Laplace transformation provides advantages in the solution of many pressure-transient analysis problems. Usually, these applications lead to a solution that needs to be inverted numerically to the real-time domain. The algorithm presented by Stehfest in 1970 is the most common tool in petroleum engineering for the numerical inversion of Laplace transforms. This algorithm, however, is only applicable to continuous functions and this limitation precludes its use for a wide variety of problems of practical interest. Other algorithms have also been used, but with limited success or popularity. A recent algorithm presented by Iseger in 2006 removes the restriction of continuity and provides opportunities for many practical applications. This paper exploits the useful features of the Iseger's algorithm in the inversion of continuous as well as singular and discontinuous functions that arise in the solution of pressure-transient analysis problems. The most remarkable applications are in the problems that require the use of piecewise continuous and piecewise differentiable functions, such as the use of tabulated data in the Laplace transform domain, deconvolution algorithms, and solutions that include step-rate changes as in the mini-DST tests.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractElectrokinetic techniques have proven to be a valuable tool in providing direct information on charge solid/liquid interface. Today, oil industrial companies are looking into electrokinetic techniques with great interest, in order to describe the oil reservoir physics occurring in and near the well bore during production. This paper introduces a new method, which uses streaming potential transient testing to characterize the electrokinetic properties of oil reservoirs. Streaming potential exists in the movement of part of electrical double layers from the charged pore surfaces when fluid flow is induced by an applied pressure gradient. A fully computerized high pressure and high temperature core holder device is utilized to simultaneously measure streaming potential and pressure transient tests. The time behavior of the transient steaming potential is identical to that of fluid pressure when laminar flow is maintained. The transient streaming potential data is a useful quantity for determining the electrokinetic (zeta) potential values produced at the reservoir rock/fluid interface, and is considered an important electrokinetic characteristic that can play a role in reservoir rock properties. In low conductivity liquids, such as petroleum fluids, the surface conduction of reservoir rocks will cause errors in streaming potential measurements and therefore any derived electrokinetic potentials are also affected. The latter is corrected by determining the total electric conductivity of reservoir rocks, including the surface conductivity. The compressibility of reservoir fluid has been shown to affect streaming potential measurements and the results of electrokinetic potentials. We believe that this work is an important addition to the hydraulic and electrokinetic characterizations of oil reservoirs.