Effects of the nonlinear gradient term on the transient pressure solution for a radial flow system

Fluid dynamics in naturally fractured tectonic reservoirs

“…In addition, for an infinite reservoir the wellbore pressure predicted by this linear Darcy solution may be significantly smaller than that predicted by the Couette solution at large times. On the other hand, Jelmert and Vik (1996) and Odeh and Babu (1988) concluded that the consideration of the nonlinear quadratic term gives results significantly smaller in pressure prediction and recommended its use as the use pressure solution; although this result was also demonstrated by (Chakrabarty et al 1993) for wellbore pressure prediction for a closed outer boundary, the authors stated that the linear pressure solution is unsatisfactory and should be applied with caution, stating that an infinite reservoir has a 5% error for large dimensionless times.…”

“…Moreover, this type of equation is compared in papers (Chakrabarty et al 1993;Odeh and Babu 1988) to validate these linear equations. Equation (51) models fluid flow in a nonlinear diffusion process for a reservoir with extension fractures, without matrix-fracture transfer; this equation expressed for radial flow becomes:…”

“…Others papers have presented solutions for the nonlinear transient flow model including a quadratic gradient term by using transformations (Friedel and Voigt 2009;Aadnoy and Finjord 1996;Chakrabarty et al 1993;Cao et al 2004); however, they assumed a homogeneous porous medium.…”

Nonlinear flow model for well production in an underground formation

“…Compared with previous publications, such as Cao et al (2004), Chakrabarty et al (1993b), Marshall (2009), this research highlights (1) newly considered use of real parameters for wells with skin factor in nonlinear flow models; (2) application of modern standard type curves to intuitively observe nonlinear transient flow behaviour; (3) recognition of flow regimes from type curves, including recognition of different external boundary responses; (4) thorough analysis of parameter sensitivity to type curves; (5) use of quantitative methods of "DV" and "RDV" to describe solution differences between nonlinear and linear models; (6) establishment of numerical modelling of nonlinear gas flow and simulation and comparison of nonlinear gas and oil flow pressure transients; and (7) consideration of real world applications through comparisons of theoretical data and field data.…”

“…The solutions of these models cannot be compared to the model discussed here. Chakrabarty et al (1993b) studied a nonlinear pressuretransient model which does not consider skin factor and plotted a group of log-log pressure-transient curves based on t D . Explanations: k is formation permeability; µ is liquid viscosity; β is dimensionless coefficient of the nonlinear term; β was calculated according to its definition under a set of fixed parameters: set liquid rate q = 25 m 3 d −1 ; liquid volume factor B = 1.004; formation thickness h = 10 m and liquid compressibility C ρ = 0.001 MPa −1 .…”