Iraj Ershaghi

Practical Application of Fractal Pressure Transient Analysis of Naturally Fractured Reservoirs

Pressure-transient tests in naturally fractured reservoirs often exhibit nonuniform responses. Various models explain such nonuniformity; however, their relevance is often not justified on a geologic basis. Fractal geometry provides a method to account for a great variety of such transients under the assumption that the network of fractures is fractal. This paper presents an application to real well test in various fractured reservoirs. The physical meaning of the fractal parameters is presented in the context of well testing. Examples showing a behavior similar to the finite-conductivity fracture model or the spherical flow are presented and explained by the alternative of fractal networks. A behavior that can be mistakenly interpreted as a double-porosity case is also analyzed.

A Prediction Technique for Immiscible Processes Using Field Performance Data (includes associated papers 13392, 13793, 15146 and 19506 )

A prediction method based on the use of performance history of a waterflood proposed in 1978 by Ershaghi and Omoregie is scrutinized here. Using a reservoir simulation approach, performance data for some hypothetical waterfloods are generated to test the application of the proposed technique to various flood patterns, reservoir properties, and field operating conditions. Recently published results on the behavior of relative permeability curves for immiscible processes are used to substantiate the assumptions inherent in the proposed technique. The limitations of the technique are discussed and applications to some actual case studies are presented.

Injection Scheduling Design for Reduced Order Waterflood Modeling

Discussion & Future Work In this work we are going to address the idea of designing a proper experiment for the purpose of approximating the two phase waterflooding process with a low order data driven model. In sum, reduced order modeling performance can be improved by providing a more informative data. A prior knowledge about the dynamics of the process can help to design and adapt an injection schedule to provide such data. Since the model structure is linear, it is of the most importance that the schedule keeps the process in its linear regime while exciting the relevant dynamics. Therefore, designing a proper injection schedule boils down to understanding the production constraints that limit the design parameters and reaching to an optimal trade-off, to have as informative of a data as possible. The novelty of this work is that we look into this problem from reservoir engineering angle as well as the requirements from system identification viewpoint.

A Method for Characterization of Flow Units Between Injection-Production Wells Using Performance Data

This paper presents a novel data mining method to characterize the flow units between injection and production wells in a waterflood, using carefully implemented variations in injection rates. The method allows the computation of weight factors representing th e influence of any of the injectors surrounding a given producer. The weight factors are used to characterize the effective contribution of injection wells to the total gross production in surrounding production wells. A wavelet approach is used to design the perturbation in the injection rates and to analyze the observed variation s in the gross production rates. Tracking the contribution of injectors to various producers can help in balancing voidage-replacement in waterflood optimization. A second application is reservoi r characterization, where information provided by the proposed procedure can help in mapping high permeability flow units such as channels and fractures as well as flow barriers between wells. The method was successfully calibrated and tested for simulated line drive and five spot patterns with various assumed flow units and flow heterogeneity conditions. The paper also includes a case study for a tight formation waterflood where the weight factors are intended to delineate the pattern of natural fractures causing preferential flows.

Waterflood Tomography: Mapping High Contrast Permeability Structures Using Injection/Production Data

The paper presents a novel method to detect the existence and determine the orientation of high permeability channels between injection and production wells in a waterflood. We apply the concept of transmission tomography and model a waterflood reservoir by considering water injection rates as inputs and measured production rates as outputs. We solve the inverse problem, in which the goal is to determine the existence and location of high permeability channels in the field by measuring the lag time in response to the variation in the injection rate. The main advantage over other methods (e.g., tracer testing) is that this technique can be applied without significantly affecting daily operation. We show that the lag times at the producers can be estimated by monitoring production rates, given that known time-varying injection rates are applied. We propose a mixture model to characterize the lag time for each injector-producer pair, where the system is initialized by assuming that multiple candidate fractures exist. Our algorithm iteratively modifies the length, orientation and location of each high permeability candidate in order to match the measured response time between wells. It is well known that the solution may not be unique if we only have limited measurement data. Thus, in order to choose between possible models, we propose to use the “total length” of high permeability channels as regularization metric. Our method will select the model that fits the measured lag time with minimum total high permeability channel length. It is also possible within our framework to adjust the regularization so that it takes into consideration other type of prior information, e.g., preferred orientation known to exist in a given field. To validate our approach, we use a commercial simulator to test a synthetic line drive and a 5-spot waterflood. In the first case, we test a five spot with hydraulic fracture located in the central production well. In the second case, we test a single fracture with 45 degree orientation located between rows of producers and injectors. Our results show that our method can provide very accurate estimates of fracture orientation, with decreased uncertainty as the well density in the field increases.

