Regional Upscaling: A New Method To Upscale Waterflooding in Heterogeneous Reservoirs for a Range of Capillary and Gravity Effects
- C. Coll (PDVSA S.A.) | A.H. Muggeridge (Centre for Petroleum Studies, Imperial College, London) | X.D. Jing (Centre for Petroleum Studies, Imperial College, and Shell Intl.)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2001
- Document Type
- Journal Paper
- 299 - 310
- 2001. Society of Petroleum Engineers
- 5.5 Reservoir Simulation, 5.1.1 Exploration, Development, Structural Geology, 5.5.3 Scaling Methods, 1.6.9 Coring, Fishing, 4.3.4 Scale, 5.1 Reservoir Characterisation, 5.7.2 Recovery Factors, 1.2.3 Rock properties, 5.4.1 Waterflooding, 5.1.5 Geologic Modeling
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This paper presents a new, two-phase upscaling methodology hereafter referred to as "regional" upscaling. A fine-grid flow simulation is performed on a representative section of the reservoir. Dimensionless numbers are then calculated for each fine-grid cell to determine the dominant flow regime in that cell. The coarse grid is selected based upon the spatial locations of the different force regimes observed in the fine-grid simulation model. Two-phase upscaling is then performed from the fine to the coarse grid using the most appropriate pseudoization technique [Kyte and Berry or vertical equilibrium (VE)] for the dominant flow regime in each region. The method is compared with different global pseudoization methods and its accuracy examined for a range of different heterogeneity models, including one for a reservoir in Lake Maracaibo in western Venezuela.
Waterflood sweep efficiency is a function of the prevailing flow regime and the reservoir heterogeneity. Recent work has shown that different styles of reservoir heterogeneity (fluvial, wave-dominated, and tidal) affect oil recovery in different ways and that all length scales of heterogeneity have a significant impact on oil recovery.1-6 However, small-scale heterogeneities cannot be represented explicitly in field-scale simulation models because of limitations in computer speed and memory. Therefore, effective permeabilities7 and pseudorelative permeabilities8 are used to represent the average effects of small-scale heterogeneity on the large-scale flow.
Although single-phase upscaling is fairly well understood,7 this is not the case for two-phase upscaling. Many different methods for developing pseudorelative permeabilities are reported in the literature,8 and it appears that the best pseudoization method to use for a particular problem will depend upon the flow regime. For example, vertical equilibrium will apply for gravity-9 or capillary gravity-10 dominated displacements; steady-state pseudos11 can be used for capillary-dominated flows, and dynamic methods are usually used for viscous-dominated flows.8,12,13 In homogeneous reservoirs, the dominant flow regime can be determined from examination of the relevant dimensionless numbers.14-16
In heterogeneous reservoirs, the flow rate will vary with permeability, so different flow regimes may prevail in different parts of the reservoir. In these circumstances, the overall flow regime determined from dimensionless numbers using effective properties and mean flow rates may not actually be the dominant flow regime in the reservoir. If two-phase upscaling techniques are then selected based on the values of these "global" dimensionless numbers, this may result in incorrect flow modeling on the large scale.
A new concept of "local" dimensionless numbers is presented to help determine local flow regimes in heterogeneous reservoirs. Based on these conditions, we can derive what we may call "force maps," which describe the dominant forces operating in different parts of the reservoir. This information can then be used to select the best coarse-grid model for upscaling and the most appropriate upscaling technique for the heterogeneity/flow regime in question.
The method is applied to a series of synthetic models of small-scale heterogeneity, typical of a range of depositional environments. It is then tested on a sector model of a reservoir in western Venezuela's Lake Maracaibo Basin with very promising results.
Global Dimensionless Numbers
The relative importance of viscous, capillary, and gravity forces on reservoir flow is usually characterized in terms of the gravity-to-viscous ratio, Ngv, and the capillary-to-viscous ratio, NPcv. There are many different definitions of these dimensionless numbers reported in the literature.14-16 In this paper we shall use those derived by Shook et al.16
where Kx, UT, ?0r0, ??, H, L, f, s, and a are, respectively, absolute permeability in the x direction, total fluid velocity, the endpoint mobility of the oil phase, fluid density difference, reservoir thickness, reservoir length, porosity, interfacial tension, and dip angle.
The standard procedure to estimate which forces are controlling the flow in heterogeneous reservoirs has been to estimate each of the numbers (NPcv and Ngv) using effective properties for the entire reservoir. From Eqs. 1 and 2 we see that these numbers are dependent on various parameters that can vary spatially within the reservoir - permeability, the endpoint oil mobility, and interfacial tension. These in turn will cause nonuniform flow rates (over and above any geometrical effects due to well positions) across the reservoir.
It is clear that in heterogeneous reservoirs, the dominant flow regime will vary across the reservoir. As a result, it is likely that water breakthrough time and overall recovery will not just be a function of Ngv and NPcv, but will also depend upon the style and magnitude of heterogeneity within the reservoir. We shall demonstrate that this is indeed the case using 2D models of different types of small-scale heterogeneity.
Heterogeneity and Recovery
Three different sedimentary structures and facies related to shallow marine, coastal, and continental depositional environments were selected as base examples to study the relationship between small-scale heterogeneity and flow regime: bioturbated, parallel lamination with bioturbation, and horizontal laminae.
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