Because of the relatively heavy oil (8 - 12 deg. API) encountered in many naturally fractured reservoirs, thermal recovery processes could be viable recovery techniques to produce oil from these reservoirs. To facilitate the simulation of these processes, a simulator to model thermal effects in naturally fractured reservoirs has been developed. The model uses the double porosity concept and is three dimensional, three phase, and compositional. It allows the rock matrix block to be subdivided into a two-dimensional (r-z) grid block in order to study effects of gravity, capillary pressure, and mass and energy transfer between fractures and matrix blocks. The simulator is fully implicit and has a coupled wellbore mathmatical formulation, and simultaneously solves the unknowns for fractures and matrix blocks. An efficient solution procedure is implemented so that the cost of modelling naturally fractured reservoirs is not significantly greater than the cost of conventional single porosity thermal simulation. An example, steam injection into a five-spot pattern, is included to illustrate the significant effects of physical properties and model construction. Oil recovery predictions are sensitive to capillary pressure values, the number of cells used to divide the matrix block, and the size of the matrix blocks. Introduction The numerical simulation of fluid flow in naturally fractured reservoirs, which consists of interconnected fractures and discontinuous matrix blocks, has progressed significantly in the pass few years since the dual porosity concept was developed by Barenblatt et al. and introduced to the petroleum industry by Warren and Root. The dual porosity concept assumes that a fracture system and a matrix system occupy the same computational grid block, Field scale fractured reservoir simulator development has progressed in several areas. Specifically there have been improvements in (a) representation of fluids in the reservoir, (b) modelling of fluid flow between fractures and matrix blocks, (c) modelling of fluid flow between matrix blocks in adjacent computational grid blocks, and (d) discretization of the matrix block. The single-phase flow equations derived by Warren and Root were extented by Kazemi et al. to the two-phase flow equations which included capillary and gravity forces. Kazemi's three-dimensional numerical simulator was used to model water drive in a five-spot pattern and a five-well reservoir. That simulator can handle uniformly or nonuniformly distributed fractures and also handle no fractures at all in the reservoir. In 1983, Thomas et al., Gilman and Kazemi, and Saidi developed fully implicit threedimensional, three-phase, fractured reservoir simulators. In order to account for the effects of gravity on the matrix/fracture flow term, various approaches were presented in these papers. Thomas et al. used pseudo-relative permeability and capillary pressure curves for both the matrix and fracture. Gilman and Kazemi proposed to assign different depths for the matrix and fracture within a computation grid. P. 169^
Fluid crossflow can significantly affect sweep efficiency in heterogeneous reservoirs. The importance of fluid crossflow relative to purely longitudinal convective transport in a twodimensional setting depends on several factors. Rock properties such as porosity, permeability, the ratio of vertical to horizontal permeability, and length scale of correlation are important factors. Fluid properties such as phase densities, phase viscosities, and interfacial tension are also factors. Coupled rock-fluid properties, for example, wettability, relative permeabilities, and capillary pressure are also factors. In addition to these factors, flow velocity, system dimensions, and boundary conditions also affect sweep efficiency. In this paper we examine the role of capillary forces, in addition to viscous and gravity forces, on sweep efficiency of immiscible displacements in a heterogeneous porous medium. A fully implicit, black oil, reservoir simulation model was used to compute displacement performance in two-dimensional, fine-grid (x-z) cross-sections. The results presented in this paper clearly show the importance of capillary crossflow as a recovery mechanism, in addition to viscous and gravity crossflow, in displacements in heterogeneous reservoirs.
Brown-field Experimental Design (ED) was successfully applied to a super-giant oilfield to generate probabilistic (P10, P50, and P90) models to define the range of field performance and to mitigate the non-uniqueness in reservoir simulation. A recent trend in reservoir simulation has been to apply probabilistic modeling, such as, brown-field ED to develop multiple (P10, P50, and P90) models. Unfortunately, these probabilistic models are also non-unique because multiple input combinations can be used to generate the probabilistic responses observed during ED.The non-uniqueness of the probabilistic models may impact their usefulness in certain circumstances. For example, if these models are used to develop short-term signposts for long-term reservoir behavior, then the models may be influenced by the selection of reservoir data (e.g., a P10 model with one combination of input may have a different short-term "signature" than an alternate P10 model despite giving comparable P10 recovery). Also, the degree of success of a downside-mitigation (or upside-capture) strategy, and its ranking with other such strategies may be influenced by the input chosen to develop the models.For the super-giant Tengiz oilfield, brown-field ED was applied to a conventional history match with the primary objective of creating probabilistic models. Additionally, we developed tools to design multiple deterministic models with specific physical interpretations. With these deterministic models we can identify the signatures for specific reservoir phenomenon, such as, minimum/maximum OOIP, minimum/maximum compartmentalization, minimum/maximum reservoir energy, etc. All models built with these tools yield acceptable visual and quantitative history matches.In this paper we discuss how brown-field ED was used to post-process a conventional history match. We present a case study for the use of brown-field ED methods and illustrate the proposed approach to mitigate the non-unique nature of reservoir simulation. While the impact non-uniqueness can be mitigated, we also recognized that it can never be completely eliminated. 2 SPE 159341 Yuzhnaya Guryev Arch Tengiz Korolev 50 km Isolated Carbonate Platforms
Summary We developed a physics-based data-driven model for history matching, prediction, and characterization of unconventional reservoirs. It uses 1D numerical simulation to approximate 3D problems. The 1D simulation is formulated in a dimensionless space by introducing a new diffusive diagnostic function (DDF). For radial and linear flow, the DDF is shown analytically to be a straight line with a positive or zero slope. Without any assumption of flow regime, the DDF can be obtained in a data-driven manner by means of history matching using the ensemble smoother with multiple data assimilation (ES-MDA). The history-matched ensemble of DDFs offers diagnostic characteristics and probabilistic predictions for unconventional reservoirs.
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