**1. Introduction**

Early frac engineers certainly recognized that hydraulic fractures were complex features. Geologists, mining engineers, and prison chain gangs all assured us that rocks break in complex manners. But the math is hard, and we aren't capable of predicting nature's com‐ plexity. We cannot accurately calculate the pressure losses through a proppant pack with complex geometry, irregular aperture, and with several fluid phases flowing at high velocity. So our predecessors were forced to simplify the description. As a first-order approximation, they assumed that fracs were simple, vertical planes, with uniform width and predictable hydraulic continuity.

Two subsequent generations of petroleum engineers have been introduced to simplified planar hydraulic fractures that have been distorted to fit on a textbook page, such as in Figure 1. Unfortunately, many engineers mistakenly envision fracs as wide, highly conductive channels instead of thin, narrow ribbons of proppant that extend deeply into the reservoir but are vulnerable in their hydraulic continuity. Fractures are commonly modeled to be symmetrical, bi-wing planes that reliably contact the targeted hydrocarbons.

**Figure 1.** The proportions of fractures are often distorted and misrepresented in simplified models. This figure implic‐ itly assumes the fracture grows symmetrically on either side of the wellbore.

Although chemical engineers clearly recognized that Darcy's flow would not describe pressure losses in porous media, early frac engineers disregarded non-Darcy and multiphase flow effects, and further assumed a single homogeneous reservoir layer was contacted by a highly conductive fracture that permanently connected the wellbore to the hydrocarbons. These assumptions allowed the "optimization" of frac treatments to become a mathematically simple routine. Two subsequent generations of petroleum engineers have filled our literature and conventional wisdom with simulations and "rules of thumb" that would allow us to optimize these mythical ideal fractures. Unfortunately, many of the assumptions are wrong, and our fracs are not optimized.