A Novel Method for Mapping Fractures and High-Permeability Channels in Waterfloods Using Injection and Production Rates

This paper extends the work reported in SPE114222 for managing waterfloods using estimation of flow characteristics from only injection and production rates. The method first estimates the finite impulse response (FIR) curve corresponding to the fluid-flow between all injector-producer pairs. This FIR curve is analogous to the pressure curves obtained from pulse testing. Reservoir parameters, such as connectivity between wells, can be estimated from this curve, which can also be used to characterize variations of relative flow as a function of storage capacity (F-C plots), thus making it possible to quantify the heterogeneity of flow paths between wells. Our proposed method is capable of identifying the flow channel relationships between all injector-producer well pairs. This helps in reservoir characterization, where information provided by the proposed procedure can describe the characteristics of flow-path between injector-producer pairs. It can also help in waterflood optimization by tracking sweep efficiency and balancing voidage-replacement. The method has been successfully tested and calibrated for simulated line drive patterns with various fracture geometry conditions. It successfully quantifies the interwell connectivity and the heterogeneous properties in the numerical simulations. Our procedure has several advantages over pulse testing and tracer tests. In comparison to pulse testing, pressure data is not required and the only data needed are injection/production rates, which are often routinely available with high temporal resolution for many reservoirs. The quality of measured production rates affects the estimated properties. Because the proposed procedure can be routinely performed and implemented, the proposed procedure leads to a dynamic approach for reservoir and fluid flow mapping, where the results can be refined over time. Additionally, our procedure could also be used for better designs of pulse or tracer tests. Finally, once the flow channels are mapped, one can balance the flood and make diagnostic predictions about future response under any given injector scenarios. Introduction In waterflooding, injection rates can often be correlated with gross rates of the surrounding producers by monitoring pressure data. To estimate this correlation we can view the whole region where injectors-producers are located as a system, with the injectors as the system inputs, and the producers as the system outputs. Many methods have been used to estimate the directional transmissivity of flow based on injection and production rate data. What makes these approaches more attractive is that injection and production rate data are now routinely available with high temporal resolution for many reservoirs. Among these works, Heffer et al. use Spearman rank correlations, Panda and Chopra use artificial neural networks to estimate the relationships between injection and production rates. Albertoni and Lake estimate the effective flow units (called interwell connectivity in their work) based on a linear model using multiple linear regression (MLR) method. Yousef et al. 4,5 improve this work by building a more complex model, named capacitance model in their work. In our previous work, we proposed an active method to further improving the estimation by avoiding collinearity between injection rates through careful selection of injection rate patterns. Tracer testing has often been used for mapping high permeability channels in waterfloods and it provides useful reservoir parameter estimations, such as reservoir swept volume, fluid velocities, and flow geometry in a reservoir. For details, see Abbaszadeh-Dehghani et al., 1982, Abbaszadeh-Dehghani et al., 1984, and Oliver , 1998. However, conducting frequent tracer tests is often uneconomical and time consuming. Moreover tracer testing cannot provide a dynamic view of the system: an estimate of the waterflood characteristics is obtained after the testing, but the model parameters cannot be updated unless a new tested (e.g., using a different tracer) is conducted.

Estimation of Geothermal Brine Viscosity

Viscosity of synthetic brines consisting of sodium chloride, potassium chloride, and calcium chloride were measured at concentrations ranging from 0.99 to 16.667 wt% and at temperatures up to 275/sup 0/C. From the use of laboratory-derived data, a method is presented whereby the viscosity of a geothermal brine may be estimated from a knowledge of its composition.

Numerical Simulation of the Effect of Critical Gas Saturation and Other Parameters on the Productivity of Methane From Geopressured Aquifers

A numerical simulation study has shown that critical gas saturation is one of the most significant parameters that controls the productivity of methane from geopressured aquifers. Ultimate fluid production from such reservoirs is restricted by insufficient gas in solution to maintain the reservoir pressure.

A Modified Spinning Drop Method for High-Temperature Applications

This paper describes experimentation with a constant-speed (3,600-rpm) spinning drop apparatus which allows the study of interfacial tension (IFT) properties of a given oil drop vs. a surfactant solution over a wide range of temperatures and for a prolonged period of time. Adding a temperature air bath and developing a method to seal the fluids in the capillary tube extends the application of the spinning drop to 302F (150/sup 0/C). IFT properties of 2 petroleum sulfonates and one nonionic system were measured against a crude oil with a gravity of 0.9 g/cm/sup 3/. Figures are presented showing schematic of modified spinning drop equipment, modified capillary tube for high temperature spinning drop apparatus, and comparison of IFTs measured by spinning drop and pendant drop methods.

Method for Handling the Complexities Associated with History Matching the Performance of a Highly Stress-Sensitive Formation

This paper presents aspects of formation stress sensitivity influencing the successful simulation of the Tar Zone in Fault Block IIA of the Wilmington Oil Field in Los Angeles County, CA, USA. The Tar Zone is a slope and basin clastic type reservoir. The significant compaction experienced during the primary phase and the subsequent rebound during the following waterflooding created a complex case of reservoir definition for projection purposes. Uncertainties regarding stress effects on physical properties such as porosity, permeability, compressibility and formation thickness complicated the representation. The history matching attempts revealed the insufficiency of using conventional compaction models in the appropriate modeling of the compactionrebound process. A new compaction-rebound feature was developed based on rock mechanics considerations and was incorporated into a commercial simulator, Computer Modelling Group’s STARS TM simulator. This method allows for meticulous representation of the spatial dynamics of compaction/rebound based on the local pressure field. A successful history match of the primary and waterflooding production was achieved with the new compaction/rebound algorithm. The model was successfully tested by predicting the 20 acre steamflooding pilot. The case under consideration is unique and relates to high pressure and temperature steamflooding. The proposed methodologies have widespread application in other stress-sensitive heavy oil reservoirs.