Circulating water excess pressure direct-driven air cooler

Abstract

The invention provides a circulating water residual pressure direct-drive air cooler which comprises an air cooler body, the air cooler body comprises a shutter, a finned tube heat exchanger is connected below the shutter, a hot fluid medium inlet and a hot fluid medium outlet are formed in one side of the finned tube heat exchanger, an air blower is arranged below the finned tube heat exchanger, a water turbine is arranged below the air blower, and a water inlet and a water outlet are formed in the other side of the finned tube heat exchanger. A water outlet of the water turbine is connected with a circulating water outlet pipe of the air cooler, and the circulating water outlet pipe of the air cooler is connected with a water outlet branch pipe A of the heat exchanger; a water inlet of the water turbine is connected with an air cooler circulating water inlet pipe, the air cooler circulating water inlet pipe is connected with a heat exchanger circulating water outlet main pipe, the heat exchanger circulating water outlet main pipe is connected with a heat exchanger water outlet, and a heat exchanger water inlet is connected with a heat exchanger circulating water inlet pipe. According to the circulating water residual pressure direct-driven air cooler, the problems that an existing air cooler is large in construction investment and high in use energy consumption are solved.

Description

Technical Field

[0001] The invention relates to the technical field of energy-saving and cooling devices, and in particular to a circulating water residual pressure direct-driven air cooler. Background Art

[0002] The main function of air coolers in factory production equipment is to cool or condense hot fluids. They are usually used in industrial fields such as refineries and petrochemicals. Especially in the severely water-scarce areas in northwest China, the water-saving advantages of air coolers are more obvious.

[0003] Although the use of air coolers has achieved the goal of saving water to a certain extent, since most of the petrochemical production equipment areas are in explosion-proof areas, air cooler motors often need to use explosion-proof motors, and air coolers are generally arranged on the top of the frame of the production equipment area, which is often high, with a large number of electrical equipment and cables, and a large overall investment. During use, there is also a large amount of electricity consumption. Therefore, from an economic perspective, the use scenarios of traditional air coolers are still subject to many restrictions. Summary of the invention

[0004] The purpose of the present invention is to provide a circulating water residual pressure direct-driven air cooler, which solves the problems of large construction investment and high energy consumption of existing air coolers.

[0005] The technical solution adopted by the present invention is: a circulating water residual pressure directly drives an air cooler, including an air cooler main body, the air cooler main body includes a shutter, a fin tube heat exchanger is connected below the shutter, a hot fluid medium inlet and a hot fluid medium outlet are arranged on one side of the fin tube heat exchanger, a blower is installed below the fin tube heat exchanger, a turbine is arranged below the blower, and the two are coaxially connected, the turbine outlet is connected to the air cooler circulating water outlet pipe, the air cooler circulating water outlet pipe is connected to the heat exchanger outlet branch pipe A; the turbine inlet is connected to the air cooler circulating water inlet pipe, the air cooler circulating water inlet pipe is connected to the heat exchanger circulating water outlet main pipe, the heat exchanger circulating water outlet main pipe is connected to the heat exchanger outlet, and the heat exchanger inlet is connected to the heat exchanger circulating water inlet pipe.

[0006] The technical solution adopted by the present invention is also characterized in that: Furthermore, a bracket is provided at the bottom of the fin-tube heat exchanger.

[0007] Furthermore, the hot fluid medium inlet is connected to the hot fluid medium inlet pipe, and the hot fluid medium outlet is connected to the hot fluid medium outlet pipe.

[0008] Furthermore, a valve E is provided on the hot fluid medium outlet pipe, and a valve F is provided on the hot fluid medium inlet pipe.

[0009] Furthermore, a valve A is provided on the circulating water inlet pipe of the heat exchanger; and a valve B is provided on the circulating water outlet main pipe of the heat exchanger.

[0010] Furthermore, a valve G is provided on the outlet branch pipe A of the heat exchanger.

[0011] Furthermore, a valve C is provided on the circulating water outlet pipe of the air cooler, and a valve D is provided on the circulating water inlet pipe of the air cooler.

[0012] Furthermore, the turbine type is preferably a mixed flow turbine.

