Advancement of sweep zones in waterflooding: conceptual insight based on flow visualizations of oil-withdrawal contours and waterflood time-of-flight contours using complex potentials

Abstract

Sweep zones are traced in synthetic reservoir models of waterflood advancement based on potential functions. Time-of-flight contours, oil-withdrawal contours and streamlines corresponding to fluid withdrawal paths are visualized. The effects of differential well rates on waterflood sweep regions for a range of well architectures are systematically investigated using reservoirs that are continuous isotropic with and without impervious fault barriers. Complex potentials are capable of solving the drainage path for any constellation of producer and injection wells, accounting for any discontinuities that affect the flow path and productivity of the wells. Flood patterns are visualized for a series of doublets and 7-spot well patterns. Loss of planned drainage symmetry occurs when an undiscovered fault barrier obstructs and diverts the waterflood. Our method is assumed effective in illustrating the value of analytical streamline simulations for first-order assessment of sweep patterns in hydrocarbon field produced with waterflooding. The critical impact of injection rates and fault barriers on the shape of the waterflooding patterns is visualized in detail. The analytical streamline simulator allows tracing of the respective flow paths of displacing oil and water in the reservoir and visualizes both oil-withdrawal contours and waterflood time-of-flight contours. Generic rules are formulated to aid sweep maximization both prior to drilling and during the surveillance of producing wells. Keywords Reservoir simulations Á Complex potentials Á Improved oil recovery Á Flood management Á Well surveillance Abbreviations AEM Analytical element method b Fault orientation angle d Distance of well pair in doublet Dt Time step EOR Enhanced oil recovery FD Finite difference K Permeability K Number of injectors l Fault half-length d s Conformal mapping angle MLA Multivariate lower algorithms h Reservoir thickness m s Well strength n Number of producers Q p Flux of producer Q i Flux of injector RF Recovery factor t Runtime V(z) Velocity field WAF Well allocation factor z Complex variable * Non-dimensional form of asterisked parameter

Rules for Flight Paths and Time of Flight for Flows in Porous Media with Heterogeneous Permeability and Porosity

“…Several studies have been completed by us applying streamline solutions to a variety of geothermal and hydrocarbon production systems, including the optimization of well locations and well production rates in order to obtain maximum water sweep across oil drainage volumes [13,42,55,56]. For example, Weijermars et al [13] studied the sweep efficiency of a line drive scheme for five injectors and five producers under different permeability and porosity distributions.…”

“…In accordance with our current study, the flow will converge and run faster through some higher permeability zones, so that an optimization plan for injection rate was designed to even the water front for five different injectors to achieve the maximum sweep efficiency. Weijermars and van Harmelen [56] studied the advancement of sweep zones in waterflooding for reservoirs with impermeable faults. The effect of such faults is equivalent to a zone with infinitely low permeability, which will cause the streamline trajectories to detour around the fault.…”

Shale Reservoir Drainage Visualized for a Wolfcamp Well (Midland Basin, West Texas, USA)

“…The closed-form solution is commonly used to map curvilinear line-integrals to identify streamlines [77,78]. Our novel approach using complex analysis methods has been applied to fluid flooding and sweeping of hydrocarbon reservoirs with finite boundaries [6] and infinite boundaries [79,80]. Investigations of how hydraulic fractures drain the matrix in shale reservoirs are also possible using our method for streamline simulation and fluid time-of-flight tracing based on complex analysis methods.…”

“…Likewise, flow toward a vertical producer wellbore is represented by a point sink (Figure 2b). The corresponding velocity field is given by [79,80]:…”

Delineation of reservoir lateral continuity for flow zones in wells using cluster analysis: Case of West Baram Delta, offshore-Sarawak

“…*Reservoir lateral extent is crucial for successful implementation of any enhanced oil recovery (EOR) methods for effective areal sweep efficiency between injection and production wells during recovery in the field (Weijermars and van Harmelen, 2017). It described that the spatial and temporal variations in reservoir petrophysical properties (porositypermeability) distribution has an enormous effect on successful implementation of any EOR methods in the field (Ebanks, 1987).…”