Summary This study investigates means for efficiently estimating reservoir performance characteristics of heterogeneous reservoir descriptions with reservoir connectivity parameters. We use simulated primary and waterflood performance for two-dimensional (2D) vertical, two- and three-phase, black oil reservoir systems to identify and quantify spatial characteristics that control well performance. The reservoir connectivity parameters were found to correlate strongly with secondary recovery efficiency and drainable hydrocarbon pore volume. We developed methods for estimating primary recovery and water breakthrough time for a waterflood. We can achieve this estimation with three to five orders of magnitude less computational time than required for comparable flow simulations. Introduction Several geostatistical methods have been developed over the past decade for generating fine-scale, heterogeneous reservoir descriptions. These methods have become popular because of their ability to model heterogeneities, quantify uncertainties, and integrate various data types. However, the quality of results obtained with these stochastic methods is strongly dependent on the underlying assumed model. Reservoir heterogeneities will not be modeled correctly if the appropriate scales of heterogeneities are not considered. Uncertainties in future reservoir performance will not be quantified if the entire range of critical spatial characteristics are not explored. Simulated reservoir performance will not match historical performance if the appropriate data constraints are not imposed. The likelihood of using an inappropriate model can be greatly reduced if production data is integrated into the reservoir description process. This is because production data is influenced by those heterogeneities that impact future rates and recoveries. This paper investigates the applicability of using reservoir connectivity characteristics based on static reservoir properties as predictors of reservoir performance. We investigate two types of reservoir connectivity-based parameters. These connectivity parameters were developed to estimate secondary recovery efficiency and drainable hydrocarbon pore volume (HCPV). We use 2D vertical cross sections in the study. Previous work1–3 investigated the correlation of spatial reservoir parameters on reservoir performance for 2D areal reservoir descriptions. We first describe the general procedure. We then follow with definitions, more specific procedure details, and a discussion of the results for the two reservoir characteristics investigated. General Method We generated sets of permeability realizations, each set honoring at least the "conventional" geostatistical constraints (i.e., the univariate permeability distribution, the permeability variogram, and the wellblock permeabilities). We used simulated annealing4–6 to generate the permeability realizations and a linear porosity vs. log (permeability) relationship to obtain porosity values at each gridblock location. Porosity and permeability were the only heterogeneous reservoir properties considered during the study; reservoir thickness was assumed to be a constant. We performed all the flow simulations at the same scale as the permeability conditional simulations. The two- and three-phase black oil flow simulations were run with Amoco's in-house flow simulator, GCOMP,7 on a Sun SPARC 10 workstation.8 We used flow simulation results and analytical calculations to determine water breakthrough time (tBt) and ultimate primary oil recovery. The results for each flow simulation were plotted vs. values of various spatial permeability and porosity-based parameters. We identified the spatial parameter having the strongest correlation with each simulated performance data type. Recovery Efficiency Definitions. Secondary recovery efficiency is considered to be impacted by interwell reservoir connectivity characteristics. However, reservoir connectivity can be defined many different ways. A method has been reported that uses horizontal and vertical permeability thresholds to transform permeabilities to binary values.9 The least resistive paths are determined by finding the minimum distance required to move from one surface (i.e., a set of adjacent gridblocks) to another, for example, from an injector to a producer. We used a binary indicator approach to simplify the computations, thus resulting in an extremely fast connectivity algorithm. However, the success of the method is dependent on the applicability of the designated cutoff values. Such an approach would be most successful for systems comprised of two rock types (e.g., clean sand and shale), each having a small variance but significantly different means. The permeability distributions used in the present study do not fit in this category. Thus, attempts to correlate secondary recovery efficiency variables with the indicator-based connectivity parameters were unsuccessful. We concluded that a more sophisticated connectivity definition, accounting for actual permeability values, was needed to better quantify interwell reservoir connectivity. As a result of further investigation, the following connectivity parameter was developed for 2D cross sections: where IRe(i, k) is the secondary recovery efficiency "resistivity index" at gridblock (i, k), ?L is the distance between the centers of adjacent gridblocks, ka is the average absolute directional permeability between two adjacent gridblocks, krw(i) is the estimated relative permeability to water for the ith column, and A is the cross-sectional area perpendicular to the direction of movement. For a horizontal step, ?L/A=?Lx/?Lz, whereas for a vertical step, ?L/A=?Lz/?Lx . The resistivity index parameter is derived from the analogy between Darcy's law for linear, single-phase fluid flow, and Ohm's law for linear electric current where I is the electrical current, ?E is the voltage drop, and R is the electrical resistance. Inspection of Eqs. 2 and 3 shows that the permeance of the fluid system, kA/µL, is analogous to the reciprocal of the electrical resistance. Eq. 1 is the multiphase flow equivalent of the reciprocal of the permeance, dropping the viscosity constant µ.

