|Publisher||Society of Petroleum Engineers||Language||English|
|Content Type||Journal Paper|
|Title||Friction Pressures of Proppant-Laden Hydraulic Fracturing Fluids|
|Authors||Shah, Subhash N., Halliburton Services; Lee, Yung N., Halliburton Services|
|Journal||SPE Production Engineering|
|Volume||Volume 1, Number 6||Pages||437-445|
|Copyright||1986. Society of Petroleum Engineers|
Friction-pressure calculations of proppant-laden fluids are very important not only in the design of any hydraulic fracturing treatment but also in real-time monitoring of fracturing treatments. Recent advances in real-time fracture analysis have necessitated an accurate knowledge of bottomhole treating pressure (BHTP). To estimate BHTP, an accurate prediction of friction pressures of fluids in the flow conduit is required.
This paper presents a new approach for predicting friction pressures of proppant-laden fracturing fluids that is based on an analytical method and uses nondimensional quantities in the analysis of flow data. From the flow data with various proppant-laden gels in multiple pipes, generalized correlations are developed and presented that incorporate such variables as proppant size, proppant density, proppant concentration, fluid density, flow rate, polymer gel concentration, and pipe size. These correlations are valid for a wide range of terminal Froude number, N Fr* (8.4 x 10(-3) to 1.3 x 10(-4), and particle Froude number, N Frp (20 to 200). These ranges include the calculated values of N Fr* and N Frp for the majority of hydraulic fracturing treatments conducted today.
The correlations are verified by comparison of the estimations with data gathered in field-size tubing and field-gathered data. Our predictions agree more closely with field data than previously published methods. Unlike previous studies, this investigation indicates that besides other factors, proppant size, pump rate, flow geometry, and polymer gel concentration play a significant role in the friction-pressure predictions of proppant-laden fluids.
Recent advances in pressure analysis have made knowing the BHTP during hydraulic fracturing treatments very critical. Various methods measure BHTP directly, but all have drawbacks and involve considerable additional cost to the treatment. It is possible to obtain the BHTP from the surface pressure with the following equation:
Pwt = Pwh + Ph -Pf.
The wellhead pressure, Pwh, can be measured with good accuracy. The hydrostatic pressure, Phi can be calculated accurately with recent advances in radioactive densimeters. Methods for predicting friction pressures of clean fracturing fluids have been well established. The friction pressures of gelled fluids through tubular goods, Pf's, are more difficult to predict accurately when they Pf's, are more difficult to predict accurately when they are crosslinked and/or contain proppants. No known methods based on fluid theory are available to predict the effect of proppant on friction pressures of non-Newtonian fluids used in hydraulic fracturing treatments. In the past, it was assumed in many cases that the increase in friction pressure resulting from proppant in the fluid is compensated pressure resulting from proppant in the fluid is compensated for by the increase in hydrostatic pressure. In other cases, simple, empirical proppant-friction factors based on field data have been used.
In this paper, a new model is proposed, and correlations based on this model are developed to calculate friction pressures of proppant-laden fracturing gels. These correlations are developed by use of an analytical method and incorporate nondimensional quantities.
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