Relief Device Sizing for Non-Newtonian Fluids
The analysis for the flow of liquids through pressure relief devices in API and ASME standards is currently predicated on the fluid viscosity behavior being Newtonian; API Std 520 Part I, 8th edition (2014), explicitly states in the Scope of the document that the document “…includes sizing procedures and methods based on steady state flow of Newtonian fluids.”1
In the API Standard 520 Part I certified liquid sizing equations, the deviation of actual relief valve flow from the idealized isentropic nozzle flow for low viscosity fluids is captured with the use of a discharge coefficient Kd (which is further reduced to apply a safety factor on the capacity of the relief valve). The amplified effect of elevated viscosity of a Newtonian fluid on the deviation of actual relief valve flow from the idealized isentropic nozzle flow is captured with the use of a viscosity correction factor, Kv. “Amplified” is used here as opposed to “additional” to recognize the factor is multiplicative instead of additive. The values of the viscosity correction factor were subsequently corroborated with the use of computational fluid dynamics analysis.2
The effects of non-Newtonian fluid behavior and/or very high viscosities on relief system design has been a topic of research by the Design Institute for Emergency Relief Systems (DIERS), and some recommendations are given in the DIERS Project Manual for two-phase flow involving high viscosity fluids §II-2(p.56-57), III-8 (p.96-97), and IV-3 (p.289-312).3 Further work on this topic was undertaken, and periodically reported upon during DIERS Users Group meetings; however, no definitive guidance was published.
While still infrequent, perhaps a more commonly encountered situation than that of two-phase flow is that of non-Newtonian and/or highly viscous liquid-only flow. Dr. Darby indicates “… in the absence of more specific information, it may be assumed that [the determination of the liquid viscosity correction factor Kv as a function of Reynolds Number] can be applied to non-Newtonian viscous fluids if the Reynolds number is modified accordingly for the specific non-Newtonian rheological model (see Chapter 7 of ).”4 This approach is consistent with the DIERS Project Manual §IV-3, in which the Reynolds Number (as well as the momentum balance for pipe flow) is modified as described, specifically for the power-law rheological model.
Recently, Moncalvo and Friedel have published data regarding the flow through a relief valve of a shear-thinning (pseudoplastic) liquid5 and even more recently a recommendation regarding how the viscosity correction factor Kv may be adjusted to account for the non-Newtonian behavior6. A similar approach is taken of defining the appropriate Reynolds Number for the non-Newtonian behavior; however, an attempt is made to account for the minimum shear rate (at the disk seat) and to use a characteristic length of the hydraulic diameter of the annulus formed between the disk and the nozzle, also referred to as the curtain area. This characteristic length was essentially selected in order to minimize the overestimation of capacity; however, it is hard to come by for liquid releases, as the lift may vary based on the flow rate (i.e. the lift is not the fully achievable lift as is characteristic of compressible fluid flow through a relief valve) and would thus require measurement in the field.
The authors found reasonable accuracy compared to measured data using the approach given by Darby, yet found some cases of deviation greater than 20% for calculated versus measured flows, particularly at very low flow rates (1-2 kg/sec or about 8,000-16,000 lb/hr) in their experimental data set. Given the inherent lack of precision in the various estimates we employ in relief device sizing (for example, calculation of the required relief rates, specification of the relieving conditions particularly temperature as viscosity is highly dependent upon it, and characterization of the rheological properties) the more detailed analysis afforded by evaluation of the minimum viscosity at the curtain area does not appear to be warranted.
 Darby R and Molavi K. Viscosity Correction Factor for Safety Relief Valves. Process Safety Progress, 1997 Summer;16(2):80-82.
 Fisher HG, Forrest HS, Grossel SS, Huff JE, Muller AR, Noronha JA, Shaw DA, Tilley BJ. Emergency Relief System Design Using DIERS Technology – The Design Institute for Emergency Relief Systems (DIERS) Project Manual. AIChE (1992).
 Darby R. Size Safety-Relief Valves for Any Conditions. Chemical Engineering. 2005 Sept; 112(9):42-50.<
 Moncalvo D, Friedel L. Single and two-phase flows of shear-thinning media in safety valves. Journal of Hazardous Materials 2009, 168(2/3), 1521e1526
 Moncalvo D, Friedel L. A viscosity correction factor for shear-thinning liquid flows in safety valves. Journal of Loss Prevention in the Process Industries 2010; 23 (2): 289-293.