Dear Mehadi,

A common situation encountered by the chemical engineer is heat transfer to fluid flowing through a tube. This can occur in heat exchangers, boilers, condensers, evaporators, and a host of other process equipment. Therefore, it is useful to know how to estimate heat transfer coefficients in this situation.

A variety of correlations are in use for predicting heat transfer rates in laminar flow. From dimensional analysis, the correlations are usually written in the form

Nu= f(Ru,Pr..)

In the case of commercial pipes, roughness of the interior surface is inevitable, whereas drawn tubes tend to be less rough. The extent of roughness depends on the nature of the surface. Mills provides a discussion of heat transfer in turbulent flow in rough pipes .The heat transfer rate is predicted in this case by using a group called the Stanton number

St.=Nu/Re.Pr =Nu/Pe

St=f/8/0.9 +(f/8)1/2[g{h+pr)-7.650}

where the friction factor f is calculated using

f ={-2.0 lg10[Ks/R/7.4-5.5.02/Re.log10(Ks/R)/7.4) +13/Re)}-2

In the above correlations, ks is known as the “equivalent sand grain roughness” Values of ks for a variety of pipes, tubes, and other types of surfaces can be found in Table 4.8 in the textbook. The symbol R represents the inside radius of the pipe., but you will first need to convert to h to h+ which is dimensionless. The symbol stands for the average height of protrusions from the surface. For equivalent sand grain roughness, we can use h=Ks For a pipe, the relationship between the dimensionless quantities (+ variables) and the physical variables is given in Equation.

Regards,

Prem Baboo

Dear Mehdi,

The answer to your question would be non-trivial. In other words, you would need to run hydrodynamic calculations or perform simulation using commercial software such as PIPESIM or OLGA (both marketed by Schlumberger) to see the effects of those parameters for your operating condition exactly. 

But in general, the three parameters that you specified will affect the outflow performance relationship (OPR), which basically quantifies the pressure at bottom of the well for a given production rate. The lower bottomhole pressure, in general (not always), the better, as it provides more driving force for production.  

1. In general, increase in tubing roughness increase your frictional pressure loss - which means you may have higher bottomhole pressure as the result.

2. The deviation influences the gravitational pressure loss. The closer the tubing is to vertical, the gravitational loss would be conceivably greater, imposing higher bottomhole pressure as well. 

3. The temperature may alter the viscosity of your fluid greatly and also change your gas properties. The heat transfer throughout your wellbore may also determine whether you will have flow restriction issues such as wax or scales.

The significance of each variables is highly dependent on the cases. For example: for a gas dominated well with very high gas flow rate and negligible liquid, the gravitational loss might be rather insignificant. If you have a high viscosity oil or oil/water emulsion, the temperature will alter your viscosity significantly as opposed to if you have gas and water in your system. In that case, the friction would be significantly altered. On the other hand, if you have liquid dominated system, then gravitational loss/ deviation effects may be dominant. There are also time-dependent behavior that may affect the well productivity such as liquid loading, liquid accumulation, slugging, for which requires more calculation to solve - particularly for horizontal well configuration.

The book "Multiphase Flow in Wells" by James P. Brill & Hemanta Mukherjee can give you several procedures to perform these calculations.

http://store.spe.org/Multiphase-Flow-in-Wells-P39.aspx

Thank you so much for your responses .