method has been widely applied; for example, a petroleum company’s crude oil distillation system required renovation due to its expansion. One contractor suggested that adding heaters was necessary to solve the problem. Considering factors such as energy efficiency, safety, and feasibility, the company decided to use narrow-point technology to upgrade the existing system; as a result, not only were no additional heaters added, but energy savings of 10% were also achieved each year. First, a target analysis of the system is conducted; based on the empirical value of DTmin proposed by Linnoff, DTmin is set at 20°C, and a comprehensive curve graph is drawn. As a result, the temperatures at the narrow points of the cold and hot flow streams are found to be 148°C and 168°C respectively, while the minimum loads required for the cold and hot utility systems are 111.2 MW and 103.4 MW respectively. In the second stage, the initial network is generated as shown in Figure C, where the loads on the coin-cooler units are 44.112, 32.165, 33.384, 8.3, 12.118, 0.67, 11.2, 22.29, and 39.95 MW respectively. The cooling load of Cl-1 to C7 is 22.26, 19.16, 10.79, 13.29, 1.30, 38, and 26.52 MW respectively. The load of heater H is: 88.12MW. In the third stage, the initial network is optimized according to the network integration rules in the narrow-point analysis method: energy relaxation is performed along the path indicated by the dashed lines in Figure 4, and the low-load heat exchanger ⑥ is removed, resulting in the scheme shown in Figure 5. Among them, C5 needs to increase by 0.67MW, heat exchanger ④ needs to increase by 0.67MW, while C3 needs to decrease by 0.67MW. The relaxed scheme is more reasonable, as it eliminates heat exchangers with low load requirements while ensuring that the minimum load is maintained for cold and hot utility systems in the target analysis. This reduces the number of heat exchange units, lowers the initial investment and thus the overall cost, while still achieving energy-saving objectives. In our country, there is still insufficient awareness of the energy-saving effects of narrow-spot technology; its application is limited, and much work remains to be done. Taking the installation of heat pumps in process systems as an example, there are three possible ways to install heat pumps: above the narrow point, below the narrow point, or across the narrow point. Above the point, that is, its heat absorption and release both occur above the narrow point. At this point, the heat pump replaces a portion of the heat provided by the heating utility system with external work W; the amount of energy input into the process remains unchanged. When a heat pump is installed below the narrow point, all the input work is converted into waste heat discharged to the cooling utility system; this not only fails to save energy but also wastes the input work and increases the load on the cooling utility system, resulting in significant energy loss, which is even less desirable. The setup across the narrow point is such that heat absorption occurs below the narrow point, while heat release occurs above it. In this way, the process acts as a net heat source below the narrow point, while above the narrow point, the heat pump supplies heat to it, thereby saving energy. Therefore, in process systems, the principle for setting up heat pumps is to cross the narrow point. The setting for crossing the narrow point merely provides a principle; to apply heat pumps appropriately, it is also necessary to understand the characteristics and operating ranges of various heat pumps, and to match them reasonably with the overall composite curve of the process. It is evident that the application of narrow-band technology is closely linked to our field of study. 6 Conclusions (1) The narrow-point analysis method can be used to design and improve engineering projects in a short period of time with minimal data. (2) The proper application of the narrow-point analysis method can save energy as well as reduce investment costs. (3) The narrow-point analysis method simplifies the design and improvement of heat exchange networks, while meeting the technical and economic requirements of engineering projects. (4) Currently, this method can be applied not only to industries such as chemicals and petroleum, but also to the optimization of thermal systems such as thermal power plants and boiler rooms.

The image wasn’t uploaded; here’s a link for you: http://www.sbgl.net/bencandy-72-7817-1.htm. I hope it helps!

Thank you for the help from above. Could you provide more detailed information? It would be great to have a more detailed example~~ Thank you:) :)

Why isn’t anyone responding? The application of narrow-spot technology in the chemical industry must be quite widespread, right?:'