CN104932449A - Determination method of heat exchanger network heat flux containing non-isothermal phase change fluid - Google Patents

Abstract

A determination method of the heat exchanger network heat flux containing the non-isothermal phase change fluid comprises the steps of determining the distribution relation of the available heat along with the temperature in a heat exchanger network based on the actual physical property of the fluid and by an actual temperature enthalpy physical property relation of the fluid; according to the influence of a non-linear physical property on the size and direction of the available heat flux in a local temperature area, dividing a whole temperature interval into a series of heat flux sub-intervals monotonously changing along with the temperature, and further determining the heat flux of the heat exchanger network according to the sizes and directions of the heat flux accumulated in the temperature areas. According to the present invention, a reliable heat flux calculation result can be obtained.

Description

A kind of heat exchanger network hot-fluid method for determination of amount comprising non-isothermal phase change fluid

Technical field

The present invention relates to the design field of industrial heat exchange network, especially a kind of heat exchanger network hot-fluid method for determination of amount comprising non-isothermal phase change fluid.

Background technology

In industrial processes, in order to meet the technology needs of technique, some cold fluids will be heated to the state of temperature that process conditions are specified, and the fluid of other heat then will be cooled to the state of temperature that process conditions are specified.By reasonably these heat, cold flow stock being carried out coupling heat exchange, make full use of the heat of industrial process internal flows, go to heat cold fluid with the fluid of heat, the fluid of the heat of cooling is removed with cold fluid, temperature logistics being reached specify and phase, the consumption to outside public work is reduced, the effect of Here it is industrial heat exchange network (heat exchanger network) by the heat of recovery system inside.Heat exchanger network is used for utilizable energy in recovery system, and reducing the demand to outside public work, is an important subsystem of the industrial systems such as petrochemical industry, chemical industry, metallurgy, papermaking, cement, food, electric power.The degree of heat exchanger network recycling industrial system internal heat directly determines energy consumption and the economy of industrial system, to energy-saving and emission-reduction important.

In the design of heat exchanger network, a major issue is that the heat that industrial system inside can be recycled has how many actually, namely how to determine that maximum heat reclaims potentiality.The maximum heat of heat exchanger network reclaims potentiality and determines the least energy consumption demand of industrial system and the size of energy-saving potential.

Folder point method is the conventional design method of heat exchanger network, and the method is according to determining that the maximum heat of heat exchanger network reclaims potentiality with thermodynamics.It is on this hypothesis of constant that folder point method is based upon material specific heat capacity, and the heat that namely fluid absorbed or discharged is directly proportional to its temperature variation.The industrial processs such as the processing of petrochemical industry, chemical industry, gas, low-temperature industrial usually comprise many distillations or rectifying, evaporation, condensation, the operating unit such as to boil, and involved fluid is usually multicomponent mixture, and the non-isothermal phase change process of fluid is very common.To the heat exchanger network of fluid comprising non-isothermal phase change, relation between its heat flux with temperature presents more significant nonlinear characteristic, now tradition folder point method just correctly cannot estimate the heat flux of heat exchanger network, even seriously judges the energy requirements of industrial system by accident.The achievement comprised in the heat exchanger network hot-fluid method for determination of amount of non-isothermal phase change fluid is not yet there is at present in open source literature report.

Summary of the invention

Correctly can not estimate the limitation of the heat flux of the heat exchanger network comprising non-isothermal phase change fluid to overcome existing folder point method, the invention provides a kind of based on the actual physical property of fluid, the heat exchanger network hot-fluid method for determination of amount that comprises non-isothermal phase change fluid.

The technical solution adopted for the present invention to solve the technical problems is:

Comprise a heat exchanger network hot-fluid method for determination of amount for non-isothermal phase change fluid, said method comprising the steps of:

1) technological parameter and the physical data of fluid is extracted

Technological parameter and the physical data of logistics comprise: composition, flow, inlet temperature T _in, outlet temperature T _out, enthalpy and specific heat capacity, adopt the warm enthalpy physical property relation of fluid reality;

2) the minimum heat transfer temperature difference Δ T of heat exchanger network is set _min