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Summary This paper describes a conditional simulation technique that constrains areal permeability fields to typical statistical information and indirectly to waterflood well performance. Near-well effective permeability and reservoir connectivity characteristics are used as indirect well-performance constraints. Results are validated by examining simulated waterflood performance of a five-spot pattern. This technique can be used to reduce the uncertainty of future well performance significantly. Additionally, the effect of alternative operating scenarios, such as infill drilling, can be evaluated more realistically. Introduction Existing geologic, petrophysical, and geophysical conditioning data are always sparse in comparison with reservoir size and complexity. Although conditional simulation techniques have been developed to account for such information, the resulting "equally probable" realizations of reservoir properties can result in simulated well performance that varies widely under normal waterflood conditions. This is true even when the variogram captures reservoir spatial correlation adequately. Reservoir descriptions must account for individual well performances before they can be considered realistic. However, the inverse problem of determining detailed spatial descriptions of reservoir properties from dynamic well-performance data is extremely complex and currently has no practical solution. Simulated annealing is considered to be one of the most flexible conditional simulation methods.1–7 Various desirable characteristics of an image can be accounted for with simulated annealing. These characteristics can be totally unrelated to each other, be of different magnitudes, and have different units of measurement. Applicability of simulated annealing to constraining images of permeability to waterflood performance is demonstrated with one-quarter of a five-spot waterflood pattern. Reservoir connectivity parameters are defined and used as additional conditional simulation constraints within the simulated annealing framework. Benefits of flexibility in specifying near-well effective permeability constraints are demonstrated; advantages and disadvantages of these parameters are identified and illustrated. Results are validated by comparing simulated waterflood performance based on permeability fields generated by use of typical constraints with those obtained that include connectivity and near-well effective permeability constraints. Background Several investigators have studied connectivity as related to stochastic reservoir characterization.8–10 Most work has focused on modeling the connectivity of fluvial sand bodies or shales. Stochastic geologic models, based on empirical relationships of sand-body geometry and deposition, have been used to generate 2D and 3D reservoir descriptions of facies that are conditioned to geologic models and well data. The facies are usually defined as reservoir rock (sand) or nonreservoir rock (shale). Well-density and location sensitivities have been conducted to determine the sand fraction that is drainable (accessibility factor) as a function of well spacing.10 Another study11 applies two measures of connectivity to the characterization of a crossbedded sandstone outcrop by use of high- and low-permeability binary indicators. Boolean techniques have been used to distribute sand bodies within a reservoir and to determine sand connectivity as a function of well spacing.12 Stochastic indicator simulation was developed to account for the connectivity of extremes (high-permeability streaks and shale barriers).13 Indicator simulation and a random-walk procedure have been used to determine the probability distribution of connected PV for a nine-spot pattern.14 All these conditional simulation techniques use a combination of geologic and statistical data to investigate connectivity and associated parameters. None of these methods use well-performance data as conditioning constraints. Reservoir engineers consider geologically sound "equally probable" realizations to be improbable if simulated well performance does not approximate historical well performance. In this study, near-well effective permeability and connectivity characteristics are used as indirect performance constraints to improve the reservoir description. Near-well permeabilities typically are estimated from transient pressure data.7,15–17 These methods estimate the type of permeability averaging represented by the pressure response at the well. Because radial symmetry is assumed, these techniques are best for estimating effective permeability of near-well radial volumes. In this case, "near-well" indicates the radial volume centered at the well that is large enough so that directional pressure-gradient effects have dissipated (e.g., those created by hydraulic fracturing) but small enough not to be distorted by regional heterogeneities. In this paper, near-well permeability is the effective permeability of the region surrounding the well that has the greatest effect on initial productivity or injectivity. The other parameter, connectivity, possibly can be estimated from tracer tests.18 However, we did not consider tracer applications. Instead, we attempted to relate connectivity to commonly measured production parameters. Connectivity Measurements In this study, reservoir connectivity is characterized by two methods: the fractional connectivity function and the flow-pattern permeability coefficient. Both techniques define connectivity on the basis of the spatial arrangement of permeability. This approach was used because permeability typically has a stronger influence on flow characteristics than any other variable. Additionally, both techniques quantify reservoir connectivity relative to specific well locations. Although existing definitions of connectivity may be used to improve predictions of overall field rates and recoveries, local connectivity measurements are required to predict interactions between specific wells and interwell permeability spatial distributions better. p. 145–152

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Vorwata is a giant gas field located in Bintuni Bay, Papua Barat Province, Indonesia. The field was discovered in 1997 and currently produces approximately 1.3 bcf/d of dry gas from the Roabiba sandstone reservoir. Initial development consists of 14 wells drilled from two platforms. The wells produce through 7-inch tubing and have been tested up to 240 mmscf/d. A Permanent Downhole Pressure Sensor (PDPS) is installed in each well to continuously monitor downhole pressure and temperature.Vorwata field is a faulted, high sand quality reservoir. The impact of faults on reservoir performance was very uncertain prior to startup. There was great concern the field could be compartmentalized, or at least strongly influenced by flow baffles and barriers. One of the primary subsurface objectives during pre-startup testing was to assess lateral and vertical reservoir connectivity within the development area.Pressure build-up tests (PBU) were conducted in each well as part of the initial clean up and testing procedure. The initial tests were very helpful in characterizing offset faults. PBUs obtained once the field was put on production are influenced by interference from offset wells, masking any boundary effects. Interpretation of the PBUs is enhanced by applying deconvolution. A pre-startup interference test successfully identified lateral and vertical pressure communication within the development area. The well/fault geometries and reservoir connectivity characteristics obtained from the PBUs and interference test have been used to condition the static and dynamic models.This paper describes the well testing program that has been implemented to reduce reservoir uncertainty in the Vorwata reservoir during the early phase of field development. Well test and pressure interference results have been integrated into full-field models to better assess future field performance and development decisions.