TECHNICAL FIELD
The subject matter described herein, in general, relates to transportation of fluids and in particular, relates to determining feasibility of transporting fluids through a pipeline.
BACKGROUND
Generally, pipeline transportation systems are used to transport fluids from one location to another. These fluids may include crude oils, hydrocarbon mixtures, furnace oils, residue oils, etc. The fluids are transported via pipelines, for example, from various extraction sites to refineries, and from the refineries to consumption centers. The transportation of these fluids through pipelines is influenced by flow behaviour of the fluid.
The flow behavior of these fluids inside a pipeline is dependent on various parameters, such as nature of the fluid, nature of its flow, pressure variation across the pipeline, pour point of the fluid, heat dissipation through pipeline walls, and various other rheological and environmental parameters.
One of the parameters that particularly influences the flow behaviour of such a fluid flowing through a pipeline is the pour point of the fluid. By definition, pour point of a fluid, particularly oils, is the lowest temperature at which the fluid can flow, and it influences fluid parameters as well. For example, when a fluid having Newtonian properties attains a temperature lower than its pour point, the rheological parameters of the fluid, such as viscosity, yield stress, and consistency, are affected non-linearly, and as a result, the fluid may exhibit non-Newtonian properties. These variations in the fluid parameters affect the flow behaviour of the fluid, and may have a detrimental effect on the transport of the fluid.
To design a pipeline transportation system, certain fluid profiles, such as temperature drop profile, are predicted by simulation methods. However, erroneous predictions of the fluid profiles may adversely affect the pipeline transportation system because during transportation, the fluid may exhibit flow properties different from those for which the pipeline transportation system is designed. Moreover, the variations in the flow behaviour during transportation may lead to pump failures and damages to the pipeline. Further, solidification of wax in these fluids may occur during their transportation, and the solidified wax may deposit on the pipeline walls. Owing to the deposition of the solidified wax, the pipelines may require cleaning at regular intervals of time, thus adding to the overall maintenance cost of the pipeline.
SUMMARY
The subject matter described herein is directed to methods and devices to determine feasibility
of transporting a fluid through a pipeline.

In an implementation, a final end temperature of the fluid at an exit of at least one segment of a pipeline is computed based on received fluid parameters and on a computation of heat generated due to friction. The feasibility of transporting the fluid through the pipeline is then determined based at least on the final end temperature. A feasibility parameter can be adjusted based on the feasibility of transporting the fluid to make transportation of the fluid feasible.
The described methods and devices provide for a realistic estimation of the temperature and pressure profiles of the fluid based on the heat generated due to friction. Further, it facilitates in determination of an optimum composition of a fluid that can be transported to the desired destination through a buried pipeline system, without causing damage to the pipeline or to pumps used in the pipeline system.
These and other features, aspects, and advantages of the present subject matter will be better understood with reference to the following description and appended claims. This summary is provided to introduce a selection of concepts in a simplified form. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter.
BRIEF DESCRIPTION OF DRAWINGS
The above and other features, aspects, and advantages of the subject matter will be better understood with regard to the following description, appended claims, and accompanying drawings where:
Fig. 1 illustrates an exemplary device for determining feasibility of transporting a fluid through a pipeline, according to an embodiment of the present subject matter.
Fig. 2(a) illustrates an exemplary method for determining feasibility of transporting the fluid through the pipeline, according to an implementation of the present subject matter.
Fig 2(b) an exemplary method for determining temperature and pressure profiles of a fluid flowing though a pipeline, according to one implementation of the present subject matter.
Fig 3(a) illustrates an exemplary curve showing temperature profile of a fluid over a length of the pipeline, according to an implementation of the present subject matter.
Fig 3(b) illustrates an exemplary curve showing pressure profile of a fluid over a length of the pipeline, according to an implementation of the present subject matter.
DETAILED DESCRIPTION
Device(s) and method(s) for determining feasibility of transporting a fluid through a pipeline, for example, a buried pipeline, are described. According to an implementation, a sample of the fluid

is tested in a laboratory to assess its fluid parameters. The fluid parameters may include, for example, thermal conductivity Kf, specific heat Cf , temperature of the fluid at the source, and rheological parameters, such as viscosity, density, yield stress, and consistency. In said implementation, the fluid is tested for its rheological parameters under various conditions, such as different operating temperatures and shear rates.
Upon determining the fluid parameters, a flow analysis of the fluid is carried out by simulating environmental and pipeline conditions. According to an aspect of the present subject matter, the pipeline is considered as being composed of a plurality of segments. Based on the flow analysis, temperature and pressure profiles of the fluid for each segment of the pipeline are determined. In an implementation, the temperature and pressure profiles of the fluid are determined based on parameters including, but not limited to, characteristics of the pipeline material, wall temperature of the pipeline wall, seasonal variations in ambient temperature, burial depth of the pipeline, soil thermal properties, and variation of the rheological parameters of the fluid with temperature. Further, the temperature and pressure profiles of the fluid are determined by taking into account the effect of heat generated in the fluid due to friction. During the transport of a fluid, such as crude oils, hydrocarbon mixtures, furnace oils, and residue oils, a significant amount of pumping power is lost due to the heat generated in the fluid due to friction. Further, the heat generated in the fluid also influences heat transfer properties of the fluid. Hence, the described method facilitates an accurate and a realistic estimation of the temperature and pressure profiles of the fluid.
The temperature and pressure profiles assist in analyzing the effect of the above mentioned parameters on the pumpability of the fluid and, in turn, the feasibility of transporting the fluid through the pipeline. According to an implementation, the feasibility of transporting the fluid is determined based on a temperature of the fluid calculated at the exit of the pipeline. In another implementation, the feasibility of transporting the fluid is determined based on the calculated temperature of the fluid at an exit of each segment of the pipeline. For example, if the temperature of the fluid, as calculated in either of the implementations, is below the pour point and a wax appearance temperature of the fluid, the transportation of the fluid through the pipeline will not be feasible.
Further, pressure drop of the fluid across a segment of the pipeline may be used to determine a required pumping power to pump the fluid through the segment of the pipeline. Such a determination may also be used for assessing the feasibility of transport of the fluid through the pipeline by, for example, comparing the required pumping power with an available pumping power. The pressure drop may also be used to assess, for example, the distance between two pumping