[0013] Furthermore, the driving force of the blower comes from the residual pressure energy at the circulating water outlet of the heat exchanger. There is no need to use a motor drive, and there is no need to configure an explosion-proof motor, related electrical equipment, or cables. The blower recovers the original ineffective resistance at the outlet of the heat exchanger.

[0014] Furthermore, the heat exchanger circulating water outlet main pipe is connected to the heat exchanger circulating water inlet pipe through the heat exchanger bypass pipe. A valve H is provided on the heat exchanger bypass pipe. When the heat exchanger fails for maintenance, the circulating water can enter the turbine through the heat exchanger bypass pipe without affecting the normal operation of the air cooler body.

[0015] The beneficial effects of the present invention are: The present invention provides an air cooler directly driven by circulating water residual pressure. The air cooler on the top of the device area frame no longer needs to be driven by a motor. Since no motor is used, the air cooler will not suddenly stop operating due to sudden power failure, and the operation is safe and stable. In addition, since there is no need to set up a motor, the investment in explosion-proof motors, cables, and supporting electrical equipment is avoided. On the other hand, since the turbine and the fan are directly driven, the efficiency loss of traditional belt transmission is avoided, and the efficient operation of the fan equipment is achieved. Furthermore, the energy consumption required for the air cooler blades comes from the waste energy originally consumed at the valve at the outlet of the circulating water side of the heat exchanger, thereby avoiding electricity consumption and greatly saving electricity bills. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a schematic diagram of the process of the circulating water residual pressure direct-driven air cooler of the present invention; Figure 2 It is a structural diagram of the circulating water excess pressure direct-driven fan air cooler of the present invention.

[0017] In the figure, 1. heat exchanger circulating water inlet pipe, 2. valve A, 3. heat exchanger, 4. valve B, 5. heat exchanger circulating water outlet main pipe, 6. heat exchanger outlet branch pipe A, 7. valve C, 8. valve D, 9. valve E, 10. valve F, 11. hot fluid medium outlet pipe, 12. hot fluid medium inlet pipe, 13. air cooler body, 14. air cooler circulating water outlet pipe, 15. air cooler circulating water inlet pipe, 16. valve G, 17. valve H, 18. heat exchanger bypass pipeline, 19. hot fluid medium inlet, 20. hot fluid medium outlet, 21. fin tube heat exchanger, 22. blower, 23. bracket, 24. turbine, 25. turbine water inlet, 26. turbine water outlet, 27. shutter. DETAILED DESCRIPTION

[0018] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] The present invention provides a circulating water residual pressure direct-driven air cooler, such as Figure 1 As shown, it includes a louver 27, a fin-tube heat exchanger 21, a blower 22, and a turbine 24. The air cooler 13 is supported as a whole by a bracket 23. The louver 27 is at the top of the air cooler. The fin-tube heat exchanger 21 is connected below the louver 27. A hot fluid medium inlet 19 and a hot fluid medium outlet 20 are provided on one side of the fin-tube heat exchanger 21, wherein the hot fluid medium inlet 19 is connected to the hot fluid medium inlet pipe 12, and a valve H17 is provided on the inlet pipe; the hot fluid medium outlet 20 is connected to the hot fluid medium outlet pipe 11, and a valve E9 is provided on the outlet pipe. A blower 22 is installed below the fin tube heat exchanger 21, and the blower 22 is coaxially connected to the turbine 24 below, wherein the turbine water outlet 26 is connected to the air cooler circulating water outlet pipe 14, and the air cooler circulating water outlet pipe 14 is provided with a valve C7, and the air cooler circulating water outlet pipe 14 is further connected to the heat exchanger outlet branch pipe A6; the turbine water inlet 25 is connected to the air cooler circulating water inlet pipe 15, and the air cooler circulating water inlet pipe 15 is provided with a valve D8.

[0020] The inlet and outlet of the heat exchanger 3 are respectively connected to the heat exchanger circulating water inlet pipe 1 and the heat exchanger circulating water outlet main pipe 5, wherein the heat exchanger circulating water inlet pipe 1 is provided with a valve A2, the heat exchanger circulating water outlet main pipe 5 is provided with a valve B4, and the heat exchanger circulating water inlet pipe 1 is divided into two branch pipes, namely, the heat exchanger outlet branch pipe A6 and the air cooler circulating water inlet pipe 15. In addition, a heat exchanger bypass pipe 18 is connected between the heat exchanger circulating water inlet pipe 1 and the heat exchanger circulating water outlet main pipe 5, and a valve H17 is provided.

