Summary
Reservoir studies performed in the industry are moving towards an integrated approach. Most data available for this purpose are mainly from well cores and/or well logs. The translation of these data into petrophysical properties, i.e., porosity and permeability, at interwell locations that are consistent with the underlying geological description is a critical process. This paper presents a methodology that can be used to achieve this goal. The method has been applied at several field applications where full reservoir characterization study is conducted.
The framework developed starts with a geological interpretation, i.e., facies and petrophysical properties, at well locations. A new technique for evaluating horizontal spatial relationships is provided. The technique uses the average properties of the vertical data to infer the low-frequency characteristics of the horizontal data. Additionally, a correction in calculating the indicator variogram, that is used to capture the facies' spatial relationship, is provided.
A new co-simulation technique to generate petrophysical properties consistent with the underlying geological description is also developed. The technique uses conditional simulation tools of geostatistical methodology and has been applied successfully using field data (sandstone and carbonate fields). The simulated geological descriptions match well the geologists' interpretation. All of these techniques are combined into a single user-friendly computer program that works on a personal computer platform.
Introduction
Reservoir characterization is the process of defining reservoir properties, mainly, porosity and permeability, by integration of many data types. An ultimate goal of reservoir characterization is improved prediction of the future performance of the reservoir. But, before we reach that goal a journey through various processes must come to pass. The more exhaustive the processes, the more accurate the prediction will be.
The most important processes in this journey are the incorporation and analysis of available geological information.1–3 The most common data types available for this purpose are in the form of well logs and/or well cores. The translation of these data into petrophysical properties, i.e., porosity and permeability, at interwell locations that are consistent with the underlying geological description is a critical step. The work presented in this paper provides a methodology to achieve this goal. This methodology is based on the geostatistical technique of conditional simulation.
The step-by-step procedure starts with the work of the geologist where the isochronal planes across the whole reservoir are determined. This step is followed by the assignment of facies and petrophysical properties at well locations for each isochronal interval.
Using these results, spatial analysis of the reservoir attributes, i.e., facies, porosity, and permeability, can be conducted in both vertical and horizontal directions. Due to the nature of how the data are typically distributed, i.e., abundant in the vertical direction but sparse in the horizontal direction, this step is far from a simple task, and practitioners have used various approximations to overcome this problem.4–6
A new technique for evaluating the horizontal spatial relationship is proposed in this work. The technique uses the average properties of the vertical data to infer the low-frequency characteristics of the horizontal data. Additionally, a correction in calculating the indicator variogram, that is used to capture the facies spatial relationship, is provided. Once the spatial relationship of the reservoir attributes has been established, the generation of internally consistent facies and petrophysical properties at the gridblock level can be done through a simulation process.
Common practice in the industry is to perform conditional simulation of petrophysical properties by adapting a two-stage approach.7–10 In the first stage, the geological description is simulated using a conditional simulation technique such as sequential indicator simulation or Gaussian truncated simulation. In the second stage, petrophysical properties are simulated for each type of geological facies/unit using a conditional simulation technique such as sequential Gaussian simulation or simulated annealing. The simulated petrophysical properties are then filtered using the generated geological simulation to produce the final simulation result. The drawback of this approach is its inefficiency, since it requires several simulations, and hence, intensive computation time.
Additionally, the effort to jointly simulate or to co-simulate interdependent attributes such as facies, porosity, and permeability has been discussed by several authors.11–13 The techniques used by these authors have produced useful results. Common disadvantages of these techniques are the requirement of tedious inference and modeling of covariances and cross covariances. Also, a large amount of CPU time is required to solve the numerical problem of a large co-kriging system.
Another co-simulation technique that eliminates the requirement of solving the full co-kriging system has been proposed by Almeida.14 The technique is based on a collocated co-kriging and a Markov-type hypothesis. This hypothesis simplifies the inference and modeling of the cross covariances. Since the collocated technique is used, an assumption of a linear relationship among the attributes needs to be applied.
The co-simulation technique developed in this work avoids the two-stage approach described above. The technique is based on a combination of simultaneous sequential Gaussian simulations and a conditional distribution technique. Using this technique there is no large co-kriging system to solve and there is no need to assume a relationship among reservoir attributes. The absence of co-kriging from the process also means that the user is free from developing the cross variograms. This improves the practical application of the technique.
An Integrated Microfacies and Well Logs-Based Reservoir Characterization of Yamama Formation, Southern Iraq