stations and the pumping power required from each of the pumping stations for the transportation of the fluid.
According to an aspect of the present subject matter, the described device and method may also be used in predicting the feasibility of transporting different compositions of the fluid through a pipeline. Subsequently, such a prediction may be used to achieve an optimum composition of the fluid that can be transported through the pipeline. The method may be used to determine the amount of additives, such as diluents and pour point depressants, to be added to the fluid, such that the transportation of the resulting composition is feasible. Further, the described method and device for determining the feasibility of transporting the fluid through the pipeline prevents pumps from damages incurred due to solidified wax in the fluid during transportation of the fluid, and also reduces the maintenance costs of the pipelines, which is mainly incurred due to the frequent cleaning of the pipelines to remove wax depositions.
Fig. 1 illustrates an exemplary device 100 for determining the feasibility of transporting a fluid through a pipeline, according to an embodiment. The fluid may include crude oil, hydrocarbon mixture, furnace oil, residue oil, etc. The device 100 can be used to determine temperature and pressure profiles of the fluid along a length of the pipeline to determine the feasibility of transport of the fluid through the pipeline.
The temperature and pressure profiles are based on various fluid parameters, for example, rheological parameters, such as density ρ, viscosity µ, yield stress τ, consistency ck, and non-Newtonian character index n, and the variation of these rheological parameters with temperature, thermal conductivity Kf, and specific heat Cf. In an implementation, the various rheological parameters of the fluid and their variation with temperature are experimentally determined by testing a sample of the fluid under laboratory conditions using, for example, a rheometer.
The device 100 may also use parameters associated with the pipeline, including but not limited to, burial depth of the pipeline, soil temperatures Ts, and other thermal and physical properties of the soil, to determine the temperature and pressure profiles of the fluid to be transported through the pipeline.
The device 100 can be a variety of devices such as desktop computers, hand-held devices, multiprocessor systems, microprocessor based programmable consumer electronics, laptops, network computers, minicomputers, and mainframe computers. The device 100 includes processor(s) 102, memory 104 and interface(s) 106. The processor(s) 102 may be implemented as one or more microprocessors, microcomputers, microcontrollers, digital signal processors, central processing units, state machines, logic circuitries, and/or any devices that manipulate signals based on

operational instructions. Among other capabilities, the processor(s) 102 are configured to fetch and execute computer-readable instructions stored in the memory 104. The interface(s) 106 provide connectivity of the device 100 to a wide variety of networks and protocol types, including wire networks, such as LAN, cable, and wireless networks, for example, WLAN, cellular, satellite, etc.
The interface(s) 106 enable an interface between a user and the device 100 to facilitate exchange of data with the device 100. According to an aspect of the present subject matter, the device 100 receives data in the form of instructions or values of various parameters, such as thermal conductivities of the fluid Kf and the pipeline Kp and the burial depth of the pipeline, to simulate the transportation of the fluid through the pipeline. The interface(s) 106 may include, for example, a scanner port, a mouse port, a keyboard port, and a display port.
The memory 104 may include any computer-readable medium known in the art including, for example, volatile memory, such as static random access memory (SRAM) and dynamic random access memory (DRAM), and non-volatile memory, such as erasable program read only memory (EPROM) and flash memory. In an embodiment, the memory 104 includes module(s) 108 and data 110.
In an embodiment, the module(s) 108 includes a transport simulation module 112, a feasibility module 114, and other module(s) 116. In an implementation, the transport simulation module 112 may logically divide the length of the pipeline into a plurality of segments and calculate flow parameters of the fluid for each of the segments to determine temperature and pressure profiles of the fluid. The feasibility module 114 determines the feasibility of transporting the fluid through the pipeline. The other module(s) 116 may include programs or coded instructions, which supplement applications or functions performed by the computing device 100.
Further, the data 110 may include parameter data 118 and other data 120. The parameter data 118 may include pipeline segment parameters and fluid parameters. The pipeline segment parameters may include, for example, burial depth Z of a segment of the pipeline, thermal conductivity of the pipeline Kp, elevation head of the segment, inner diameter D of the pipeline, thermal conductivity of the soil Ks, roughness k of the segment, temperature of the soil Ts surrounding the segment, thickness t of the pipeline, and length L of the segment. It will be understood that the inner diameter D of the pipeline and the thickness t of the pipeline can be approximated to be the same for all the segments of the pipeline. According to an aspect of the present subject matter, the soil temperature Ts for a segment is the temperature of the surrounding soil determined at a midpoint of the segment.