3) cold and hot fluid temperature adjustmemt is carried out

The temperature of cold fluid is raised Δ T _min/ 2, the temperature of per share hot fluid is reduced Δ T _min/ 2, thus the temperature of temperature higher than cold fluid guaranteeing hot fluid, and meet minimum heat transfer temperature difference Δ T _minrequirement, cold and hot fluid temperature adjustmemt is respectively with reference to formula (1)-(2):

$T_{C,j}^{*}=T_{C,j}+{\mathrm{\ΔT}}_{\min }/2---\left(1\right)$

$T_{H,i}^{*}=T_{H,i}-{\mathrm{\ΔT}}_{\min }/2---\left(2\right)$

In formula (1)-(2), Δ T _minfor step 2) the minimum heat transfer temperature difference of specifying; T _h,iand T _c,jbe respectively the actual temperature of hot-fluid stock i and cold flow stock j; T ^* _h,iand T ^* _c,jbe respectively the temperature that hot-fluid stock i and cold flow stock j carries out after temperature adjustmemt;

4) initial temperature is divided interval

With step 3) in import and export temperature after cold and hot fluid correction be foundation, divide temperature range, by all cold and hot fluid through step 3) revise after inlet temperature and outlet temperature by order arrangement from high to low, be designated as: T ₁, T ₂..., T _n1, T _n1+1, wherein N1+1 is the number of temperature end points, and the warm area number divided is N1, and warm area is numbered from 1 to N1, a kth warm area [T _k, T _k+1] with temperature range T _k+1to T _kdefinition, and T _k> T _k+1;

5) available heat in each warm area is calculated

In step 4) each temperature range of dividing, according to the first law of thermodynamics, based on fluid real temperature enthalpy relation, to calculate in each temperature range available heat with the numerical value change relation of temperature, with reference to formula (3)-formula (7):

$Q_K\left(T\right)=\underset{i\∈{\left\{\mathrm{hot}\right\}}_k}{\mathrm{\Σ}}(H_i\left(Y_k^h\right)-H_i\left(T^h\right))-\underset{j\∈{\left\{\mathrm{cold}\right\}}_k}{\mathrm{\Σ}}(H_j\left(T_k^c\right)-H_j\left(T^c\right))---\left(3\right)$

$T_k^h=T_k+{\mathrm{\ΔT}}_{\min }/2---\left(4\right)$

$T_k^c=T_k-{\mathrm{\ΔT}}_{\min }/2---\left(5\right)$

T ^h＝T+ΔT _min/2 (6)

T ^c＝T-ΔT _min/2 (7)

In formula (3)-(7), Q _k(T) be the available heat in a kth temperature range, the size of available heat changes with temperature T; Temperature T ∈ [T _k+1, T _k]; { hot} _krepresent the hot fluid collection that hot-fluid stocks all in a kth temperature range is formed; { cold} _krepresent the cold fluid collection that cold flow stocks all in a kth temperature range is formed; K=1,2,3 ..., N1; The enthalpy H of fluid is the function of temperature and flow; for hot fluid i is in temperature the enthalpy at place, temperature calculated by formula (4); H _i(T ^h) for hot fluid i is at temperature T ^hthe enthalpy at place, temperature T ^hcalculated by formula (6); for cold fluid j is in temperature the enthalpy at place, temperature calculated by formula (5); H _j(T ^c) for cold fluid j is at temperature T ^cthe enthalpy at place, temperature T ^ccalculated by formula (7);

6) turnover that whether there is direction of heat flow in each temperature range is judged

Utilize step 5) in each temperature range of obtaining available heat with the numerical value change relation of temperature, find the extreme point of each warm area available heat, extreme point refers to that available heat variation with temperature relation there occurs change, from warm area 1 to warm area N1, find out the extreme point of available heats all in each warm area respectively;

7) temperature range is repartitioned

By step 4) in the temperature end points of all original warm areas and step 6) the corresponding temperature spot of the extreme point that finds combines, by the order arrangement from high temperature to low temperature, repartition temperature range, warm area number is designated as N2, and temperature range number of endpoint is N2+1;

8) available heat of each temperature range is recalculated

In step 7) on the basis of the new temperature range divided, according to formula (3)-formula (7), recalculate the available heat in all temperature ranges;

9) the heat history flow of each warm area is calculated

In step 7) each temperature range of dividing, calculate the heat history flow that each temperature range can be delivered to next temperature range, with reference to formula (8):

