A new 3-D three phase compositional reservoir simulator based on extension of the streamline method has been developed. This paper will focus on the new methods developed for compositional streamline simulation as well as the advantages and disadvantages of this strategy compared with more traditional approaches. Comparisons with a commercially available finite difference simulator will both validate the method and illustrate the cases in which this method is useful to the reservoir engineer. Introduction Streamline methods have been used as a tool for numerical approximation of the mathematical model for fluid flow since the 1800's (Helmholtz28 and later Muskat45) and have been applied in reservoir engineering since the 1950's and 1960's19,29–31,21,57. The reason behind using the approach has been both the needs for solving the governing equations accurately and achieving reasonable computational efficiency. Streamline methods continued to be explored through the 1970's by LeBlanc and Caudle37, Martin et al40,41 and Pitts et al50 and 1980's by Lake et al36,70, Cox11, Bratvedt et al8 and Wingard et al71, but the focus of reservoir simulation was on developing finite difference simulators. In the 1990's streamline methods have emerged as an alternative to finite difference simulation for large, heterogeneous models that are difficult for traditional simulators to model adequately. These efforts are described in numerous papers notably by Renard56, Batycky et al1–4, Peddibhotla et al48,49, Thiele et al64–66, Ingebrigtsen33, Ponting52 and in an overview paper by King and Datta-Gupta35. The application of the method has been described by numerous other authors10,12–17,26,34,53–55,69. Use of the streamline simulator used for the work in this paper has also been extensively described24,39,42,47,58,61,62,68. Several similar approaches such as the method of characteristics18,27,38,43,44, particle tracking20,63 and front-tracking25,7 have also been used in reservoir simulation. Conventional finite difference methods suffer from two drawbacks, numerical smearing and loss of computational efficiency for models with a large numbers of grid cells. Large models (105 –106 cells) are routinely generated in order to accurately represent geologically heterogeneous, multi-well problems.. Finite difference methods based on an IMPES approach suffer from the time step length limiting CFL condition, so as the number of cells increases the maximum time step length get shorter for a given model. For a large number of cells the shortness of the time step can render the total CPU time for a simulation impractical. Fully implicit finite difference simulators can take longer time steps but require the inversion of a much larger matrix than the IMPES approach. This is an even larger issue with compositional simulation where a large number of components will make the matrix very large. Also the non-linearity of the governing equations might require a limitation on the time step length again making very large models impractical to run. This can be improved by using an adaptive implicit aproach73. Conventional streamline methods are based on an IMPES method. In these methods the pressure is solved implicitly and then streamlines are computed based on this pressure solution. In this way the 3D domain is decomposed into many one-dimensional streamlines along which fluid flow calculations are done. This method assumes that the pressure is constant throughout the movement of fluids. One weakness with this concept is the lack of connection between the changing pressure field and the movement of fluids. This can cause instabilities and limitations on the time step length.

Because of increased speed and accuracy, 3D streamline simulation now can be used in a wide range of reservoirs. Large reservoirs with hundreds or thousands of wells, several hundred thousand grid blocks and an extensive production history always have been a challenge for finite-difference simulation. The size and complexity of these reservoirs generally have limited simulation to sections or patterns. The streamline technique enables simulation of these reservoirs by reducing the 3D domain to a series of 1D streamlines along which the fluid flow computations are performed, offering computational benefits orders of magnitude greater. Additionally, increased accuracy is achieved by maintaining the sharp flood fronts from the displacement processes and reducing grid orientation effects. The streamline simulation results substantially have more value as a reservoir management tool when used in conjunction with traditional reservoir engineering techniques such as standard finite-difference simulators. Several case studies that highlight a variety of situations where streamline methods proved highly beneficial are presented in this paper. These studies will help the practicing reservoir engineer decide whether to apply streamline methods and the optimal timing for the application. Introduction Streamline and streamtube methods have been used in fluid flow computations for many years31,48. Early applications for hydrocarbon reservoir simulation were reported by Fay and Pratts22 in the 1950's, Higgins et al32–34 in the early 1960's, and Pitts and Crawford53, LeBlanc and Caudle41 and Martin and Wegner et al43,44 in the 1970's. Streamline/streamtube methods numerically solve the complex fluid flow models for multiphase flow in porous media with a reasonable balance between the computational efficiency and the physics modeled. As computers became more powerful, attention turned toward developing simulators based on finite-difference (FD) methods60, including more physical effects. However, computer models of reservoirs have grown in complexity and geological models with tens of millions of grid cells can now be created. Conventional finite-difference methods suffer from two drawbacks, numerical smearing and computational efficiency for models with a large numbers of grid cells. For models with a large number of wells, the number of cells required to achieve acceptable accuracy between wells can be prohibitive. Also, accurate modeling of geological heterogeneities can require a very large number of cells. A finite-difference method based on an IMPES approach suffers from the time-step length limiting Courant-Friedrichs-Lewy (CFL) condition. As the number of cells grows higher, the maximum time-step length gets shorter for a given model. For a very large number of cells, the shortness of the time step can render the total CPU time impractical for a simulation. The advantage of the fully implicit approach is stability of the solutions. The time-step length is only limited by the nonlinearities; however, these can be strong and, in practice, keep the time-step length relatively short. A disadvantage of the fully implicit approach is the tendency to smear the solution (numerical dispersion) even more than the IMPES approach.

This paper presents a new numerical method for solving saturation equations without stability problems and without smearing saturation fronts. A reservoir simulator based on this numerical method is under development. A set of test problems is used to compare the simulation results of the new simulator with those of an existing flnite-difference simulator (FDS).

Advances in reservoir characterization and modeling have given the industry improved ability to build detailed geological models of petroleum reservoirs. These models are characterized by complex shapes and structures with discontinuous material properties that span many orders of magnitude. Models that represent fractures explicitly as volumetric objects pose a particular challenge to standard simulation technology with regard to accuracy and computational efficiency. We present a new simulation approach based on streamlines in combination with a new multiscale mimetic pressure solver with improved capabilities for complex fractured reservoirs. The multiscale solver approximates the flux as a linear combination of numerically computed basis functions defined over a coarsened simulation grid consisting of collections of cells from the geological model. Here, we use a mimetic multipoint flux approximation to compute the multiscale basis functions. This method has limited sensitivity to grid distortions. The multiscale technology is very robust with respect to fine-scale models containing geological objects such as fractures and fracture corridors. The methodology is very flexible in the choice of the coarse grids introduced to reduce the computational cost of each pressure solve. This can have a large impact on iterative modeling workflows.

No abstract