The fluid parameters may include, for example, thermal conductivity of the fluid Kf, specific heat Cf of the fluid, temperature of the fluid at a source, and the rheological parameters, such as viscosity µ, density ρ, yield stress τ, consistency ck, and non-Newtonian character index n.
The parameter data 118 may also include data providing information about the variation of the various rheological parameters of the fluid with temperature. Further, the parameter data 118 may be pre-stored or may be input by a user during run-time using the interface 106. The other data 120 may include data generated as a result of the execution of one or more modules in the module(s) 108.
In operation, the transport simulation module 112 determines the transport of the fluid through the various segments of the pipeline as well as determines the temperature and pressure profiles of the fluid across those segments. In one implementation, for determining the temperature and pressure profiles, the transport simulation module 112 uses values of various pipeline segment parameters and fluid parameters from the parameter data 118. Further, the transport simulation module 112 may receive the values of various parameters from a user via the interface 106 during run-time. In one implementation, the transport simulation module 112 may store these values in the parameter data 118. In another implementation, the transport simulation module 112 may use pre-stored values of the pipeline segment parameters, such as burial depth Z, soil temperature Ts, and the thermal conductivity of the pipeline Kp, and the fluid parameters in the parameter data 118.
The transport simulation module 112 uses the various fluid parameters and pipeline segment parameters from the parameter data 118 to determine flow parameters of the fluid. The flow parameters are used determine the transport of the fluid through the pipeline. The flow parameters may include flow rate Q of the fluid through the pipeline, fanning friction factor f, heat transfer coefficients of the fluid Hf, the segment Hp and the soil Hs, etc. In an implementation, the flow parameters, such as flow rate Q, may be pre-stored in the parameter data 118.
The determination of the temperature and pressure profiles by the transport determination module 112 can be used to assess the effect of the fluid parameters and the pipeline segment parameters on the pumpability of the fluid to be pumped through the pipeline. In an implementation, the feasibility module 114 uses the determined temperature and pressure profiles to determine the pumpability of the fluid and, in turn, the feasibility of transporting the fluid through the pipeline.
The determination and analysis is performed by the transport simulation module 112 and the feasibility module 114, respectively, both being explained further in detail using standard fluid flow and heat transfer equations for steady state flow of Newtonian fluids, as an example. However, flow analysis for other fluids, such as non-Newtonian fluids, may also be obtained in a similar manner by using an appropriate model and equations for rheological evaluation of the fluids under consideration.

For theoretical purposes, it may be assumed that the heat transferred in a radial direction is not fully controlled by an insulation material of the pipeline. In addition, the values of burial depth Z of a segment, elevation head, and thermal properties, such as thermal conductivities of the fluid Kf, the soil Ks, and the pipeline Kp, are assumed to be constant.
In an implementation, a temperature of the fluid is estimated at an exit of a segment of the pipeline, and is hereinafter referred to as end temperature Te. Further, the various fluid parameters, such as viscosity µ, density ρ, yield stress τ, specific heat Cf and thermal conductivity Kf, are calculated at the end temperature Te. These fluid parameters are used to calculate flow parameters of the fluid, which are further used to calculate a computed temperature Tc at the exit of the segment. The computed temperature Tc and the end temperature Te estimated at the exit of the segment are compared for convergence.
When the computed temperature Tc and the end temperature Te converge, the converged computed temperature Tc is referred to as the final end temperature Tf at the exit of the segment. However, when the computed temperature Tc and the end temperature Te at the exit of the segment do not converge, then the end temperature Te at the exit of the segment is re-estimated using various methods. For example, the end temperature Te may be re-estimated by calculating a mean of the computed temperature Tc and the end temperature Te from the previous iteration. Further, the flow parameters and subsequently, computed temperature Tc is calculated based on the re-estimated end temperature Te, and the computed temperature Tc is again compared to the re-estimated end temperature Te for convergence. The re-estimation of the end temperature Te and the calculation of the computed temperature Tc is repeated until the computed temperature Tc converges to an end temperature Te. It will be understood that other iterative methods of regression and convergence analysis may also be used for the purpose of calculating the final end temperature Tf at an exit of a segment.
In one implementation, an end temperature TeI at an exit of an ith segment can be estimated using the following relation:
(Equation Removed)
where the end temperature Tfj.i is the final end temperature determined for the previous segment, i.e.,
at (i-l)th segment of the pipeline, and N is the number of iterations to be performed for checking the
convergence of the computed temperature Tc to the end temperature Te for the segment. Further, in
said implementation, the final end temperature Tfj.i and the soil temperature Ts are measured in
degrees centigrade (°C). However, other units of temperature measurement such as Fahrenheit or
Kelvin may be used. Similarly, though the following description uses SI units of measurement for

illustrative purposes, it will be understood that other systems and units of measurements may also be used.
After the estimation of the end temperature Te at an exit of a segment, the fluid parameters, such as viscosity µ, density ρ, yield stress τ, are determined at the end temperature Te. In an implementation, these fluid parameters are computed at the end temperature Te using the data stored in parameter data 118. For example, the value of a rheological parameter may be computed by interpolating between the values of the rheological parameter obtained in the laboratory testing. Based on these fluid parameters, the flow parameters of the fluid are calculated. For example, the nature of flow of the fluid through the segment is determined. In one implementation, such a determination may be made from the value of Reynolds number Re for the fluid, for example, a value of Reynolds number Re below 2000 depicts that the flow is laminar, whereas a value of Reynolds number Re above 4000 depicts that the flow of the fluid is turbulent. The Reynolds number Re may be determined using the following relation:
(Equation Removed)
where the inner diameter D of the segment is measured in metres (m), the velocity v of fluid through the segment is measured in metres per second (m/sec), the density p of the fluid is measured in kilogram per cubic metre (kg/m3), and the viscosity n of the fluid is measured in Pascal seconds (Pa.sec) at the end temperature Te. The velocity v of the fluid, used in the above relation, may be determined by using the following relation:
(Equation Removed)
where the estimated flow rate Q of the fluid through the pipeline, is measured in kilolitres per hour (kL/hr).
Alternatively, the velocity v of the fluid may be determined using the following relation:
(Equation Removed)
where m is the mass flow rate of the fluid measured in kilogram per second (kg/sec).
According to an aspect of the present subject matter, once the nature of flow is established, the value of a friction factor f may be computed. The relation for computing the friction factor f may vary according to the nature of flow of the fluid. For example, the friction factor f for a fluid exhibiting laminar flow may be calculated using the Hagen-Poiseuille's equation:

