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Production engineering formulas and calculations Chapter  4  215



             Output(s)

                K L :  Dimensionless Fracture Length (dimensionless)
                K u :  Reciprocal Dimensionless Fracture Width (dimensionless)
                K s :  Dimensionless Fluid-Loss Coefficient (dimensionless)
                K ηL :  Dimensionless Variable (dimensionless)


             Formula(s)

                                                                  p ffiffi
                                                        K ¼ CLh=i t
                                                          L
                                                              p ffiffi
                                                        K ¼ C t=w  w
                                                          u
                                                              p ffiffi
                                                        K ¼ C t=V
                                                         s        spt
                                                                i  3
                                                                     μ
                                                    K ¼ 21:8
                                                     ηL
                                                              hC 2   Et
             Reference: Williams, B. B., Gidley, J. L., & Schechter, R. S. (1979). Acidizing fundamentals. Henry L. Doherty Memorial
             Fund of AIME, Society of Petroleum Engineers of AIME, Page: 40.


             4.25    Downhole operating pressure (hydraulic fracturing)

             Input(s)

                ΔP f :  Pressure Loss Sourced by Friction (psi)
                ΔP p :  Pressure Loss sourced by Perforations(psi)
                ΔP h :  Hydrostatic Pressure Change (psi)
                P inj :  Injection Pressure (psi)
                D:   Fracture Elevation Depth (ft)
                G f :  Fracture Gradient (psi/ft)


             Output(s)

                P F :  Downhole Operating Pressure (psi)


             Formula(s)

                                                         P ¼ G  D
                                                           F   f
                                                       P + ΔP  ΔP  ΔP    p
                                                                   f
                                                              h
                                                        inj
                                                  G ¼
                                                    f
                                                               D
             Reference: Saydam, T., (1967). Principles of Hydraulic Fracturing, ARI Publishing Co., Page: 25.
             4.26    Entrance hole size (perforation)

             Input(s)

                σ y :  Yield Strength of Casing of Interest (ksi)
                σ yr :  Yield Strength of Reference Casing (ksi)
                d r :  Entrance Hole Diameter in Reference Casing (in.)
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