[0021] The circulating water residual pressure direct-drive air cooler of the present invention avoids the problem that the air cooler on the original device area frame needs to use explosion-proof motors, electrical equipment, and cables, greatly reducing construction investment. Due to the direct drive method, transmission loss is avoided, and the equipment operation efficiency is effectively improved. During use, the ineffective resistance originally existing at the circulating water outlet valve of the heat exchanger is also recycled, greatly reducing the power consumption of the air cooler.

[0022] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0023] Example 1 The circulating water residual pressure directly drives the air cooler, comprising an air cooler body 13, the air cooler body 13 comprising a shutter 27, a fin-tube heat exchanger 21 is connected below the shutter 27, a hot fluid medium inlet 19 and a hot fluid medium outlet 20 are arranged on one side of the fin-tube heat exchanger 21, a blower 22 is installed below the fin-tube heat exchanger 21, a turbine 24 is arranged below the blower 22, and the two are coaxially connected, the turbine outlet 26 is connected to the air cooler circulating water outlet pipe 14, the air cooler circulating water outlet pipe 14 is connected to the heat exchanger outlet branch pipe A6; the turbine water inlet 25 is connected to the air cooler circulating water inlet pipe 15, the air cooler circulating water inlet pipe 15 is connected to the heat exchanger circulating water outlet main pipe 5, the heat exchanger circulating water outlet main pipe 5 is connected to the heat exchanger 3 outlet, and the heat exchanger 3 inlet is connected to the heat exchanger circulating water inlet pipe 1.

[0024] Example 2 The circulating water residual pressure directly drives the air cooler, comprising an air cooler body 13, the air cooler body 13 comprising a shutter 27, a fin-tube heat exchanger 21 is connected below the shutter 27, a bracket 23 is arranged at the bottom of the fin-tube heat exchanger 21, a hot fluid medium inlet 19 and a hot fluid medium outlet 20 are arranged on one side of the fin-tube heat exchanger 21, the hot fluid medium inlet 19 is connected to the hot fluid medium inlet pipe 12, the hot fluid medium outlet 20 is connected to the hot fluid medium outlet pipe 11, a valve E9 is arranged on the hot fluid medium outlet pipe 11, and a valve F10 is arranged on the hot fluid medium inlet pipe 12; A blower 22 is installed below the fin tube heat exchanger 21, and a turbine 24 is arranged below the blower 22, and the two are coaxially connected. The turbine outlet 26 is connected to the air cooler circulating water outlet pipe 14, and the air cooler circulating water outlet pipe 14 is connected to the heat exchanger outlet branch pipe A6; the turbine water inlet 25 is connected to the air cooler circulating water inlet pipe 15, and the air cooler circulating water inlet pipe 15 is connected to the heat exchanger circulating water outlet main pipe 5, and the heat exchanger circulating water outlet main pipe 5 is connected to the heat exchanger 3 outlet, and the heat exchanger 3 inlet is connected to the heat exchanger circulating water inlet pipe 1, and the heat exchanger circulating water inlet pipe 1 is provided with a valve A2; the heat exchanger circulating water outlet main pipe 5 is provided with a valve B4.

[0025] Example 3 The circulating water residual pressure directly drives the air cooler, comprising an air cooler body 13, the air cooler body 13 comprising a shutter 27, a fin-tube heat exchanger 21 is connected below the shutter 27, a bracket 23 is arranged at the bottom of the fin-tube heat exchanger 21, a hot fluid medium inlet 19 and a hot fluid medium outlet 20 are arranged on one side of the fin-tube heat exchanger 21, the hot fluid medium inlet 19 is connected to the hot fluid medium inlet pipe 12, the hot fluid medium outlet 20 is connected to the hot fluid medium outlet pipe 11, a valve E9 is arranged on the hot fluid medium outlet pipe 11, and a valve F10 is arranged on the hot fluid medium inlet pipe 12; A blower 22 is installed below the fin tube heat exchanger 21, a turbine 24 is provided below the blower 22, and the two are coaxially connected, the turbine outlet 26 is connected to the air cooler circulating water outlet pipe 14, the air cooler circulating water outlet pipe 14 is provided with a valve C7, the air cooler circulating water outlet pipe 14 is connected to the heat exchanger outlet branch pipe A6, the heat exchanger outlet branch pipe A6 is provided with a valve G16; The turbine water inlet 25 is connected to the air cooler circulating water inlet pipe 15, the air cooler circulating water inlet pipe 15 is provided with a valve D8, the air cooler circulating water inlet pipe 15 is connected to the heat exchanger circulating water outlet main pipe 5, the heat exchanger circulating water outlet main pipe 5 is connected to the heat exchanger 3 outlet, the heat exchanger 3 inlet is connected to the heat exchanger circulating water inlet pipe 1, the heat exchanger circulating water inlet pipe 1 is provided with a valve A2; the heat exchanger circulating water outlet main pipe 5 is provided with a valve B4.

