Academic literature on the topic 'Finely-gridded'

Abstract Full-field EOR performance predictions are generally obtained from scale-up tools, since three-dimensional finite-difference simulations would be too CPU intensive. Existing scale-up techniques require the user to define pattern elements and then to derive performance curves to apply to each injector-producer pair in the elements. Accurate assignment of these elements is difficult because the actual shape and size of the swept volumes are sensitive to reservoir faulting, well rate changes, and regional flux. In reality, the actual sweep region is not an input parameter, but should be determined by the regional pressure field which changes as well rates vary and new wells are drilled. Thus, a major source of error in using existing scale-up tools is trying to define representative pattern elements. In the current paper, we describe a scale-up technique in which the user does not have to define pattern elements or injector-producer pairs. In the new technique, the pressure field is computed at each time step and then a front-tracking algorithm propagates water and miscible injectant throughout the reservoir. By using an analogy between oil mobilization and adsorption/desorption of tracers, the miscible-gas process is modeled. The parameters for the model are obtained by fine-scale, two-dimensional, compositional, finite-difference simulations in a vertical cross-section. In the new approach, the injected solvent is divided into an effective and an ineffective portion. This approach reduces a three-dimensional problem to a two-dimensional, areal one in which the declining displacement efficiency of the solvent, which is caused by vertical effects, is captured by decreasing the injected concentration of effective solvent with time. In this paper, we show how the new scale-up tool has been used to model the miscible WAG process in the Eastern Peripheral Wedge Zone of the Prudhoe Bay field. We show a comparison between field response and model predictions. Introduction Good reservoir management requires the prediction of reliable oil and gas rates. In general, the degree of difficulty in making these predictions depends on the displacement process. For example, good predictions of primary depletion or gravity drainage by gas-cap expansion can usually be obtained by coarsely gridded finite-difference simulations. However, processes where injected water or gas must be tracked from injector to producer typically require finely-gridded simulations. Accurate prediction of oil and gas rates frequently require finely gridded simulations which contain (1) rock-measured relative permeabilities and (2) a reservoir description that accurately predicts high-permeability zones (thieves) and low-permeability barriers (e.g., shale location, size, and continuity). At Prudhoe Bay, modeling of miscible gas processes generally requires vertical grid blocks of the order of one foot to match field-measured saturation profiles. At the present time, three-dimensional, compositional modeling of gas displacement processes that satisfy these two requirements require at least a week of CPU time on IBM-590 workstation for a single pattern. Thus, it is not currently practical to use finely gridded finite-difference simulators to model large sections of a field. Traditionally, three approaches have been used to address this problem -- pseudo relative permeabilities, tank models, and streamtubes. Pseudo relative permeabilities are generally successful only when the saturation history experienced in the coarse-grid simulation will always be similar to the fine-grid simulation. Tank models can be difficult to apply when the original pattern changes by infill drilling or well conversions, and streamtube models have had difficulty when the initial conditions are not homogeneous along each streamline. To address the above problems, a new approach was created that can reproduce the response and timing characteristics of the produced components, but also has the ability to propagate and track injected fronts. In addition, the model does not require user-supplied injector-producer allocation factors. We explain, below, our new front-tracking technique and how this new scale-up tool has been used to model the miscible WAG process in the Eastern Peripheral Wedge Zone of Prudhoe Bay. P. 329

AbstractWe present first efforts to establish a network of absolutely calibrated continuous infrared spectra of standard stars across the 1-35μm range in order to calibrate arbitrary broad and narrow passbands and low-resolution spectrometers from ground-based, airborne, balloon, and satellite-borne sensors. The value to photometry of such calibrated continuous spectra is that one can integrate arbitrary filters over the spectra and derive the stellar in-band flux, monochromatic flux density, and hence the magnitude, for any site. This work is based on new models of Sirius and Vega by Kurucz which were calculated by him, for the first time, with realistic stellar metallicities and a customized finely-gridded infrared wavelength scale. We have absolutely calibrated these two spectra and have calculated monochromatic flux densities for both stars, and isophotal wavelengths, for a number of infrared filters. Preliminarily, the current IRAS point source flux calibration is too high by 2, 6, 3, and 12% at 12, 25, 60, and 100μm, respectively.