$C_k=C_{k-1}+\underset{i\∈{\left\{\mathrm{hot}\right\}}_k}{\mathrm{\Σ}}(H_i\left(T_k^h\right)-H_i\left(T_{k+1}^h\right))-\underset{j\∈{\left\{\mathrm{cold}\right\}}_k}{\mathrm{\Σ}}(H_j\left(T_k^c\right)-H_j\left(T_{k+1}^c\right))---\left(8\right)$

In formula (8), C _kfor being delivered to the heat history flow of kth+1 warm area from a kth warm area; C ₀=0; K=1,2,3 ..., N2, positive and negative according to the accumulative heat flux of each temperature range, can judge the direction that the possibility of heat recovery and heat transmit, C _kfor on the occasion of, then represent that the direction of heat flow that is delivered to kth+1 warm area from temperature range k is for just, namely there is unnecessary heat and can pass to next warm area and recycled in higher temperatures district; C _kfor negative value, then expression warm area k is delivered to the direction of heat flow of kth+1 warm area is negative, and namely this warm area needs to absorb heat from the external world, and this warm area does not exist unnecessary heat and can recycle for next warm area.

Technical conceive of the present invention is: based on the actual physical property of fluid, adopt the warm enthalpy physical property relation of fluid reality, determine the distribution relation of available heat with temperature of heat exchange network inside, the impact of the size and Orientation of heat flux can be used on local warm area according to non-linear physical property, whole temperature range is divided into the sub-range of a series of heat flux with temperature monotone variation, obtains the size and Orientation of each warm area heat history flow.

The present invention utilizes the extreme point of local warm area available heat warm area to be divided into the sub-range of a series of heat flux with temperature monotone variation, can reflect the impact that nonlinear of the fluid temperature enthalpy physical property designs heat exchange network so objectively.When the specific heat capacity of fluid is definite value, in each temperature range, available heat variation with temperature increases monotonously or reduces; And under the impact of nonlinear of the fluid temperature enthalpy physical property relation, in each temperature range likely there is situation of reversing in available heat variation with temperature situation, namely there is extreme point, extreme point refers to the state point that available heat variation with temperature relation changes, available heat variation with temperature may occur first increasing and reduces or first reduce to increase two kinds of different situations again, reflects the two kind different distributions situations of size and Orientation with temperature of the heat flux of recoverable in heat exchanger network under the impact of non-thread enthalpy physical property warm in nature.Maximum point corresponds to available heat presents first increases and then decreases separation with the reduction of temperature; Minimum point corresponds to available heat and presents with the reduction of temperature the separation first reducing to increase afterwards.When there is maximum point, at the warm area higher than maximum point, there is unnecessary heat for comparatively low-temperature space recycling, can carry out the heat recovery of internal system; When there is minimum point, at the warm area higher than minimum point, need to absorb the heat demand that heat could meet this warm area from the external world, this warm area cannot provide unnecessary heat to low-temperature space, can not carry out the heat recovery and utilization of internal system.So maximum value and minimal value two kinds of situations are by bringing different available heats and accumulation heat with the distribution relation of temperature, must be distinguished and be processed separately.

Beneficial effect of the present invention is: 1, the method is based on the actual physical property of fluid, adopts the warm enthalpy physical property relation determination available heat of fluid reality with the distribution of temperature, compares classic method, can obtain reliable heat flux result of calculation; 2, the method with the impact of the size and Orientation of heat flux, whole temperature range is divided into the sub-range of a series of heat flux with temperature monotone variation, and classic method can cannot determine the non-linear impact integrated on heat according to non-linear physical property to local warm area.

Accompanying drawing explanation

Fig. 1 is local warm area available heat variation with temperature graph of a relation.

Fig. 2 is based on the heat history discharge diagram of the actual physical property of fluid from high-temperature region to low-temperature space.

Fig. 3 is based on the heat history discharge diagram of constant specific heat appearance from high-temperature region to low-temperature space.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described.