[0026] Example 4 The circulating water residual pressure directly drives the air cooler, comprising an air cooler body 13, the air cooler body 13 comprising a shutter 27, a fin-tube heat exchanger 21 is connected below the shutter 27, a bracket 23 is arranged at the bottom of the fin-tube heat exchanger 21, a hot fluid medium inlet 19 and a hot fluid medium outlet 20 are arranged on one side of the fin-tube heat exchanger 21, the hot fluid medium inlet 19 is connected to the hot fluid medium inlet pipe 12, the hot fluid medium outlet 20 is connected to the hot fluid medium outlet pipe 11, a valve E9 is arranged on the hot fluid medium outlet pipe 11, and a valve F10 is arranged on the hot fluid medium inlet pipe 12; A blower 22 is installed below the fin tube heat exchanger 21, and a turbine 24 is arranged below the blower 22, and the two are coaxially connected. The turbine 24 is preferably a mixed flow turbine. The turbine outlet 26 is connected to the air cooler circulating water outlet pipe 14, and the air cooler circulating water outlet pipe 14 is provided with a valve C7. The air cooler circulating water outlet pipe 14 is connected to the heat exchanger outlet branch pipe A6, and the heat exchanger outlet branch pipe A6 is provided with a valve G16; The turbine water inlet 25 is connected to the air cooler circulating water inlet pipe 15, the air cooler circulating water inlet pipe 15 is provided with a valve D8, the air cooler circulating water inlet pipe 15 is connected to the heat exchanger circulating water outlet main pipe 5, the heat exchanger circulating water outlet main pipe 5 is connected to the heat exchanger 3 outlet, the heat exchanger 3 inlet is connected to the heat exchanger circulating water inlet pipe 1, the heat exchanger circulating water inlet pipe 1 is provided with a valve A2; the heat exchanger circulating water outlet main pipe 5 is provided with a valve B4.

[0027] Example 5 The circulating water residual pressure directly drives the air cooler, comprising an air cooler body 13, the air cooler body 13 comprising a shutter 27, a fin-tube heat exchanger 21 is connected below the shutter 27, a bracket 23 is arranged at the bottom of the fin-tube heat exchanger 21, a hot fluid medium inlet 19 and a hot fluid medium outlet 20 are arranged on one side of the fin-tube heat exchanger 21, the hot fluid medium inlet 19 is connected to the hot fluid medium inlet pipe 12, the hot fluid medium outlet 20 is connected to the hot fluid medium outlet pipe 11, a valve E9 is arranged on the hot fluid medium outlet pipe 11, and a valve F10 is arranged on the hot fluid medium inlet pipe 12; A blower 22 is installed below the fin tube heat exchanger 21, and a turbine 24 is arranged below the blower 22, and the two are coaxially connected. The turbine 24 is preferably a mixed flow turbine. The turbine outlet 26 is connected to the air cooler circulating water outlet pipe 14, and the air cooler circulating water outlet pipe 14 is provided with a valve C7. The air cooler circulating water outlet pipe 14 is connected to the heat exchanger outlet branch pipe A6, and the heat exchanger outlet branch pipe A6 is provided with a valve G16; The turbine water inlet 25 is connected to the air cooler circulating water inlet pipe 15, the air cooler circulating water inlet pipe 15 is provided with a valve D8, the air cooler circulating water inlet pipe 15 is connected to the heat exchanger circulating water outlet main pipe 5, the heat exchanger circulating water outlet main pipe 5 is connected to the heat exchanger 3 outlet, the heat exchanger 3 inlet is connected to the heat exchanger circulating water inlet pipe 1, the heat exchanger circulating water inlet pipe 1 is provided with a valve A2; the heat exchanger circulating water outlet main pipe 5 is provided with a valve B4.