Summary A study using full-field reservoir modeling optimized the design of a miscible CO2 flood project for the Sharon Ridge Canyon Unit. The study began with extensive data gathering in the field and building a full-field three-dimensional geologic model. A full-field simulation model with relatively coarse gridding was subsequently built and used to history match the waterflood. This waterflood model highlighted areas in the field with current high oil saturations as priority targets for CO2 flooding and generated a forecast of reserves from continued waterflooding. Predictions for the CO2 flood used an in-house four-component simulator (stock tank oil, solution gas, water, CO2. A full-field CO2 model with more finely gridded patterns was built using oil saturations and pressures at the end of history in the waterflood model. The CO2 model identified the best patterns for CO2 flooding and was instrumental in selecting a strategy for sizing the initial flood area and in determining the size, location, and timing of future expansions of the CO2 flood. Introduction The Sharon Ridge Canyon Unit (SRCU) is located in West Texas, about 70 miles northeast of the city of Midland. The Unit covers 13,712 acres. Fig. 1 shows the Horseshoe Atoll, a trend of more than 40 oil fields covering several West Texas counties. SRCU is geologically continuous with the Diamond M Unit and the giant Kelly-Snyder Field (SACROC Unit) to the northeast. Production is from the Canyon Reef formation, a thick carbonate buildup of late Pennsylvanian Canyon and Cisco age, and occurs at an average depth of 6600 feet. There are active CO2 floods in this formation at SACROC, Reinecke, and the Salt Creek field. Sharon Ridge was discovered in 1949 and developed on 40 acre spacing by 1953 with about 340 wells. The reservoir initially contained undersaturated oil at 3135 psi. Production was by expansion drive until 1952 when pressure fell below the bubble point of 1850 psi over most of the field. In 1955, the field was unitized and a peripheral waterflood was started to stabilize reservoir pressure. The waterflood is now at a mature stage with oil recovery approaching 50% of the original oil-in-place (OOIP). There has been limited infill drilling with 22 wells drilled at 20-acre spacing. Screening studies identified SRCU as a good candidate for a miscible CO2 flood project. These studies included core flood displacements, pattern element simulation models, and detailed evaluations of similar fields with CO2 floods. Laboratory core displacements showed a remaining oil to waterflood of over 40% with subsequent injection of CO2 reducing oil saturation to less than 10%. Simulations with small element models have also shown significant incremental oil recovery from injection of CO2 at SRCU. SRCU has reservoir properties similar to SACROC which has reported significant additional oil recovery from miscible CO2 flooding (Ref. 1). The goal of full-field modeling was to design a miscible CO2 flood with maximum economic potential. Key issues for project design include the amount and location of remaining oil, reservoir sweep efficiency, flood rate, gas injection volume, strategy for handling increased produced gas, and projection of continued secondary operations. To address these issues, we built three different full-field three-dimensional (3D) models: geologic model, coarse-grid waterflood model, and fine-grid CO2 flood model. Recent advances in computer technology made this approach possible as opposed to the prior approach of running type-element models and scaling up those results to field rates. The approach of using field-scale simulation models to study optimizations for another CO2 flood in West Texas has been reported in Ref. 2. Thus, advancing technology and prior experience led us to embark on this ambitious approach to use full-field modeling to design our CO2 flood. Geologic Modeling Geology. The reservoir is a thick carbonate buildup that is predominately limestone. Fig. 2 shows the structure on the top of the reservoir. Geographic areas of the field have been named: North End, South End, and Southeast Pinnacle. The topography is extremely variable, with the hydrocarbon column averaging 115 feet and ranging to a maximum of 450 feet in the South End area of the field. A large portion of the North End has over 90 feet of gross reservoir thickness above the original oil-water contact. Table 1 is a summary of reservoir rock and fluid properties. The reservoir has been subdivided into five depositional sequences or zones, four of which are shown in Fig. 3. The lower zones (4, 5) are found over almost the entire field while upper zones (1, 2, 3) are more areally restricted. Zones are usually separated by intervals of low porosity limestone with few shales in the reservoir. Most wells drilled during initial field development did not penetrate the entire reservoir, thus limiting description of the lower zones. A more detailed discussion of the geologic setting and depositional facies is available in Ref. 3. Model Design. Building a full-field 3D geologic model of SRCU presented several unique challenges, including having modern porosity logs on only a few wells and only 90 full penetrations of the reservoir. To address this problem of limited data, an extensive data acquisition program was implemented. This program included deepening 19 wells, coring 11 wells, and obtaining 49 miles of new two-dimensional (2D) seismic lines. After gathering these data, all new and old core, well log, and seismic data were integrated to develop a sequence stratigraphic reservoir framework.

