Application of fast, simple and yet powerful analytic tools, capacitance-resistive models (CRMs), are demonstrated with four field examples. Most waterfloods lend themselves to this treatment. This spreadsheet-based tool is ideally suited for engineers who manage daily flood performance. We envision CRM's application to precede any detailed full-field numerical modeling. We have selected field case studies in a way to demonstrate CRMs capabilities in different settings: a tank representation of a field, its ability to determine connectivity between the producers and injectors, and understanding flood efficiencies for the entire or a portion of a field. Significant insights about the flood performance over a short period can be gained by estimating fractions of injected fluid being directed from an injector to various producers and the time taken for an injection signal to reach a producer. Injector-to-producer connectivity may be inferred directly during the course of error minimization. Because the method circumvents geologic modeling and saturation matching, it lends itself to frequent usage without intervention of expert modelers. Introduction History matching reservoir performance is a difficult inverse problem. Ordinarily, history matching entails minimizing the difference between the observed and computed response in terms of gas/oil ratio, water/oil ratio, and reservoir drainage-area pressures. Systematic approaches have emerged to simplify history matching because manual matching by adjusting global and/or local geological and flow properties is tedious and time-consuming. Two classes of matching algorithms have emerged; one dealing with an automated approach involving error minimization, and the other dealing with 3D streamline assisted property adjustments in a systematic way. Some of the automated methods used for history matching include a gradient-based approach (Thomas et al. 1972, Chen et al. 1974, Bissell et al. 1997, Yang and Watson 1998, Zhang et al. 2000, and Gomez et al. 2001), sensitivity-analysis technique (Hirasaki 1973, Dogru and Seinfeld 1981, and Watson 1989), stochastic modeling technique (Tyler et al. 1993 and Calatayud et al. 1994), and optimal-control theory (Chavent et al. 1975 and Wasserman et al. 1975). In addition, history matching with streamlines (Milliken et al. 2001, Cheng et al. 2007) has gained popularity for its computational speed. Because history matching with a single geologic model does not assure attaining the 'correct' model, uncertainty in forecasting remains. Tavassoli et al. (2004) made this point very eloquently. The lack of forecasting certainty has prompted some to pursue history matching and forecasting with ensemble of models carrying geologic uncertainty. For instance, Landa et al. (2005) by using clustered computing showed how uncertainty in static modeling can be handled in both history matching and forecasting phases. Similarly, Liu and Oliver (2005) explored applications of ensemble Kalman filter in history matching where continuous model updating with time is sought for an ensemble of initial reservoir models. In yet another approach, Sahni and Horne (2006) have used wavelets for generating multiple history-matched models using both geologic and production data uncertainty. In spite of the advances made in automated-history matching with grid-based simulations, manual history matching is the norm in most business settings. The purpose of this study is two-fold; first, to alleviate the tedious task of history matching, manual or automated, by providing clues about producer/injector connectivity, and second, to provide a day-to-day waterflood management tool without the intervention of specialists requiring high-end computing.

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This study presents a simplified two-phase flow model using the drift-flux approach to well orientation, geometry, and fluids. For estimating the static head, the model uses a single expression for liquid holdup, with flow-pattern-dependent values for flow parameter and rise velocity. The gradual change in the parameter values near transition boundaries avoids discontinuity in the estimated gradients, unlike most available methods. Frictional and kinetic heads are estimated using the simple homogeneous modeling approach. We present a comparative study involving the new model as well as those that are based on physical principles, also known as semimechanistic models. These models include those of Ansari et al, Gomez et al., and OLGA. Two other widely used empirical models, Hagedorn and Brown and PE- 2, are also included. The main ingredient of this study entails the use of a small but reliable dataset, wherein calibrated PVT properties minimizes uncertainty from this important source. Statistical analyses suggest that all the models behave in a similar fashion and that the models based on physical principles appear to offer no advantage over the empirical models. Uncertainty of performance appears to depend upon the quality of data input, rather than the model characteristics. Introduction Modeling two-phase flow in wellbores is routine in every-day applications. The use of two-phase flow modeling throughout the project life cycle with an integrated asset modeling network has rekindled interest in this area. Plethora of models, some based on physical principles and others based on pure empiricism, often beg the question which one to use in a given application. Although a few comparative studies (Ansari et al. 1994; Gomez et al. 2000; Kaya et al. 2001) attempt to answer this question, often reliability of the data base has left this issue unsettled. One of the main objectives of this paper is to present a simplified two-phase flow model, which is rooted in drift-flux approach. The drift-flux approach (Hasan and Kabir, 2002, pp. 21–62, Shi et al. 2005a, 2005b) has served the industry quite well, as exemplified by its simplicity, transparency, and accuracy in various