(Equation Removed)
Further, the friction factor f for the fluid, when the flow is turbulent and the inner surface of the pipe is smooth, may be calculated using the Blassius equation, which is given by:
(Equation Removed)
Similarly, when the flow is turbulent and the surface of the pipe is rough, then the friction factor f may be calculated from the Colebrook and White equation, which is given by:
(Equation Removed)
where the roughness k of the pipe is measured in metres (m).
Furthermore, in an implementation, an overall heat transfer coefficient U is computed for a particular segment. The overall heat transfer coefficient U may be computed from a heat transfer coefficient of the fluid Hf, a heat transfer coefficient of the segment Hp, and a heat transfer coefficient of the soil Hs surrounding the segment. Further, for computing the heat transfer coefficients of the fluid Hf, the segment Hp and the soil Hs, Nusselt number Nu, Prandtl number Pr, and Hedstrom number He for the fluid are evaluated. For laminar flow, the Nusselt number Nu may be given by the following relation:
(Equation Removed)
In the above relation, C is represented as:
(Equation Removed)
The Hedstrom number He may be computed from the below mentioned equation:
(Equation Removed)
where the yield stress T for the fluid is measured in Pascals (Pa). Further, for turbulent flow, the Nusselt number Nu may be computed from the relation:
(Equation Removed)
In the above relation, a and b are coefficients and may be calculated as follows:
(Equation Removed)

Likewise. Prandtl number Pr may be computed from the following relation:
(Equation Removed)
where the specific heat Cf of the fluid is measured in Joules per kilogram per Kelvin (J/kg.K) The heat transfer coefficient of the fluid Hf may be determined from the relation:
(Equation Removed)
Further, the heat transfer coefficient of the segment Hp may be determined from the following relation:
(Equation Removed)
The heat transfer coefficient of the soil Hs surrounding the segment may be determined using the following relation:
(Equation Removed)
In the above relation, argument Arg is computed from the following relation:
(Equation Removed)
where the term Zbar is computed using the relation:
(Equation Removed)
As mentioned previously, the heat transfer coefficients of the fluid Hf, the segment Hp, and the soil Hs may be used to compute the overall heat transfer coefficient U, which is given by the following relation:
(Equation Removed)
In an implementation, the effect of fouling may also be considered and a fouling factor f may be included in the computation of the overall heat transfer coefficient U. The overall heat transfer coefficient U may then be calculated by modifying relation (20) to include the fouling factor f. The relation may be given by:

(Equation Removed)
In an implementation, the overall heat transfer coefficient U can be used to determine the heat transfer characteristics of the fluid and pipeline system for the segment under consideration.
For example, the overall heat transfer coefficient may be used to calculate number of transfer units NTU for the segment. The number of transfer units NTU may be obtained from the following relation:
(Equation Removed)
Further, a pressure drop ∆p in the segment of the pipeline, for the purpose of determining the pressure profile of the fluid, can be obtained using the relation:
(Equation Removed)
The pressure drop ∆p in the segment can be used to determine viscous heating Ø in the segment of the pipeline due to friction between the fluid and the walls of the segment of the pipeline. The viscous heating Ø is a measure of a loss in pumping power P in heating of the fluid due to viscosity between the layers of the fluid, i.e., loss in pumping power P due to frictional heating in the fluid. The viscous heating Ø also influences the temperature drop over the segment and over the whole length of the pipeline. The viscous heating in the segment can be calculated using the following relation:
(Equation Removed)
where the viscous heating Ø is measured in Watt (W).
In one implementation, the computed temperature Tc of the fluid is calculated based on an entrance temperature Te„t of the fluid at an entrance of the segment of the pipeline. In said implementation, the entrance temperature Tent of the fluid at the entrance of a first segment of the pipeline may be the temperature of the fluid at the source. Further, it may be understood that the entrance temperature Tent of the fluid for one segment is the final end temperature Tf at the exit of the previous segment.
In an implementation, the computed temperature Tc may be computed based on the heat
generated due to friction. The heat generated in the fluid due to friction influences the heat transfer
properties of the fluid, and has a significant effect on the final end temperature Tf of the fluid at the

exit of the segment. Hence, the described method facilitates a realistic determination of the temperature and pressure profiles of the fluid.
A heat generation coefficient qr may be used to represent the heat generated due to friction. The heat generation coefficient qf may be determined from the following relation:
(Equation Removed)
When the heat generated due to friction is large, for example, when a value of the heat generation coefficient qf is greater than 0.1, then the heat balance equation is given by the following relation:
(Equation Removed)
In the above equation, the following assumptions are considered:
(Equation Removed)
Based on the heat balance equation, the computed temperature Tc is obtained from the following relation:
(Equation Removed)
Further, when the heat generated due to friction is small, for example, when the value of the heat generation coefficient qf is less than 0.1, then the heat balance equation is given by:
(Equation Removed)
where(Equation Removed)

