Technique to Integrate Production and Static Data in a Self-Consistent Way

This work presents a technique to integrate production data into the reservoir characterization workflow. The application of the technique ensures that the construction of earth models for reservoir simulation will be geologically sound and consistent not only with all the observed static and production data, but also with the earth modeling workflow philosophy, regardless of its complexity. The technique can be considered as an advanced reservoir simulation history matching process with a complex level of parameterization. The observed production data is applied to adjust the key parameters in the workflow used to construct the static model. The magnitude of the parameter adjustments is dependent on the uncertainty associated with the parameters. The problem is posed as an inverse problem and it requires the computation of the sensitivity coefficients of the field responses (production data) with respect to the parameters for inversion. This paper also introduces the concept of "static" sensitivity coefficients and explores their usefulness. An example is presented where the parameters for inversion included variogram parameters along with the mean and variance of a reference porosity histogram. The inversion was performed by adjusting parameters in the fine scale model while the production data was computed in an upscaled model. Introduction Reservoir simulation models are essential in modern reservoir management. Reservoir models are used to predict the future performance of the field under different scenarios with the objective of optimizing the application of resources. The quality and uncertainty in the reservoir models will translate into the quality of the predictions. It has been recognized that high quality models should be geologically sound and be consistent with all the data available. The task of constructing a reservoir model with such characteristics is not a simple one. The difficulty resides in processing substantially different types of data. One subject of a large research effort in the industry is integrating geological, static and dynamic data. In general, the current reservoir modeling approach consists of two steps. The first step is constructing "static" models using static data, such as well logs, cores, geostatistics, seismic, etc. Very complex workflows are used in this step to ensure consistency with all the static data and the geological information. Next, in a separate step, the models generated in the previous step are adjusted to honor the production data observed in the field. Current techniques to make the adjustments are disconnected from the complex work made in the previous step in the static data side. As a result the final reservoir model may match the production data but may have lost the consistency with the static and geological data. Forecasts performed with these models will be more uncertain than with the models generated while full consistency is preserved. This work addresses this problem and provides one alternative for consideration. The work presented in this paper is an extension of previous work in the area of inversion using object-modeling techniques combined with reservoir simulation . Description of the Method The application of the method described in this work is conceptually simple, although its implementation is complex. The procedure can be outlined as two steps. 1. Earth scientists construct a first reservoir model by using mainly static data, such as surfaces inferred from seismic information, well logs, core analysis, stratigraphic interpretations, geostistical data analysis, analog studies, outcrop information and geological setting models. For large fields this task usually requires a substantial amount of efforts and time. Integrated earth modeling software, such as GOCAD, is used to implement complex workflows that are specific to each reservoir. By the time the first static model is completed, an agreement and a definition about what is the correct workflow process for the field under study have been reached, and what are the most uncertain and relevant parameters and their SPE 71597 Technique to Integrate Production and Static Data in a Self-Consistent Way Jorge L. Landa, SPE, Chevron Petroleum Technology Co. 2 JORGE L. LANDA SPE 71597 respective ranges of variability have been detected. The workflow must describe the full process of reservoir model construction including upscaling and reservoir simulation. The list of uncertain and relevant parameters may include what is traditionally considered “hard” data, such as well logs. 2. An inverse problem is set, where the question posed is: what are the values that should be assigned to the “uncertain” parameters to generate a new reservoir model that will reproduce the historical production data when it is subjected to numerical simulation. The key elements in this step are the selection of the parameters for inversion and the computation of the sensitivity coefficients of the production data with respect to the parameters of inversion. The last element is described in detail in the next section (Mathematical Theory). The above process seems similar to a simulation historymatching problem. What distinguishes it from the other methods in the literature is the choice of parameters for inversion. In this work the parameters for inversion are of the "workflow" and "hard-data" types. By doing this kind of selection it is guaranteed to end up with a reservoir model that will honor both the static and dynamic data, be geologically sound and, more importantly, be consistent with the workflow philosophy. The essence of the method is based on two concepts: What is traditionally considered as "hard" data in model construction is not actually "hard". There is always uncertainty associated with this type of data. Thus, it makes sense to change them during the history matching process. The parameters used in the reservoir model workflow are the result of subjective interpretations, such as data analysis, guess work, analog comparisons, etc. Therefore, it is reasonable to change them in the process of history matching. In order to preserve the soundness of the history matched model, the changes indicated above should be restricted to ranges determined by the level of uncertainty associated with each parameter. The method can be viewed from two perspectives: From the earth science point of view, as a method to preserve geological information. From the inversion point of view, as a method to reduce the inversion parameter space by choosing a "natural" parameter set. The example included in this paper demonstrates the whole process. Mathematical Theory The inversion part of the process is based on the GaussNewton algorithm for parameter estimation. New features have been added to handle regularization of ill conditioned matrices and to restrict the parameter search space within prescribed constraints in an efficient way. The mathematical theory for this method has been extensively described in the literature. The particularities of the implementation for this work have been presented in previous publications and they will not be repeated here. A critical step in the inversion method used in this work is the efficient computation of the sensitivity coefficients (derivatives) of the calculated production data with respect to unconventional parameters of inversion. In the example presented later the derivatives of the oil/water/gas production and pressures at wells with respect to parameters, such as the azimuth of a geostatistical variogram or the mean of a histogram need to be calculated. In previous work it has been demonstrated that it is possible to compute the derivatives of the primary variables of an implicit numerical simulator with respect to any kind of parameter by using Eqn. 1.