With reference to Fig. 1 ~ Fig. 3, a kind of heat exchanger network hot-fluid method for determination of amount comprising non-isothermal phase change fluid, comprises the following steps:

1) technological parameter and the physical data of fluid is extracted

Technological parameter and the physical data of logistics comprise: composition, flow, inlet temperature T _in(initial temperature), outlet temperature T _out(target temperature of specifying), enthalpy and specific heat capacity.Described method, based on the actual physical property of fluid, adopts the warm enthalpy physical property relation of fluid reality, instead of the specific heat capacity of hypothesis material is constant.

2) the minimum heat transfer temperature difference Δ T of heat exchanger network is set _min

The minimum heat transfer temperature difference Δ T of setting heat exchanger network _min.Δ T _minbeing the expulsive force of heat transfer, is the necessary condition ensureing to carry out between cold and hot fluid heat exchange.

3) cold and hot fluid temperature adjustmemt is carried out

If hot fluid will pass to cold fluid heat, in order to ensure the carrying out of conducting heat, then the temperature of hot fluid is higher than the temperature of cold fluid, and its temperature difference should be not less than step 2) the minimum heat transfer temperature difference requirement that sets.The temperature of cold and hot fluid is revised, the temperature of cold fluid is raised Δ T _min/ 2, the temperature of per share hot fluid is reduced Δ T _min/ 2, thus the temperature of temperature higher than cold fluid guaranteeing hot fluid, and meet minimum heat transfer temperature difference Δ T _minrequirement.Cold and hot fluid temperature adjustmemt is respectively with reference to formula (1)-(2):

$T_{C,j}^{*}=T_{C,j}+{\mathrm{\ΔT}}_{\min }/2---\left(1\right)$

$T_{H,i}^{*}=T_{H,i}-{\mathrm{\ΔT}}_{\min }/2---\left(2\right)$

In formula (1)-(2), Δ T _minfor step 2) the minimum heat transfer temperature difference of specifying; T _h,iand T _c,jbe respectively the actual temperature of hot-fluid stock i and cold flow stock j; T ^* _h,iand T ^* _c,jbe respectively the temperature that hot-fluid stock i and cold flow stock j carries out after temperature adjustmemt.

4) initial temperature is divided interval

With step 3) in import and export temperature after cold and hot fluid correction be foundation, divide temperature range.By all cold and hot fluid through step 3) revise after inlet temperature and outlet temperature by from high to low order arrangement, be designated as: T ₁, T ₂..., T _n1, T _n1+1, wherein N1+1 is the number of temperature end points, and the warm area number divided is N1, and warm area numbering is from 1 to N1.Such as, a kth warm area [T _k, T _k+1] with temperature range T _k+1to T _kdefinition, and T _k> T _k+1.

5) available heat in each warm area is calculated

In step 4) each temperature range of dividing, according to the first law of thermodynamics, based on fluid real temperature enthalpy relation, to calculate in each temperature range available heat with the numerical value change relation of temperature, with reference to formula (3)-formula (7):

$Q_K\left(T\right)=\underset{i\∈{\left\{\mathrm{hot}\right\}}_k}{\mathrm{\Σ}}(H_i\left(Y_k^h\right)-H_i\left(T^h\right))-\underset{j\∈{\left\{\mathrm{cold}\right\}}_k}{\mathrm{\Σ}}(H_j\left(T_k^c\right)-H_j\left(T^c\right))---\left(3\right)$

$T_k^h=T_k+{\mathrm{\ΔT}}_{\min }/2---\left(4\right)$

$T_k^c=T_k-{\mathrm{\ΔT}}_{\min }/2---\left(5\right)$

T ^h＝T+ΔT _min/2 (6)

T ^c＝T-ΔT _min/2 (7)

In formula (3)-(7), Q _k(T) be the available heat in a kth temperature range, the size of available heat changes with temperature T; Temperature T ∈ [T _k+1, T _k]; { hot} _krepresent the hot fluid collection that hot-fluid stocks all in a kth temperature range is formed; { cold} _krepresent the cold fluid collection that cold flow stocks all in a kth temperature range is formed; K=1,2,3 ..., N1; The enthalpy H of fluid is the function of temperature and flow; for hot fluid i is in temperature the enthalpy at place, temperature calculated by formula (4); H _i(T ^h) for hot fluid i is at temperature T ^hthe enthalpy at place, temperature T ^hcalculated by formula (6); for cold fluid j is in temperature the enthalpy at place, temperature calculated by formula (5); H _j(T ^c) for cold fluid j is at temperature T ^cthe enthalpy at place, temperature T ^ccalculated by formula (7).

