Page 24 - Fundamentals of Reservoir Engineering

CONTENTS XXIV

Fig. 10.1 Hysteresis in contact angle in a water wet reservoir, (a) wetting phase increasing
(imbibition); (b) wetting phase decreasing (drainage) 338

Fig. 10.2 Water entrapment between two spherical sand grains in a water wet reservoir 339

Fig. 10.3 Drainage and imbibition capillary pressure functions 339

Fig. 10.4 Capillary tube experiment for an oil-water system 340

Fig. 10.5 Determination of water saturation as a function of reservoir thickness above the
maximum water saturation plane, S w = 1−S or, of an advancing waterflood 341

Fig. 10.6 Linear prototype reservoir model, (a) plan view; (b) cross section 344

Fig. 10.7 Approximation to the diffuse flow condition for H>> h 346

Fig. 10.8 (a) Capillary pressure function and; (b) water saturation distribution as a function
of distance in the displacement path 348

Fig. 10.9 Typical fractional flow curve as a function of water saturation, equ. (10.12) 349

Fig. 10.10 Mass flow rate of water through a linear volume element Adx 350
φ
Fig. 10.11 (a) Saturation derivative of a typical fractional flow curve and (b) resulting water
saturation distribution in the displacement path 352

Fig. 10.12 Water saturation distribution as a function of distance, prior to breakthrough in
the producing well 353

Fig. 10.13 Tangent to the fractional flow curve from S w = S wc 354

Fig. 10.14 Water saturation distributions at breakthrough and subsequently in a linear
waterflood 355
Fig. 10.15 Application of the Welge graphical technique to determine the oil recovery after
water breakthrough 357

Fig. 10.16 Fractional flow plots for different oil-water viscosity ratios (table 10.2) 360

Fig. 10.17 Dimensionless oil recovery (PV) as a function of dimensionless water injected
(PV), and time (exercise 10.2) 364

Fig. 10.18 Displacement of oil by water under segregated flow conditions 365

Fig. 10.19 Illustrating the difference between stable and unstable displacement, under
segregated flow conditions, in a dipping reservoir; (a) stable: G > M−1; M > 1;
β < θ. (b) stable: G > M−1; M < 1; β > θ. (c) unstable: G < M−1. 366

Fig. 10.20 Segregated displacement of oil by water 369

Fig. 10.21 Linear, averaged relative permeability functions for describing segregated flow in
a homogeneous reservoir 370

Fig. 10.22 Typical fractional flow curve for oil displacement under segregated conditions 371