On substituting the value of d0 from the above equation into the heat balance equation, the following heat balance equation is achieved:
(Equation Removed)
The computed temperature Tc is calculated based on the heat balance equation, and is obtained from the following relation:
(Equation Removed)
where, effective number of transfer units NTUeff are obtained from the following relation:
(Equation Removed)
As mentioned previously, the computed temperature Tc of the fluid at the exit of the segment is checked for convergence towards the previously estimated end temperature Te at the exit of the

segment. When the computed temperature Tc and the end temperature Te converge, the computed temperature Tc is selected as the final end temperature Tf at the exit of the segment. The final end temperature Tf of the fluid may be used to compute a wall temperature Tw of the segment of the pipeline. For computing the wall temperature Tw of the segment of the pipeline a relation such as the following relation may be used:
(Equation Removed)
The wall temperature Tw may be used for determining actual viscosity characteristics of the fluid, and for manipulating heat transfer properties of the pipeline material. For example, a layer of insulating material may be provided around a segment of the pipeline based on the wall temperature Tw of the segment. The wall temperature Tw may also be used to assess the possibility of freezing the water in the soil around the segment.
Further, pumping power P required for the segment can be computed based on the viscous heating 0, which results in a pressure drop Ap, in the segment and the pumping power P required for
the previous segment. For example, the pumping power P; for the ith segment can be obtained from an expression such as the following expression:
(Equation Removed)
where the pumping power Pj for the ith segment and the pumping power PM for the (i-1)th segment is measured in Watts (W). It will be understood that the pumping power P for a segment can be calculated using various relations known to a person skilled in the art.
To achieve the flow simulation for the pipeline, the transport simulation module 112 performs the flow analysis for each segment of the pipeline. Based on the flow analysis, the transport simulation module 112 determines the temperature and pressure profiles of the fluid along the length of the pipeline.
The feasibility module 114 may use the temperature and pressure profiles of the fluid to determine the feasibility of transporting the fluid through the pipeline. In an implementation, the feasibility of transporting the fluid is determined by comparing the final end temperature Tfexit of the fluid at the exit of the last segment of the pipeline to the pour point and a wax appearance temperature of the fluid. In another implementation, the feasibility module 114 may determine the feasibility by comparing the final end temperature Tf at the exit of each segment with the pour point temperature or the wax temperature or both. The feasibility module 114 may also use the pressure

drop ∆p in each segment of the pipeline to determine the feasibility of transporting the fluid through the pipeline.
The temperature and pressure drop profiles of a fluid may be used to adjust a feasibility parameter, such as a composition of the fluid, the pumping power P and a length at which a heating unit may be disposed to heat the fluid during transportation, thereby ensuring that the temperature of the fluid does not drop below its pour point. The temperature and pressure profiles may, hence, be used to design the pipelines for transporting the fluid and similar fluids. For example, the temperature and pressure drop profiles of the fluid may be used to determine and identify one or more sites along the length of the pipeline at which pump stations and heating units may be provided.
Although the flow analysis done by the transport simulation module 112 is explained using the afore mentioned relations. However, one may use other equations for computing the flow parameters. Additionally or alternately, these equations may be selected according to the preferences of a user, the characteristics of the fluid, etc.
Fig. 2(a) and Fig. 2(b) illustrate an exemplary method for determining the feasibility of transporting a fluid through a pipeline, in accordance with an implementation of the present subject matter.
The exemplary methods may be described in the general context of computer executable instructions embodied on a computer-readable medium. Generally, computer executable instructions can include routines, programs, objects, components, data structures, procedures, modules, functions, etc., that perform particular functions or implement particular abstract data types. The methods may also be practiced in a distributed computing environment where functions are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, computer executable instructions may be located in both local and remote computer storage media, including memory storage devices.
The order in which the methods illustrated in Fig. 2(a) and Fig. 2(b) are described is not intended to be construed as a limitation, and any number of the described method blocks can be combined in any order to implement the methods, or alternative methods. Additionally, individual blocks may be deleted from the methods without departing from the spirit and scope of the subject matter described herein. Furthermore, the methods can be implemented in any suitable hardware, software, firmware, or combination thereof
Referring to Fig. 2(a), an exemplary method 200A can be used to determine the feasibility of transporting a fluid through a pipeline. In an implementation, the method 200A is used to determine the feasibility of transporting the fluid through a buried pipeline. In an implementation, the pipeline is

considered as being divided into a plurality of segments and the flow parameters of the fluid are calculated for each segment. In said implementation, the pipeline may be divided into the segments by a module, such as the transport simulation module 112. Further, the pipeline may be divided into the segments based on a user preference. However, it will be understood that the method 200A may be performed on the pipeline as a whole as well.
At block 202, various fluid attributes are received. The fluid attributes include, for example, pour point of the fluid, wax appearance temperature of the fluid and fluid parameters. The fluid parameters may include specific heat Cf of the fluid, thermal conductivity Kf of the fluid, rheological parameters of the fluid, etc. The fluid attributes may be obtained by testing a sample of the fluid in a laboratory. The sample of the fluid may be prepared by using known methods.
For example, a sample of crude oil can be prepared by heating the crude oil in a barrel at about 85°C in an oven for about 8 hours, and rolling the barrel for 15 minutes to homogenize the crude oil. Samples may then be extracted from different parts of the barrel and tested under various conditions, such as operating temperatures. In an implementation, the pour point and the wax appearance temperature of the fluid may be experimentally obtained using standard test methods. Further, the rheological parameters of the fluid are experimentally evaluated in a laboratory. In an implementation, the evaluation of the fluid for rheological parameters is performed over a predefined cooling cycle. The cooling cycle may be based on various factors, for example, seasonal variations of the surrounding temperatures, and the temperatures of the source and the destination.
For the purpose of illustration, table 1 is provided below to show the effect of temperature on viscosity ji of various compositions of a fluid A and a fluid B. The compositions enlisted in table 1 include composition-1, 2, 3, 4,and 5. Composition-1 includes only fluid A, composition-2 includes 25% of fluid A and 75% of fluid B, composition-3 includes20% of fluid A and 80% of fluid B, composition-4 includes 15% of fluid A and 85% of fluid B, and composition-5 includes 10% of fluid A and 90% of fluid B. The variations in the viscosities of the compositions depicted in the table are obtained from rheological evaluations of the various compositions of the fluids A and B.
Table 1: Variation of Viscosity with temperature
(Table Removed)