In each temperature range, available heat variation with temperature situation reflects the size of the heat flux of recoverable in heat exchanger network, direction and the distribution situation with temperature thereof.

6) turnover that whether there is direction of heat flow in each temperature range is judged

Utilizing step 5) available heat, with the numerical value change relation of temperature, finds the extreme point of each warm area available heat in each temperature range of obtaining.Extreme point refers to the turning point that available heat variation with temperature relation changes.From warm area 1 to warm area N1, find out the extreme point of available heats all in each warm area respectively.

7) temperature range is repartitioned

By step 4) in the temperature end points of all original warm areas and step 6) the corresponding temperature spot of the extreme point that finds combines, by the order arrangement from high temperature to low temperature, repartition temperature range, warm area number is designated as N2, temperature range number of endpoint is N2+1, and the number of temperature range is now with step 4) original warm area compare and may increase to some extent.If but step 6) do not find any extreme point, then warm area number remains unchanged.

8) available heat of each temperature range is recalculated

In step 7) on the basis of the new temperature range divided, according to formula (3)-formula (7), recalculate the available heat in all temperature ranges.

9) the heat history flow of each warm area is calculated

In step 7) each temperature range of dividing, calculate the heat history flow that each temperature range can be delivered to next temperature range, with reference to formula (8):

$C_k=C_{k-1}+\underset{i\∈{\left\{\mathrm{hot}\right\}}_k}{\mathrm{\Σ}}(H_i\left(T_k^h\right)-H_i\left(T_{k+1}^h\right))-\underset{j\∈{\left\{\mathrm{cold}\right\}}_k}{\mathrm{\Σ}}(H_j\left(T_k^c\right)-H_j\left(T_{k+1}^c\right))---\left(8\right)$

In formula (8), C _kfor being delivered to the heat history flow of kth+1 warm area from a kth warm area; C ₀=0; K=1,2,3 ..., N2.Positive and negative according to the accumulative heat flux of each temperature range, can judge the direction that the possibility of heat recovery and heat transmit.C _kfor on the occasion of, then represent that the direction of heat flow that is delivered to kth+1 warm area from temperature range k is for just, namely there is unnecessary heat and can pass to next warm area and recycled in higher temperatures district; C _kfor negative value, then expression warm area k is delivered to the direction of heat flow of kth+1 warm area is negative, and namely this warm area needs to absorb heat from the external world, and this warm area does not exist unnecessary heat and can recycle for next warm area.

In the present embodiment, concrete steps are as follows:

The first step, extract flow data.The logistics data that the present embodiment adopts, as shown in table 1.

Second step, arranges the minimum heat transfer temperature difference Δ T of heat exchanger network _min.In present case, take ther mal network minimum heat transfer temperature difference Δ T _min=10 DEG C.

3rd step, carries out cold and hot fluid temperature adjustmemt.According to minimum heat transfer temperature difference Δ T _minrequirement, revise with reference to formula (1)-(2) temperature to cold and hot fluid, correction result is in table 2.

4th step, divides initial temperature interval.According to step 3) in import and export temperature after cold and hot fluid correction, 5 temperature ranges are divided into: 165 DEG C of-145 DEG C of warm areas, 145 DEG C of-140 DEG C of warm areas, 140 DEG C of-85 DEG C of warm areas by the order from high temperature to low temperature, 85 DEG C of-55 DEG C of warm areas, 55 DEG C of-25 DEG C of warm areas.

5th step, calculates the available heat in each warm area.To step 4) each temperature range of dividing, based on fluid real temperature enthalpy relation, with reference to formula (3)-formula (7), to calculate in each temperature range available heat with the numerical value change relation of temperature.For 140 DEG C of-85 DEG C of warm areas, Fig. 1 gives 140 DEG C-85 DEG C warm area available heat variation with temperature graphs of a relation.