Summary The shape factor concept, originally introduced by Barenblatt in 1960, provides an elegant and powerful upscaling method for fractured reservoir simulation. The shape factor determines the fluid and heat transfer between matrix and fractures when there is a difference in pressure or temperature between matrix blocks and the surrounding fractures. An appropriate specification of the shape factor is therefore critical for accurate modeling. Since its introduction, many different values for the shape factor have been proposed in the literature, among which the well-known Warren-Root and Kazemi shape factors. The aim of this paper is to show that the selection of the appropriate shape factor should not only depend on the "shape" and dimensions of matrix blocks, but should also take into consideration the character of the dominant underlying physical recovery mechanisms. We will show that by taking into account the dominant physical recovery mechanism, the apparent discrepancies in the shape factor values reported in the literature can be overcome. We derive a general expression for the shape factor that not only captures existing shape factor expressions, but also allows extensions to recovery mechanisms requiring a dual permeability approach. The paper is organized as follows. First, we briefly review the shape factors presented in the literature. We then derive the general expression for the (single-phase) matrix-fracture shape factor. Subsequently, we analytically derive a new shape factor that captures the transient in pressure/temperature diffusion processes. To compare and contrast the impact of the various shape factors, we consider three cases of increasing complexity. First, we consider pressure/temperature diffusion in a single 1D matrix block following a step change in the boundary conditions. Next, we consider isothermal gas/oil gravity drainage from a homogeneous stack. We compare fine-grid single-porosity simulations (in which the matrix is finely gridded and in which the fractures are explicitly represented) with coarse-grid dual-permeability simulations (in which the matrix-fracture interaction is modeled by shape factors). In the third step, we consider gas-oil gravity drainage of the same stack model, but now under steam injection. In this case, steam is injected at the top, and oil recovered from the base of the fracture system. Again, we compare fine-grid single-porosity simulations with coarse-grid dual-permeability simulations. We show that in this case, the constant (asymptotic) shape factor provides a good approximation to the heating of the stack. We will show, however, that with a constant (time-independent) shape factor, the initial fast heating of the matrix blocks cannot be captured. We show that the new transient shape factor, however, enables coarse-grid dual-permeability modeling of thermal recovery processes such that they reproduce fine-grid results. Introduction The modeling of matrix-fracture interaction using shape factors has been an active area of research for over 40 years now, and has attracted considerable attention both in the context of single- and multi-phase matrix-fracture modeling (Barenblatt et al. 1960; Warren and Root 1963; Kazemi et al. 1976; Thomas et al. 1983; Coats 1989; Ueda et al. 1989; Zimmerman et al. 1993a; Chang 1993; Lim and Aziz 1995; Gilman and Kazemi 1983; Beckner et al. 1987, 1988; Rossen and Shen 1989; Bech et al. 1991; Bourbiaux et al. 1999). In their 1960 landmark paper, Barenblatt et al. introduced the shape factor concept to model the (single-phase) fluid transfer between matrix and fractures (1960). The central idea of Barenblatt et al. was not to study the behavior of individual matrix blocks and their surrounding fractures, but instead to introduce two abstract interacting media: one medium, the "matrix," in which the physical matrix blocks are lumped, and one medium, the "fractures," in which the fractures are lumped. Whenever a pressure difference exists between the matrix and the fractures, a fluid flow between the media will occur. The shape factor is then defined by the following relation, which ties the (single-phase) matrix-fracture fluid flow to the instantaneous pressure difference between matrix and fractures:q = s (km / µ) V (p*m - pf), ....[ EQ. 1 ] where V denotes the volume of the matrix block. In 1963, Warren and Root used Barenblatt's shape factor concept in the context of well-testing using dual porosity models. They postulated shape factors for 1-, 2-, and 3D matrix blocks, as given in Table 1. In 1976, Kazemi et al. proposed different shape factors, which were derived using a finite-difference discretization. Kazemi et al. also postulated the generalization of the shape factor concept from single- to multiphase flow by introducing the phase relative permeability into Eq. 1. Thomas et al. (1983) found that they could accurately reproduce fine-grid single-porosity simulation results of water/oil countercurrent imbibition (in cubical blocks) if in their single-cell dual-porosity model they used a shape factor 25 / L2. In their dual-porosity simulation, however, they also used pseudorelative permeability curves and a pseudocapillary pressure, so it is not obvious whether the good fit was mainly caused by the shape factor they used, or by the pseudosaturation functions. Coats reported that the shape factor proposed by Kazemi is too low by a factor of 2, and derived new 1-, 2-, and 3D shape factors (1989); see Table 1. Ueda et al. (1989) also argued that the Kazemi shape factor should be multiplied by a factor 2 to 3, based on their work in which they compared dual porosity (two-phase) simulations with 1- and 2D fine-grid simulations. In 1993, Zimmerman et al. published a semi-analytical method for modeling of matrix-fracture flow in a dual-porosity model where the matrix blocks are modeled as spherical blocks (1993a). In their paper, they also show that the shape factor for spherical matrix blocks is given by p2 / R2 where R is the radius of the matrix block. In the same year, Chang derived an explicit formula for the single-phase shape factor for rectangular matrix blocks based on the full transient solution of the diffusion equation introducing new 1-, 2-, and 3D results to the shape-factor literature (1993). The same result was independently obtained in 1995 by Lim and Aziz. Both Chang and Lim and Aziz stressed that the shape factor, which had previously been regarded as a constant, is actually a function of time. In view of the wide spectrum of results and the apparent lack of consensus regarding which shape factor to use in simulations, a more detailed analysis into the reasons for the different shape factors cited in Table 1 seems desirable. We want to underline that in this paper we focus our attention to single-phase shape factors, thus avoiding the additional complications that arise in the discussion of two-phase matrix-fracture interaction because of relative permeability and capillary pressure. This allows us to more clearly illustrate the different approaches that the previously mentioned authors used.