The fluid A has a pour point of 45°C, and crystallizes at temperatures below the pour point. Hence, the values of viscosity with temperature for composition-1 (only fluid A) could not be experimentally determined and are not shown in table 1.
In an implementation, the values of the various fluid attributes may be obtained by the transport simulation module 112, from a database, such as the parameter data 118. Further, the values of the various fluid attributes may be pre-stored in the parameter data 118 or may be input by a user during run-time. The user may input the values using interfaces, such as the interface(s) 106.
At block 204, various pipeline segment parameters are obtained for a segment of the pipeline. The pipeline segment parameters include, for example, the burial depth Z of the segment, thermal conductivity of the pipeline Kp, elevation head of the segment, inner diameter D of the pipeline, thermal conductivity of the soil Ks, roughness k of the segment, temperature of the soil Ts surrounding the segment, thickness t of the pipeline, and the length L of the pipe segment for which the computations are performed. The inner diameter D of the pipeline and the thickness t of the pipeline are approximated to be same for all the segments of the pipeline.
In an implementation, the pipeline segment parameters are pre-stored in the parameter data 118. In another implementation, the pipeline segment parameters are input by a user via the transport simulation module 112 using the interface(s) 106 and are stored in the parameter data 118
At block 206, the fluid parameters and the pipeline segment parameters are used to determine temperature and pressure profiles of the fluid along a length of the pipeline. In an implementation, the transport simulation module 112 may determines the temperature and pressure profiles of the fluid by analyzing the flow of the fluid through the pipeline, for example, by determining various flow parameters of the fluid. The flow parameters include flow rate Q of the fluid through the pipeline, fanning friction factor f, heat transfer coefficients of the fluid Hf, the segment Hp and the soil Hs, etc. In an implementation, the flow parameters, such as flow rate Q may be pre-stored in the parameter data 118. In an implementation, the flow analysis of the fluid is achieved for each segment of the pipeline. For example, the final end temperature Tf of the fluid is computed at the exit of each segment of the pipeline based on the flow parameters. The final end temperatures Tf at the exit of each of the segments of the pipeline is used to obtain the temperature profile of the fluid across the

pipeline. Similarly, the pressure drop ∆p across each segment of the pipeline is computed and the pressure profile for the fluid across the pipeline can be determined. The determination of the temperature and pressure profiles of the fluid is explained in detail with reference to description of Fig. 2(b). The results of the determination of the temperature and pressure profiles may be illustrated as a visual representation, for example, a graph.
At block 208, the feasibility of transporting the fluid through the pipeline is determined. In an implementation, a module, such as the feasibility module 114, makes such a determination based on a final end temperature Tfexit of the fluid at the exit of the pipeline. For example, the final end temperature Tfexit of the fluid is compared to the pour point and the wax appearance temperature of the fluid. In addition, the final end temperature Tf of the fluid at the exit of each segment of the pipeline may be compared to the pour point and the wax appearance temperature of the fluid to determine the feasibility of transporting the fluid through the pipeline.
Additionally or alternatively, the pressure drop ∆p of the fluid computed for each segment of the pipeline may be used to determine the feasibility of transporting the fluid. The pressure drops ∆p
may be used to compute the pumping power P required for pumping the fluid across the pipeline, and further to determine the feasibility of pumping the fluid through the pipeline without damaging the pump and the pipeline.
If the determination made at block 208 ascertains that the transportation of the fluid is not feasible, then block 210 is invoked. Or else, block 212 is invoked.
At block 210, at least one feasibility parameter is adjusted to attain feasibility of transportation of the fluid through the pipeline. According to an aspect, a user adjusts the feasibility parameter. In an implementation, the feasibility parameter may be the composition of the fluid, which is adjusted by adding additives, such as diluents and pour point depressants, to the fluid. The method 200A is repeated from block 202 through block 208 for a blend of the fluid obtained by adding such additives. Hence, the method 200A may be used for obtaining such a composition of the fluid that is transportable through the pipeline with minimum damage to the pump and the pipeline.
Additionally or alternatively, the feasibility parameter may be the pumping power P required to transport the fluid through the pipeline. In said implementation, an appropriate pumping power P may be employed in the pipeline system to transport the fluid through the pipeline. The method may be repeated from block 202 through block 208 to determine the feasibility of transporting the fluid through the pipeline with the adjusted parameter. However, in said implementation, the method may be repeated from block 206 onwards.