6th step, judges the turnover that whether there is direction of heat flow in each temperature range.In the present embodiment, 140 DEG C of-85 DEG C of warm areas and 55 DEG C of-25 DEG C of warm areas, the hot-fluid of these two warm areas receives the impact of non-linear fluid, has occurred the extreme point of available heat respectively, and the temperature that these 2 extreme points are corresponding is respectively 126.1 DEG C and 27.79 DEG C.For 140 DEG C of-85 DEG C of warm areas, Fig. 1 gives 140 DEG C-85 DEG C warm area available heat variation with temperature graphs of a relation, and within the scope of 140 DEG C-126.1 DEG C, available heat increases gradually with the decline of temperature; And within the scope of 126.1 DEG C-85 DEG C, available heat reduces gradually with the decline of temperature; 126.1 DEG C be extreme point.

7th step, repartitions temperature range.By step 4) in the temperature end points of all original warm areas and step 6) the corresponding temperature spot of the extreme point that finds combines, 7 temperature ranges are reclassified as: 165 DEG C of-145 DEG C of warm areas by the order from high temperature to low temperature, 145 DEG C of-140 DEG C of warm areas, 140 DEG C of-126.1 DEG C of warm areas, 126.1 DEG C of-85 DEG C of warm areas, 85 DEG C of-55 DEG C of warm areas, 55 DEG C of-27.79 DEG C of warm areas, 27.79 DEG C of-25 DEG C of warm areas.

8th step, recalculates the available heat of each temperature range.In step 7) on the basis of the new temperature range divided, according to formula (3)-formula (7), recalculate the available heat in all temperature ranges, result of calculation is as shown in table 3.

9th step, calculates the heat history flow of each warm area.In step 7) each temperature range of dividing, with reference to formula (8), calculate the heat history flow that each temperature range can be delivered to next temperature range, result of calculation is as shown in table 3.Fig. 2 gives based on the heat history discharge diagram of the actual physical property of fluid from high-temperature region to low-temperature space.

Table 1

Table 2

Table 3

Tradition folder point method supposes that the specific heat capacity of all fluids is constant, and as a comparison, Fig. 3 gives the distribution situation of the heat history flow from high-temperature region to low-temperature space adopting classic method to obtain.In the computation process of classic method, owing to not considering the change effect of the non-thread of fluid enthalpy relation warm in nature to the available heat in the temperature range of local and heat history flow, have estimated the heat flux of heat exchanger network mistakenly.

Above-described embodiment is used for explaining and the present invention is described, instead of limits the invention, and in the protection domain of spirit of the present invention and claim, any amendment make the present invention and change, all fall into protection scope of the present invention.

Claims (1)

1. comprise a heat exchanger network hot-fluid method for determination of amount for non-isothermal phase change fluid, it is characterized in that: said method comprising the steps of:

1) technological parameter and the physical data of fluid is extracted

Technological parameter and the physical data of logistics comprise: composition, flow, inlet temperature T _in, outlet temperature T _out, enthalpy and specific heat capacity, adopt the warm enthalpy physical property relation of fluid reality;

2) the minimum heat transfer temperature difference Δ T of heat exchanger network is set _min

3) cold and hot fluid temperature adjustmemt is carried out

The temperature of cold fluid is raised Δ T _min/ 2, the temperature of per share hot fluid is reduced Δ T _min/ 2, thus the temperature of temperature higher than cold fluid guaranteeing hot fluid, and meet minimum heat transfer temperature difference Δ T _minrequirement, cold and hot fluid temperature adjustmemt is respectively with reference to formula (1)-(2):

$T_{C,j}^{*}=T_{C,j}+\mathrm{\Δ}{T}_{\min }/2---\left(1\right)$

$T_{H,i}^{*}=T_{H,i}-\mathrm{\Δ}{T}_{\min }/2---\left(2\right)$

In formula (1)-(2), Δ T _minfor step 2) the minimum heat transfer temperature difference of specifying; T _h,iand T _c,jbe respectively the actual temperature of hot-fluid stock i and cold flow stock j; T ^* _h,iand T ^* _c,jbe respectively the temperature that hot-fluid stock i and cold flow stock j carries out after temperature adjustmemt;

4) initial temperature is divided interval

With step 3) in import and export temperature after cold and hot fluid correction be foundation, divide temperature range, by all cold and hot fluid through step 3) revise after inlet temperature and outlet temperature by order arrangement from high to low, be designated as: T ₁, T ₂..., T _n1, T _n1+1, wherein N1+1 is the number of temperature end points, and the warm area number divided is N1, and warm area is numbered from 1 to N1, a kth warm area [T _k, T _k+1] with temperature range T _k+1to T _kdefinition, and T _k> T _k+1;

