A Modified Blasingame Production Analysis Method for Vertical Wells Considering the Quadratic Gradient Term

Fluid flow in actual oil reservoirs is consistent with material balance, which should be described by the nonlinear governing equation, including the quadratic gradient term (QGT). Nonetheless, the widely-used Blasingame production decline analysis (BPDA) is established based on the conventional governing equation neglecting the QGT, which leads to some errors in the interpretation of production data under some conditions, such as wells producing at a large drawdown pressure. This work extends BPDA to incorporate the effect of the QGT by modifying material balance time and normalized rate functions. The step-by-step procedure for the proposed production decline analysis (PPDA) is presented and compared with that for BPDA. The simulated cases for various production scenarios are used to validate PPDA. A field case is employed to show the applicability of PPDA in practice. Comparisons between the results obtained by BPDA and PPDA are analyzed in detail. It is found that BPDA overestimates the permeability and original oil-in-place, while PPDA works well. Compared with BPDA, PPDA can be employed to obtain more accurate original oil-in-place and reservoir properties, especially when wells produce at a large drawdown pressure.

Two healing lengths in a two-band GL-model with quadratic terms: Numerical results

A two-band and quartic interaction order Ginzburg–Landau model in the presence of a single vortex is studied in this work. Interactions of second (quadratic, with coupling parameter [Formula: see text]) and fourth (quartic, with coupling parameter [Formula: see text]) order between the two superconducting order parameters ([Formula: see text] with i = 1,[Formula: see text]2) are incorporated in a functional. Terms beyond quadratic gradient contributions are neglected in the corresponding minimized free energy. The solution of the system of coupled equations is solved by numerical methods to obtain the [Formula: see text]-profiles, where our starting point was the calculation of the superconducting critical temperature [Formula: see text]. With this at hand, we evaluate [Formula: see text] and the magnetic field along the z-axis, [Formula: see text], as function of [Formula: see text], [Formula: see text], the radial distance [Formula: see text] and the temperature [Formula: see text], for [Formula: see text]. The self-consistent equations allow us to compute [Formula: see text] (penetration depth) and the healing lengths of [Formula: see text] ([Formula: see text] with i = 1,[Formula: see text]2) as functions of T, [Formula: see text] and [Formula: see text]. At the end, relevant discussions about type-1.5 superconductivity in the compounds we have studied are presented.

Similar Constructive Method of Solution for the Nonlinear Percolation Model in Composite Reservoir

This paper presents a percolation model for the composite reservoir, in which quadratic-gradient effect, well-bore storage, effective radius and three types of outer boundary conditions: constant pressure boundary, closed boundary and infinity boundary are considered. With Laplace transformation, the percolation model was linearized by the substitution of variables and obtained a boundary value problem of the composite modified zero-order Bessel equation. Using the Similar Constructive Method this method, we can gain the distributions of dimensionless reservoir pressure for the composite reservoirs in Laplace space. The similar structures of the solutions are convenient for analyzing the influence of reservoir parameters on pressure and providing significant convenience to the programming of well-test analysis software.