A Semianalytic Model for the Productivity Testing of Multiple Wells

Abstract

Summary We present a semianalytic method for modeling the productivity testing of vertical, horizontal, slanted, or multilateral wells. The method is applicable to both oil and gas reservoirs and automatically accounts for well interference. The use of analytic expressions ensures that short-time transient behavior and long-time semisteady-state behavior are handled appropriately, whether close to the well or further into the reservoir. Calculation times are still very limited—on the order of a few minutes to a few seconds when all wells are vertical. This makes the tool suitable for evaluating well testing and determining well productivity. We based the approach on an earlier derived productivity prediction tool, in which the steady-state equations were solved. It has now been extended to solve the time-dependent diffusion equation. In our current method, the equations have first been transformed using the Laplace transformation. The expressions for the producing wells are combined with auxiliary sources outside the reservoir. The crux of the semianalytic method involves an adjustment of the positions and strengths of these sources in order to approximate the boundary conditions at the reservoir boundaries. The solution obtained is transformed back into the time domain by use of a Stehfest algorithm. The new approach has been validated with numeric tools, including both reservoir simulators and well-test interpretation software. Validations were performed with artificial cases and with field production data, using both single-well and multiple-well production tests. The results of these tests were excellent.

Well testing of radial jet drilling wells in geothermal reservoirs

“…( 1), η ¼ k φμc t is the diffusivity coefficient. Similarly as the steady state pressure solution for RJD wells was derived in Egberts and Peters [24], we will construct a solution for the pressure field from 3D point source solutions exploiting the principle of superposition [25]. One may derive a transient point source solution solving Eq.…”

Harmonic pulse testing for well performance monitoring

“…Fluid flow in a reservoir drained by a horizontal well cannot be described by a 2D equation in the near wellbore zone. An alternative approach is required, and we have developed a similar approach to that described by Fokker and Verga (2008). Thus, we first split the well into segments of equal lengths (L seg ).…”

“…Flow in the reservoir close to a horizontal well cannot be described by a 2D equation. We used a similar approach to that of Fokker and Verga (2008). We split the well up into segments, calculated the pressure response of each segment due to the flow into said segment and into the others, and chose the fluxes into each segment in a way that the total flow was the prescribed value and the pressures were the same for all segments.…”

Theoretical Approach for the Calculation of the Pressure Drop in a Multibranch Horizontal Well with Variable Mass Transfer

“…Currently, a series of complex production wells are applied to certain challenging reservoirs to maximize oil recovery. − With the development of drilling techniques, multibranch horizontal well technology can improve well productivity by expanding reservoir drainage. − Moreover, the application of this technology can prevent the transportation of large volumes of fluid along a single long horizontal borehole, which would result in pressure losses in the wellbore and would cause a decrease in well productivity. − Therefore, branch wells with complex structures can have a higher production rate with a lower production pressure drop. More specifically, the application of multibranch horizontal wells to bottom water reservoirs appears to be promising in minimizing water cresting or coning. − Depending on whether the radial inflow on the wellbore exists or not, the flow of the wellbore is divided into two types: the variable mass flow and the constant mass flow.…”