[0028] Example 6 The circulating water residual pressure directly drives the air cooler, comprising an air cooler body 13, the air cooler body 13 comprising a shutter 27, a fin-tube heat exchanger 21 is connected below the shutter 27, and a bracket 23 is arranged at the bottom of the fin-tube heat exchanger 21; A hot fluid medium inlet 19 and a hot fluid medium outlet 20 are provided on one side of the fin tube heat exchanger 21, the hot fluid medium inlet 19 is connected to the hot fluid medium inlet pipe 12, the hot fluid medium outlet 20 is connected to the hot fluid medium outlet pipe 11, a valve E9 is provided on the hot fluid medium outlet pipe 11, and a valve F10 is provided on the hot fluid medium inlet pipe 12; A blower 22 is installed below the fin tube heat exchanger 21, and a turbine 24 is provided below the blower 22, and the two are coaxially connected, the turbine outlet 26 is connected to the air cooler circulating water outlet pipe 14, the air cooler circulating water outlet pipe 14 is connected to the heat exchanger outlet branch pipe A6, the air cooler circulating water outlet pipe 14 is provided with a valve C7, and the heat exchanger outlet branch pipe A6 is provided with a valve G16; The driving force of the blower 22 comes from the residual pressure energy at the circulating water outlet of the heat exchanger 3. There is no need to use a motor drive, and there is no need to configure an explosion-proof motor, related electrical equipment, or cables. The blower 22 recovers the original ineffective resistance at the outlet of the heat exchanger.

[0029] The turbine water inlet 25 is connected to the air cooler circulating water inlet pipe 15, the air cooler circulating water inlet pipe 15 is connected to the heat exchanger circulating water outlet main pipe 5, the air cooler circulating water inlet pipe 15 is provided with a valve D8, the heat exchanger circulating water outlet main pipe 5 is connected to the heat exchanger 3 outlet, the heat exchanger 3 inlet is connected to the heat exchanger circulating water inlet pipe 1, the heat exchanger circulating water inlet pipe 1 is provided with a valve A2; the heat exchanger circulating water outlet main pipe 5 is provided with a valve B4.

[0030] The heat exchanger circulating water outlet main pipe 5 is connected to the heat exchanger circulating water inlet pipe 1 through the heat exchanger bypass pipe 18. A valve H17 is provided on the heat exchanger bypass pipe 18. When the heat exchanger 3 fails for maintenance, the circulating water can enter the turbine 24 through the heat exchanger bypass pipe 18 without affecting the normal operation of the air cooler body 13.

[0031] The working principle of the circulating water residual pressure direct-driven air cooler of the present invention is: The circulating water enters the heat exchanger 3 through the heat exchanger circulating water inlet pipe 1 to complete the cooling of the hot material. At this time, valve A2 and valve B4 are in the open state, and valve H17 is in the closed state. The circulating water after heat exchange is sent to the air cooler turbine inlet 25 through the heat exchanger circulating water outlet main pipe 5 and the air cooler circulating water inlet pipe 15 in turn. After completing the residual pressure drive of the air cooler 13, the circulating water is sent from the air cooler turbine outlet 26 through the air cooler circulating water outlet pipe 14 to the heat exchanger outlet branch pipe A6 to complete the entire transportation process. Valve C7 and valve D8 are in the open state, and valve G16 is in the closed state.

[0032] When the air cooler of the present invention is used, valves E9 and F10 are in an open state, and the hot material transfers heat to the tube wall of the finned tube heat exchanger 21 in the form of convection, and the heat is transferred to the outer wall of the tube in the form of heat conduction, and then to the fins of the outer wall. The air flow passes through the finned tube under the promotion of the blower 22, and the heat of the finned tube is taken away through the shutter 27, thereby achieving the purpose of cooling the hot material. Among them, the fan blades of the blower 22 are driven by the turbine 24. Since the turbine 24 is directly connected to the blower 22 coaxially, when the circulating water enters the turbine 24, the fan of the blower 22 rotates synchronously with the turbine rotor, realizing the "powerless operation" of the air cooler 13.