Further, the feasibility parameter may be a length of the pipeline at which a heating unit may be provided for heating the fluid through the pipeline. The heating unit, for example, does not allow the fluid to attain a temperature below its pour point. The length of the pipeline at which the heating unit may be provided, is determined from the temperature and pressure profiles of the fluid determined by the transport simulation module 112.
It will be understood that other feasibility parameters that are pertinent in determining the feasibility of transporting the fluid through the pipeline may also be considered.
If the determination made at block 208 ascertains that the transportation of the fluid through the pipeline is feasible, then at block 212, the execution of the method 200A for the fluid is discontinued.
Referring to Fig. 2(b), an exemplary method 200B to determine the temperature and pressure profiles of the fluid, achieved at block 206, is described. In an implementation, such a determination is achieved for each segment of the pipeline. A module, such as the transport simulation module 112, implements the method 200B to determine the temperature and pressure profiles of the fluid.
At block 220, the end temperature Te of the fluid at an exit of a segment of the pipeline is estimated. In an implementation, the end temperature Te of the fluid is estimated based on the soil temperature Ts surrounding the segment.
At block 222, the values of fluid parameters and flow parameters are determined at the end temperature Te. The fluid parameters may include, for example, thermal conductivity of the fluid Kf, specific heat Cf of the fluid, and rheological parameters of the fluid, such as yield stress τ, consistency Ck, and non-Newtonian character index n. Further, the variation of the rheological parameters with temperature is also determined at block 222. Furthermore, fluid parameters, such as the rheological parameters, may be calculated by interpolating between the values of the respective parameter obtained by rheological testing of the fluid in the laboratory.
Based on the fluid parameters evaluated at the end temperature Te, the transport simulation module 112 may determine flow parameters of the fluid, such as the nature of flow of the fluid, the friction factor f, the heat transfer coefficient for the fluid Hf, the heat transfer coefficient for the segment Hp, and the heat transfer coefficient for the soil Hs surrounding the segment. The heat transfer coefficients Hf, Hs, and Hp may be used to further determine the overall heat transfer coefficient U for the pipeline system.
In another implementation, the effect of fouling in the pipeline may be considered to evaluate the overall heat transfer coefficient U. In said implementation, a fouling factor / may be considered

while evaluating the overall heat transfer coefficient U. The overall heat transfer coefficient U may also be computed by the transport simulation module 112.
At block 224, a pressure drop ∆p of the fluid across the segment of the pipeline, viscous heating Ø in the segment, and a heat generation coefficient qf are determined by the transport simulation module 112 based on the flow parameters determined at block 222. The pressure drop ∆p
for the segment is determined based on the friction factor f for the segment of the pipeline and the density p of the fluid calculated at the end temperature Te. The viscous heating Ø is a measure of the pumping power P lost due to frictional heating in the fluid, and may be determined based on the pressure drop Ap. Further, the heat generation coefficient qf represents the heat generated due to friction in the fluid, and may be determined based on the viscous heating Ø and the overall heat transfer coefficient U.
At block 226, the computed temperature Tc of the fluid at the exit of the segment is determined by the transport simulation module 112. In an implementation, the computed temperature Tc of the fluid is calculated based on an entrance temperature Te„t of the fluid at an entrance of the segment of the pipeline, and the heat generation coefficient qf and the viscous heating Ø determined at block 224. The entrance temperature Teni of the fluid for one segment may be the final end temperature Tf calculated at the exit of the previous segment.
At block 228, a determination is made to ascertain whether the computed temperature Tc determined at block 226 converges to the end temperature Te estimated at block 222. If the determination made at block 228 indicates that the computed temperature Tc converges to the end temperature Te ("YES" path from block 228), then block 230 is invoked. When the computed temperature Tc converges to the end temperature Te then the converged temperature Tc is referred to as the final end temperature Tf.
At block 230, the wall temperature Tw for the segment and the pumping power P for the segment are determined. In an implementation, the wall temperature Tw and the pumping power P are determined by the transport simulation module 112. In said implementation, the wall temperature Tw is determined based on the final end temperature Tf. The wall temperature Tw is determined to assess actual viscosity characteristics of the fluid, and to control the heat transfer properties of the pipeline material. For example, a layer of insulating material may be provided around a segment of the pipeline based on the wall temperature Tw of the segment. The wall temperature Tw may also be used to determine the possibility of freezing the water in the soil around the segment. Further, the pumping power P for the segment can be calculated using various relations known in the art.

If the determination made at block 228 indicates that the computed temperature Tc does not converge to the end temperature Te ("NO" path from block 228), then block 220 is invoked again. Accordingly, the end temperature Te for the segment is estimated again, and the method is repeated. In an implementation, when block 220 is invoked after block 230, then the end temperature Te is estimated based on the previously estimated end temperature Te and the computed temperature Tc using an iterative technique. For example, the end temperature Te is obtained by computing a mean of the end temperature Te and the computed temperature Tc from the previous iteration.
In an implementation, the method is repeated until the computed temperature Tc converges to the end temperature Te. In another implementation, the method is repeated for a predefined number of iterations N, and if the computed temperature Tc does not converge to the end temperature Te, then the computed temperature Tc obtained at the end of the last iteration is selected as the final end temperature Tf of the fluid for the segment. The method is then repeated for each segment of the pipeline and accordingly the temperature and pressure profile of the fluid along the length of the pipeline is determined.
Fig 3(a) and Fig 3(b) illustrate exemplary graphs depicting temperature and pressure profiles, respectively, of a fluid over a length of the pipeline. For the purpose of illustration, a graph 300A shown in Fig. 3(a) is plotted to depict the temperature profiles for various compositions of two fluids, fluid A and fluid B. In graph 300A, the final end temperature Te of the composition of the fluid is plotted against a length of the pipeline. The length of the pipeline is measured in kilometres (km). The various compositions of the fluids are considered to be pumped from the source at a temperature of 90°C. Curve 302 shows the temperature profile of composition-1 having only fluid A, over the length of the pipeline. Similarly, curves 304, 306, 308 and 310 show the temperature variation of composition-2 including 25% of fluid A and 75% of fluid B, composition-3 including 20% of fluid A and 80% of fluid B, composition-4 including 15% of fluid A and 85% of fluid B, and , composition-5 including 10% of fluid A and 90% of fluid B, respectively.
In the illustration, the curve 302 shows that the temperature of composition-1 is almost equal to its pour point temperature of 45°C. From the curve 302 it may be inferred that the transportation of composition-1 may require heating of fluid along the length of the pipe. However, it may be difficult to provide such heating along the length of the pipe, without which the fluid may attain a temperature below its pour point. On attaining a temperature below the pour point, the fluid may not be pumpable. Hence, the temperature profile shown in graph 300A may be used to infer the pumpability of a composition.

