# title
Streamline simulation: A technology update

# abstract
<jats:p>Distinguished Author Series articles are general, descriptive representations that summarize the state of the art in an area of technology by describing recent developments for readers who are not specialists in the topics discussed. Written by individuals recognized to be experts in the area, these articles provide key references to more definitive work and present specific details only to illustrate the technology. Purpose: to inform the general readership of recent advances in various areas of petroleum engineering.</jats:p>                <jats:sec>                   <jats:title>Introduction</jats:title>                   <jats:p>Streamline and streamtube methods have been used by the oil industry for several decades. In recent years, there has been an increased interest in the technology. This is primarily driven by two factors. First, with the developments in reservoir characterization, we can now routinely generate high-resolution reservoir models consisting of multi-million cells. This has resulted in a gap between geologic modeling and flow simulation. Second, with increased model resolution, there is an increased acknowledgment of uncertainty. We are interested in assessment of uncertainty in reservoir description and performance prediction with multiple "plausible" reservoir models. Conventional numerical simulators often are inadequate to satisfy these needs in a timely fashion.</jats:p>                   <jats:p>The primary advantages of streamline methods are faster computation, improved accuracy (subgrid resolution and reduced numerical dispersion and grid-orientation effects), ability to screen highly detailed geologic models, quantitative flow visualization, and rapid history matching or production-data integration into high-resolution reservoir models. The speed and versatility of the method have led to many novel applications. The disadvantages of streamline models are the difficulties in incorporating complex physical processes and cross-streamline mechanisms. Streamline models are not a substitute for conventional grid-based simulators but can play an important role in bridging the gap between geologic modeling and flow simulation.</jats:p>                </jats:sec>                <jats:sec>                   <jats:title>Background</jats:title>                   <jats:p>Today's streamline simulation was preceded by at least four other methods for modeling convection-dominated flow in the reservoir. Line-source/sink methods have been widely used by the petroleum industry.1,2 These methods use analytic solutions to the pressure and velocity distribution in the reservoir. The primary limitation of these methods is the requirement for homogeneous properties and constant reservoir thickness. Streamtube methods are more general and have been applied successfully for field-scale modeling of waterflooding and miscible flooding.35 In these methods, the flow domain is divided into a number of streamtubes and fluid-saturation calculations are performed along these streamtubes. However, the need to keep track of the streamtube geometries can become quite cumbersome in three dimensions. Thus, most applications of streamtube methods have been limited to two dimensions or some form of hybrid approaches to account for 3D effects. Particle-tracking methods have been used by the oil industry to model tracer transport in hydrocarbon reservoirs and also for groundwater applications.6 These methods track the movement of a statistically significant collection of particles along appropriate path lines; while they generally work well near steep fronts, they do not work as well for smooth profiles. Another drawback is the loss of resolution of the front with the progression of time and the statistical variance in the concentration response. Finally, front-tracking methods introduce fluid fronts (interfaces) as a degree of freedom in the computation.7,8 The primary limitations of these methods are the computational burden associated with complications that arise from the close approach or intersection of frontal contours.</jats:p>                   <jats:p>Although current streamline technology uses many of the concepts from the past, it has some new elements. We can now conduct simulations in 3Dheterogeneous media. This has been greatly facilitated by the introduction of the streamline "time-of-flight" concept that has eliminated the need to keep track explicitly of the streamtube geometry.9,10 The time of flight is simply the travel time of a neu-tral tracer along streamlines. A key underlying concept in streamline simulation is decoupling the effects of geologic heterogeneity from transport (saturation) calculations. This decoupling is accomplished by use of the streamline time of flight as a coordinate variable.9 The impact of geologic heterogeneity is embedded in the streamline time of flight. Furthermore, in the time-of-flight coordinate, the multidimensional saturation equations are reduced to a series of 1Dcalculations along streamlines, which greatly facilitates saturation computations because they are now decoupled from the underlying geologic grid. Currently, such calculations are sufficiently general to model time-varying velocity fields, compressible flow, gravity, and nonuniform conditions such as those arising from infill drilling and pattern conversions.1114Ref. 15, a review paper, provides a comprehensive list of references on streamline simulation.</jats:p>                </jats:sec>                <jats:sec>                   <jats:title>Method</jats:title>                   <jats:p>Streamline simulators approximate 3D fluid-flow calculations by a sum of 1Dsolutions along streamlines. The choice of streamline directions for the 1Dcalculations makes the approach extremely effective for modeling convection-dominated flows in the reservoir. This is typically the case when heterogeneity is the predominant factor governing flow behavior.</jats:p>                </jats:s