Modeling fractured reservoirs, especially those with complex, nonorthogonal fracture network, can prove to be a challenging task. This work proposes a general integral solution applicable to two-dimensional (2D) fluid flow analysis in fractured reservoirs that reduces the original 2D problem to equivalent integral equation problem written along boundary and fracture domains. The integral formulation is analytically derived from the governing partial differential equations written for the fluid flow problem in reservoirs with complex fracture geometries, and the solution is obtained via solving system of equations that combines contributions from both boundary and fracture domains. Compared to more generally used numerical simulation methods for discrete fracture modeling such as finite volume and finite element methods, this work only requires discretization along the boundary and fractures, resulting in much fewer discretized elements. The validity of proposed solution is verified using several case studies through comparison with available analytical solutions (for simplified, single-fracture cases) and finite difference/finite volume finely gridded numerical simulators (for multiple, complex, and nonorthogonal fracture network cases).

In this study, we present an analytical approach based on rescaled exponential models that are able to analyze production data from oil/water systems producing under boundary-dominated flow conditions. The model is derived by coupling two-phase oil/water material balances with multiphase well deliverability equations. Nonlinearities introduced by relative permeability in multiphase oil/water systems are accounted for via depletion-dependent parameters applied to each of the flowing phases. This study shows that So–Sw–p relationships based on Muskat's standard assumptions can be successfully deployed to correlate saturation and pressure changes in these two-phase systems without the need for user-provided surface production ratios or well-stream composition information. The validity of the proposed model is verified by closely matching predictions against finely gridded numerical models for cases constrained by both constant and variable bottomhole pressure production. In addition, a straight-line analysis protocol is structured to estimate the original oil and water in place on the basis of available production data using rescaled exponential models. Finally, we explore conditions for validity of the assumptions used in the proposed model, including the So–Sw–p formulation, by conducting extensive sensitivity analysis on input parameters.

Abstract Well spacing and stimulation design are amongst the highest impact design variables which can dictate the economics of an unconventional development. The objective of this paper is to showcase a numerical simulation workflow, with emphasis on the hydraulic fracture simulation methodology, which optimizes well spacing and completion design simultaneously. The workflow is deployed using Cloud Computing functionality, a step-change over past simulation methods. Workflow showcased in this paper covers the whole cycle of 1) petrophysical and geomechanical modeling, 2) hydraulic fracture simulations and 3) reservoir simulation modeling, followed by 4) design optimization using advanced non-linear methods. The focus of this paper is to discuss the hydraulic fracture simulation methods which are an integral part of this workflow. The workflow is deployed on a dataset from a multi-well pad completed in late 2018 targeting two landing zones in the Vaca Muerta shale play. On calibrated petrophysical and geomechanical model, hydraulic fracture simulations are conducted to map the stimulated rock around the wellbores. Finely gridded base model is utilized to capture the property variation between layers to estimate fracture height. The 3d discrete fracture network (DFN) built for the acreage is utilized to pick the natural fracture characteristics of the layers intersected by the wellbores. The methodology highlights advances over the past modeling approaches by including the variation of discrete fracture network between layers. The hydraulic fracture model in conjunction with reservoir flow simulation is used for history matching the production data. On the history matched model, a design of experiments (DOE) simulation study is conducted to quantify the impact of a wide range of well spacing and stimulation design variables. These simulations are facilitated by the recent deployments of cloud computing. Cloud computing allows parallel running of hundreds of hydraulic fracturing and reservoir simulations, thereby allowing testing of many combinations of stimulation deigns and well spacing and reducing the effective run time from 3 months on a local machine to 1 week on the cloud. Output from the parallel simulations are fitted with a proxy model to finally select the well spacing and stimulation design variables that offer the minimum unit development cost i.e. capital cost-$ per EUR-bbl. The workflow illustrates that stimulation design and well spacing are interlinked to each other and need to be optimized simultaneously to maximize the economics of an unconventional asset. Using the workflow, the team identified development designs which increase EUR of a development area by 50-100% and reduce the unit development cost ($/bbl-EUR) by 10-30%.