Further, graph 300B is plotted to illustrate a pressure profile of various compositions of the fluid A and the fluid B, composition-1, 2, 3, 4, and 5. The pressure drops ∆p for the various compositions in each segment of the pipeline is plotted against length of the pipeline. Accordingly, curve 320 shows the pressure profile of composition-1, curve 322 shows the pressure profile of composition-2, curve 324 shows the pressure profile of composition-3, curve 326 shows the pressure profile of composition-4, and curve 328 shows the pressure profile of composition-5.
As seen from curve 320 for composition-1 in the illustration, the pressure drops ∆p for the fluid along the length of the pipeline indicate that the pumping power P requires augmentation for the fluid to be transported. The amount by which the pumping power P is to be increased may be calculated from the pressure drops ∆p for the fluid. However, it may or may not be feasible to augment the pumping power P with the required amount of power, based on the pump used and the distance from the pumping station. Hence, the pressure profiles may be used to infer the feasibility of transporting the fluid through the pipeline.
The described subject matter and its equivalent thereof have many advantages, including those which are described below. The described methods and systems provide for determination of an optimum composition of a fluid that can be transported to a desired destination through a buried pipeline system, without causing much damage to the pump or the pipeline. Further, the method facilitates in locating one or more sites along the length of the pipeline where a pump may be provided to achieve the required pumping power to transport the fluid. Similarly, one or more sites may be identified where a heating unit may be provided to prevent the fluid from attaining temperatures below its pour point temperature. Furthermore, the method may be used to estimate inter station spacing.
Although the subject matter has been described in considerable detail with reference to certain preferred embodiments thereof, other embodiments are possible. As such, the spirit and scope of the appended claims should not be limited to the description of the preferred embodiment contained therein.

I/We claim:
1. A method comprising:
receiving fluid parameters of a fluid to be transported;
computing a final end temperature of the fluid at an exit of at least one segment of a pipeline, based on the fluid parameters and on heat generated due to friction;
determining whether transporting the fluid tlirough the pipeline is feasible, based at least on the final end temperature; and
adjusting a feasibility parameter based on the determining to make transportation of the fluid feasible.
2. The method as claimed in claim 1, wherein the computing further comprises
iteratively calculating a computed temperature at the exit of the at least one segment of the pipeline, based on an end temperature; and
selecting the computed temperature as the final end temperature based on a convergence of the computed temperature and the end temperature.
3. The method as claimed in claim 1, wherein the fluid parameters include experimentally determined rheological parameters of the fluid.
4. The method as claimed in claim 1, wherein the determining comprises comparing the final end temperature of the fluid with at least one of a pour point of the fluid and a wax appearance temperature of the fluid.
5. The method as claimed in claim 1, wherein the determining is further based on a pressure drop of the fluid in the at least one segment of the pipeline.
6. The method as claimed in claim 1, further comprising determining a temperature profile and a pressure profile of the fluid over the plurality of segments of the pipeline.
7. The method as claimed in claim 1, wherein the feasibility parameter comprises at least one of a composition of the fluid, a pumping power, and a length of the pipeline at which a heating unit is disposed.
8. A device (100) comprising:
a processor (102);
a memory (104) operatively coupled to the processor (102), the memory (104) comprising,
a transport simulation module (112) configured to determine a temperature profile of a fluid along a length of a pipeline, based on heat generated in the fluid due to friction while transporting the fluid through the pipeline; and
a feasibility module (114) configured to determine whether transporting the fluid through the pipeline is feasible, based on the determination by the transport simulation module (112).
9. The device (100) as claimed in claim 8, wherein the transport simulation module (112) is further configured to determine a pressure profile of the fluid along the length of the pipeline based on a pressure drop in each of a plurality of segments of the pipeline.
10. The device (100) as claimed in claim 9 wherein the feasibility module (114) is further configured to determine whether transporting the fluid is feasible, based on the pressure profile of the fluid.
11. The device (100) as claimed in claim 8, further comprising at least one interface (106) to provide fluid parameters, a pour point of the fluid, and a wax appearance temperature of the fluid to the transport simulation module (112).
12. The device (100) as claimed in claim 11, wherein the at least one interface (106) provides
experimentally determined fluid parameters to the transport simulation module (112).
13. The device (100) as claimed in claim 8, wherein the transport simulation module (112) is
configured to determine the temperature profile based on a final end temperature of the fluid at an
exit of each of a plurality of segments of the pipeline.
14. The device (100) as claimed in claim 13, wherein the feasibility module (114) determines the
feasibility of transporting the fluid based on a comparison of the final end temperature with at least
one of a pour point of the fluid and a wax appearance temperature of the fluid.
15. The device (100) as claimed in claim 13, wherein the transport simulation module (112) is further configured to compute the final end temperature by iteratively calculating a computed temperature based at least in part on fluid parameters and on the heat generated in the fluid due to friction.