[0033] Considering the equipment maintenance, the valves need to be operated during the equipment maintenance. When the heat exchanger 3 needs maintenance, valves A2 and B4 are closed, the heat exchanger is cut out, and valve H17 is opened. At this time, the circulating water bypasses the heat exchanger 3 and enters the air cooler turbine 24, which does not affect the normal operation of the air cooler 13; when the air cooler 13 needs maintenance, valves C7 and D8 are closed, the air cooler 13 is cut out, and valve G16 is opened. At this time, the circulating water bypasses the heat exchanger 3 for heat exchange and then bypasses the air cooler 13 to return to the circulating water system, which does not affect the normal operation of the heat exchanger 3.

Claims

1. Circulating water residual pressure direct-driven air cooler, characterized in that: The air cooler comprises an air cooler body (13), the air cooler body (13) comprising a shutter (27), a fin-tube heat exchanger (21) being connected below the shutter (27), a hot fluid medium inlet (19) and a hot fluid medium outlet (20) being arranged on one side of the fin-tube heat exchanger (21), a blower (22) being arranged below the fin-tube heat exchanger (21), a water turbine (24) being arranged below the blower (22), and the two being coaxially connected, the water outlet (24) of the water turbine being arranged 6) is connected to the air cooler circulating water outlet pipe (14), the air cooler circulating water outlet pipe (14) is connected to the heat exchanger outlet branch pipe A (6); the turbine water inlet (25) is connected to the air cooler circulating water inlet pipe (15), the air cooler circulating water inlet pipe (15) is connected to the heat exchanger circulating water outlet main pipe (5), the heat exchanger circulating water outlet main pipe (5) is connected to the heat exchanger (3) outlet, and the heat exchanger (3) inlet is connected to the heat exchanger circulating water inlet pipe (1).

2. The circulating water residual pressure direct-driven air cooler according to claim 1, characterized in that: A bracket (23) is provided at the bottom of the fin-tube heat exchanger (21).

3. The circulating water residual pressure direct-driven air cooler according to claim 1, characterized in that: The hot fluid medium inlet (19) is connected to the hot fluid medium inlet pipe (12), and the hot fluid medium outlet (20) is connected to the hot fluid medium outlet pipe (11).

4. The circulating water residual pressure direct-driven air cooler according to claim 3, characterized in that: The hot fluid medium outlet pipe (11) is provided with a valve E (9), and the hot fluid medium inlet pipe (12) is provided with a valve F (10).

5. The circulating water residual pressure direct-driven air cooler according to claim 1, characterized in that: The heat exchanger circulating water inlet pipe (1) is provided with a valve A (2); the heat exchanger circulating water outlet main pipe (5) is provided with a valve B (4).

6. The circulating water residual pressure direct-driven air cooler according to claim 1, characterized in that: A valve G (16) is provided on the water outlet branch pipe A (6) of the heat exchanger.

7. The circulating water residual pressure direct-driven air cooler according to claim 1, characterized in that: The air cooler circulating water outlet pipe (14) is provided with a valve C (7), and the air cooler circulating water inlet pipe (15) is provided with a valve D (8).

8. The circulating water residual pressure direct-driven air cooler according to claim 1, characterized in that: The water turbine (24) is preferably a Francis turbine.

9. The circulating water residual pressure direct-driven air cooler according to claim 1, characterized in that: The driving force of the blower (22) comes from the residual pressure energy at the outlet of the circulating water of the heat exchanger (3), and there is no need to use a motor drive, and there is no need to configure an explosion-proof motor, related electrical equipment, or cables. The blower (22) recovers the original ineffective resistance at the outlet of the heat exchanger.

10. The circulating water residual pressure direct-driven air cooler according to claim 1, characterized in that: The heat exchanger circulating water outlet main pipe (5) is connected to the heat exchanger circulating water inlet pipe (1) via a heat exchanger bypass pipe (18). A valve H (17) is provided on the heat exchanger bypass pipe (18). When the heat exchanger (3) is faulty for maintenance, the circulating water can enter the turbine (24) via the heat exchanger bypass pipe (18) without affecting the normal operation of the air cooler body (13).

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