Fikri John Kuchuk

Pressure-transient behavior of horizontal wells with and without gas cap or aquifer

In this paper analytic solutions are presented in real time and as Laplace transforms for horizontal wells in reservoirs bounded at the top and bottom by horizontal planes. Two types of boundary conditions are considered at these planes, and the Laplace-transform pressure solutions are used to include wellbore-storage and skin effects. Solutions are based on the uniform-flux, line-source solution, but differ from most existing solutions owing to the use of pressure averaging to approximate the infinite-conductivity wellbore condition and use of the correct equivalent wellbore radius for an anisotropic reservoir. New flow periods (regimes) are identified, and simple equations and existence criteria are presented for the various flow periods that can occur during a transient test.

Transient Pressure Behavior of Reservoirs with Discrete Conductive Faults and Fractures

Fractures and faults are common features of many well-known reservoirs. They create traps, serve as conduits to oil and gas migration, and can behave as barriers or baffles to fluid flow. Naturally fractured reservoirs consist of fractures in igneous, metamorphic, sedimentary rocks (matrix), and formations. In most sedimentary formations both fractures and matrix contribute to flow and storage, but in igneous and metamorphic rocks only fractures contribute to flow and storage, and the matrix has almost zero permeability and porosity. In this study, we present a mesh-free semianalytical solution for pressure transient behavior in a 2D infinite reservoir containing a network of discrete and/or connected finite- and infinite-conductivity fractures. The proposed solution methodology is based on an analytical-element method and thus can be easily extended to incorporate other reservoir features such as sealing or leaky faults, domains with altered petrophysical properties (for example, fluid permeability or reservoir porosity), and complicated reservoir boundaries. It is shown that the pressure behavior of discretely fractured reservoirs is considerably different from the well-known Warren and Root dual-porosity reservoir model behavior. The pressure behavior of discretely fractured reservoirs shows many different flow regimes depending on fracture distribution, its intensity and conductivity. In some cases, they also exhibit a dual-porosity reservoir model behavior.

Transient Pressure Behavior of Commingled Reservoirs

This paper presents a new general analytic formulation for pressure-transient behavior of commingled systems (layered reservoirs without crossflow). The formulation includes the effects of surface and downhole flow-rate variations and of wellbore storage resulting from the wellbore volumes location below the flow-rate measuring point (at any location in the wellbore, including the surface and sandface). The method can be applied to a variety of layered reservoirs. Each individual subzone (reservoir) in the system can be different, with different initial and outer-boundary conditions, and each zone can start to produce at a different time. The well completion for each layer can also be different. New Laplace-domain solutions are presented for partially penetrating slanted wells and partially penetrated wells with and without a gas cap. The solution for slanted wells is based on that of Cinco-Ley et al. but includes the correct effective wellbore radius for the case of an anisotropic formation. Solutions to a few selected commingled systems are also presented to explore the application of the formulation.

Deconvolution of wellbore pressure and flow rate

Determination of the influence function of a well/reservoir system from the deconvolution of wellbore flow rate and pressure is presented. Deconvolution is fundamental and is particularly applicable to system identification. A variety of different deconvolution algorithms are presented. The simplest algorithm is a direct method that works well for data without measurement noise but that fails in the presence of even small amounts of noise. The authors show, however, that a modified algorithm that imposes constraints on the solution set works well, even with significant measurement errors.

Estimation of the Permeabilities and Skin Factors in Layered Reservoirs With Downhole Rate and Pressure Data

This paper addresses the problem of estimating horizontal and vertical permeabilities, skin factor, and average fluid pressure within the drainage area in each layer in a multilayered reservoir in the presence of formation crossflow between the layers and commingling through the wellbore. A multistep testing procedure is proposed that involves downhole measurement of the pressure and fluid flow rate. The measurements are made successively above the individual layers as transients are induced in the reservoir. A history-matching procedure is used to analyze the data from the entire multistep test simultaneously. The performance of this approach is compared with that of separate, conventional interpretation of each step in five examples with synthetic data. The simultaneous analysis benefits from the synergy between the steps and consistently yields better estimates. A linearized sensitivity analysis is developed to determine the probable errors in the parameter estimates. It indicates whether a given set of measurements with a given level of measurement noise contains sufficient information to determine the individual parameters uniquely.

Solution of pressure diffusion in radially composite reservoirs

This paper presents a new general method for solving the pressure-diffusion equation in cylindrically radial composite reservoirs, where the rock and fluid properties may change radially as a function ofr. Composite systems, such as formations with wellbore filtrate invasion and reservoirs with peripheral water encroachment, can be encountered as a result of drilling, secondary oil recovery, and water influx.The new solution method utilizes the reflection and transmission concept of electromagnetics to solve fluid flow problems in three-dimensional cylindrically radial reservoirs, where heterogeneity is in only one direction. The Greens function for a point source in a three-dimensional radially composite system is developed by using the reflection and transmission method. The method as well as the point source solution are sufficiently general that they may be applied to similar fluid flow and well testing problems involving single-phase flow.The method is applied to three illustrative fluid flow problems. The first example is for a fully penetrated vertical well in a one-dimensionaln zone composite reservoir. For this example, the solutions one- and two-zone are well known. These two solutions therefore provide a test for the solution method. The second example presents a solution for the pressure distribution in ann zone radially composite reservoir due to an infinite-conductivity (permeability) vertical fracture in ther direction. For this vertical fracture case, the solutions given in the literature for a single-zone radially bounded reservoir and for a two-zone radially unbounded reservoir are incorrect. The third example provides a new solution for a partially penetrated (limited entry) well in a radially composite reservoir. The solutions for all three examples are presented in the Laplace transform domain; therefore the wellbore storage and skin effects can easily be included.