5) available heat in each warm area is calculated

In step 4) each temperature range of dividing, according to the first law of thermodynamics, based on fluid real temperature enthalpy relation, to calculate in each temperature range available heat with the numerical value change relation of temperature, with reference to formula (3)-formula (7):

$Q_k\left(T\right)=\underset{i\∈{\left\{\mathrm{hot}\right\}}_k}{\mathrm{\Σ}}(H_i\left(T_k^h\right)-H_i\left(T^h\right))-\underset{j\∈{\left\{\mathrm{cold}\right\}}_k}{\mathrm{\Σ}}(H_j\left(T_k^c\right)-H_j\left(T^c\right))---\left(3\right)$

$T_k^h=T_k+\mathrm{\Δ}{T}_{\min }/2---\left(4\right)$

$T_k^c=T_k-\mathrm{\Δ}{T}_{\min }/2---\left(5\right)$

T ^h＝T+ΔT _min/2 (6)

T ^c＝T-ΔT _min/2 (7)

In formula (3)-(7), Q _k(T) be the available heat in a kth temperature range, the size of available heat changes with temperature T; Temperature T ∈ [T _k+1, T _k]; { hot} _krepresent the hot fluid collection that hot-fluid stocks all in a kth temperature range is formed; { cold} _krepresent the cold fluid collection that cold flow stocks all in a kth temperature range is formed; K=1,2,3 ..., N1; The enthalpy H of fluid is the function of temperature and flow; for hot fluid i is in temperature the enthalpy at place, temperature calculated by formula (4); H _i(T ^h) for hot fluid i is at temperature T ^hthe enthalpy at place, temperature T ^hcalculated by formula (6); for cold fluid j is in temperature the enthalpy at place, temperature calculated by formula (5); H _j(T ^c) for cold fluid j is at temperature T ^cthe enthalpy at place, temperature T ^ccalculated by formula (7);

6) turnover that whether there is direction of heat flow in each temperature range is judged

Utilize step 5) in each temperature range of obtaining available heat with the numerical value change relation of temperature, find the extreme point of each warm area available heat, extreme point refers to that available heat variation with temperature relation there occurs change, from warm area 1 to warm area N1, find out the extreme point of available heats all in each warm area respectively;

7) temperature range is repartitioned

By step 4) in the temperature end points of all original warm areas and step 6) the corresponding temperature spot of the extreme point that finds combines, by the order arrangement from high temperature to low temperature, repartition temperature range, warm area number is designated as N2, and temperature range number of endpoint is N2+1;

8) available heat of each temperature range is recalculated

In step 7) on the basis of the new temperature range divided, according to formula (3)-formula (7), recalculate the available heat in all temperature ranges;

9) the heat history flow of each warm area is calculated

In step 7) each temperature range of dividing, calculate the heat history flow that each temperature range can be delivered to next temperature range, with reference to formula (8):

$C_k=C_{k-1}+\underset{i\∈{\left\{\mathrm{hot}\right\}}_k}{\mathrm{\Σ}}(H_i\left(T_k^h\right)-H_i\left(T_{k+1}^h\right))-\underset{j\∈{\left\{\mathrm{cold}\right\}}_k}{\mathrm{\Σ}}(H_j\left(T_k^c\right)-H_j\left(T_{k+1}^c\right))---\left(8\right)$

In formula (8), C _kfor being delivered to the heat history flow of kth+1 warm area from a kth warm area; C ₀=0; K=1,2,3 ..., N2, positive and negative according to the accumulative heat flux of each temperature range, can judge the direction that the possibility of heat recovery and heat transmit, C _kfor on the occasion of, then represent that the direction of heat flow that is delivered to kth+1 warm area from temperature range k is for just, namely there is unnecessary heat and can pass to next warm area and recycled in higher temperatures district; C _kfor negative value, then expression warm area k is delivered to the direction of heat flow of kth+1 warm area is negative, and namely this warm area needs to absorb heat from the external world, and this warm area does not exist unnecessary heat and can recycle for next warm area.