applications. The second objective is to show a comparative study with a few models using a small but reliable data base to get a perspective on relative performance. Here, data reliability stems from two elements: rate and fluid PVT properties. Pressure data are typically gathered with permanent downhole and wellhead sensors while rate data are measured with surface flow meters or test separators. In each case, the black-oil fluid PVT model was conditioned with laboratory data to ensure reliability and consistency. Proposed Model Total pressure gradient during any type of fluid flow is the sum of the static, friction, and kinetic gradients, the expressions for which are given in Eq. A-1 in the Appendix. For most vertical and inclined wells, the static head component-which directly depends on the volume average-mixture density-dominates. Thus, in simple terms, two-phase flow modeling boils down to estimating density of the fluid mixture or gas-volume fraction. Because gas-volume fraction depends on whether the flow is bubbly, slug, churn, or annular, we individually model each flow regime. However, for all flow regimes the gas (or lighter) phase moves faster than the liquid (or heavier) because of its buoyancy and its tendency to flow close to the channel center. This allows us to express in-situ gas velocity as the sum of bubble rise velocity, v8, and channel center mixture velocity, Covm. However, in-situ velocity is the ratio of superficial velocity to volume fraction. Therefore, the generalized form of gas-volume fraction relationship with measured variables- superficial velocity of gas and liquid phases-can be written as Equation (1) For downflow, buoyancy acts in the direction opposite to flow. Thus, in Eq. 1, the negative sign in front of the rise velocity applies to downflow and the positive sign is meant for upflow. While Eq. 1 is universal in its application, the values of the flow parameter Co, and rise velocity v8, are dependent on the type of flow and flow pattern. Table 1 presents these values.

Oil production strategies traditionally attempt to combine and balance complex geophysical, petrophysical, thermodynamic and economic factors to determine an optimal method to recover hydrocarbons from a given reservoir. Reservoir simulators have traditionally been too large and run times too long to allow for rigorous solution in conjunction with an optimization algorithm. It has also proven very difficult to marry an optimizer with the large set of nonlinear partial differential equations required for accurate reservoir simulation. A simple capacitance-resistive model that characterizes the connectivity between injection and production wells can determine an injection scheme that maximizes the value of the reservoir asset. Model parameters are identified using linear and nonlinear regression. The model is then used together with a nonlinear optimization algorithm to compute a set of future injection rates which maximize discounted net profit. Research previously conducted has shown that this simple dynamic model provides an excellent match to historic data. Based on a number of simulated and two actual fields, the optimal injection schemes based on the capacitance-resistive model yield a predicted increase in hydrocarbon recovery of up to 60% over the extrapolated historic decline. An advantage of using a simple model is its ability to describe large scale systems in a straightforward way with computation times that are short to moderate. However, applying the capacitance-resistive model to large reservoirs with many wells presents several new challenges. Reservoirs with hundreds of wells have longer production histories that often represent a variety of different reservoir conditions. New wells are created, wells are shut in for varying periods of time and production wells are converted to injection wells. Additionally, history matching large reservoirs by nonlinear regression is more likely to produce parameters that are statistically insignificant, resulting in a parameter dense model that does not accurately reflect the physical properties of the reservoir. Several modeling techniques and heuristics are presented that provide a simple, accurate reservoir model that can be used to optimize the value of the reservoir over future time periods. 1.0 Practical Aspects of Capacitance-Resistive Modeling Traditional reservoir simulators use detailed material balances to calculate reservoir pressures and oil saturations at multiple points in the reservoir. Finite difference equations valid for each grid-block require estimation of various parameters (compressibilities, permeabilities, porosities, etc.) throughout the reservoir. If these parameters are considered to be time-varying, (as they often are), they must be updated as the simulation progresses. This can be a daunting task for large simulations that can contain millions of grid-blocks. In spite of the difficulty, there have been several attempts to optimize oil production using traditional models (Barnes, 1990; Fang and Lo, 1996; Kosimidis et al., 2004 and 2005; Wang et al., 2002). Albertoni and Lake (2003) first proposed an inter-well connectivity model as an attempt to simplify the reservoir to a system of inputs (injection wells) and outputs (production wells). Subsequent versions of the capacitance-resistive model (CRM) expanded the number of model parameters and examined their physical meaning (Albertoni, 2003; Yousef, 2005; Yousef et al., 2006). Several attempts have been made to use the CRM to maximize predicted oil production (Liang et al., 2007; Sayarpour et al., 2007; Sayarpour, 2008). To solve for the necessary model parameters, the model requires only historic injection rates and total production rates - data that are typically already measured and collected. The CRM does not require a priori estimation of physical reservoir properties. However, history matching the model to historic data provides valuable information about the reservoir.