Background

Research Objectives

Recent Activities

Computer-Aided Interpretation

Well Testing for Heterogeneous Formations

Optimization of Wellbore Production Systems

Measurement of Flow Rate

Background
Starting in 1983, Stanford University Department of Petroleum Engineering undertook cooperative research on automated well test analysis with Schlumberger. By the end of 1986, Schlumberger had invested over $100,000 in this project. In 1987 the scope of the project was expanded, and the SUPRI-D consortium was formed with additional companies joining the group. In 1998, the consortium had 14 member companies.

The research has looked at many different aspects of automated well test interpretation (see later for a complete list). In addition, as a result of the greater insights awarded by the computerization of the interpretation, several other useful results were discovered (for example, a method of measuring in-situ relative permeability from a well test has been developed). Thirty technical papers and several reports have made these findings available to the industry, and many of the techniques and ideas have been incorporated into oil company and service company methodology and software.

Innovative well test interpretation techniques that can make use of the new measurements and new computer capability now available have already been shown to provide more results, more reliable results and less expensive tests. We aim to explore new ways to improve further on these successes, and to investigate novel approaches.

Research Objectives TOP
Automated well test analysis using computers has been available since the early 1970's, but gained widespread attention relatively recently. In the first year of this project, Rosa and Horne (1983) developed techniques that made it relatively straightforward to implement almost any type curve model in an automated procedure, and showed that automated analysis can result in more definitive interpretation. It was also discovered that, by removing the requirement that specific graphical features (such as the semilog straight line) be recognizable by eye, the automated procedure was able to interpret data that could not be analyzed by hand. Examples include tests that were cut short just before the semilog straight line (infinite acting) behavior, and tests in which multiple flow rates occurred. As an example, Horne, Perrick and Barua (1986) compared the automated analysis of a 15 hour truncated test with the results from the full 200 hours of data - the results were identical, demonstrating the ability of nonlinear regression to correctly analyze the short data set (which had no semilog straight line).

Installing the algorithms on a wellsite or remotely connected computer makes it possible (with surface recording electronic gauges) to perform the analysis in real time while the test is actually in progress. In this way tools need be left in the hole only as long as is necessary to meet the design objectives for the test. On the other hand, if unexpected results appear the test could be extended to achieve a resolution of the problem and a subsequent retesting would be unnecessary. Based on the algorithms we and others have developed, this goal has already been achieved. However, the techniques do require the presence of a reservoir engineer to monitor the test, either at the wellsite or at the remote computer. This joint manual/automated approach is likely to be standard procedure for some years, however we have directed our research towards a future goal in which the computer can perform the analysis by itself. We have explored different approaches to this goal involving artificial intelligence.

In addition, we would like to formulate standard methods by which reservoir models in algorithmic form could be made as widely accessible as the standard log-log type curve. The two inch square cycle log-log type curve has become a convenient form by which authors have made reservoir models available to be used by others. However, as graphical methods gradually give way to computerized analysis, the industry needs to formulate a standard format of subroutine or table look-up so that reservoir models can easily be transferred from one automated computer program to another. This could be a great advantage to the industry and would save the need for recoding or the reliance on commercial software packages.

A third area of interest is the development of methodology (other than automated analysis) to use newly available measurement technology. In this area, we developed techniques for the estimation of in- situ gas-oil relative permeabilities and water-oil relative permeabilities.

Recent Activities TOP
The research undertaken does not necessarily fall into specific categories, as it is our intention to follow innovative lines of approach as they present themselves. However, it is possible to group some typical areas of undertaking based on some of the current research topics and their likely extrapolations. The broad objective is the enhancement of interpretation of well tests by obtaining estimates for more parameters, by using non-traditional measurements, by reaching the estimates faster (using computers) and by obtaining more reliable estimates with less dependence on subjective judgment.

The following sections outline four typical research areas that are of current interest. These four typical areas are described as an indication of our current state of thinking within the overall research area.

Computer Aided Interpretation TOP
We are interested in the integration of flow rate data into a well test interpretation. The advantages in doing this are several. Whereas a single rate test contains only one short time transient, one intermediate time transient and one late time transient, a test in which the rate varies with time continuously adds the effects of early and intermediate time transients. Including more information from the reservoir allows us to infer more information about the reservoir.

One of the primary difficulties in including the flow rate data arises from the problem of identifying the reservoir model, since traditional methods of model recognition are based on characteristics of the constant rate derivative type curves. In order to extract a recognizable constant rate response, it is necessary to use deconvolution. We have conducted several investigations into effective methods of deconvolution, including both Laplace space and real space techniques.

A new way of presenting the diagnostic plot was developed in SUPRI-D by Bourgeois and Horne (1991), who proposed the use of the Laplace pressure, , and its derivative as a means of displaying conventional plots in Laplace space. The advantage of the Laplace space presentation is that deconvolution is straightforward and numerically stable. An example of a Laplace pressure type curve is shown in Fig. 1. Bourgeois also showed that there is significant advantage in using the Laplace pressure during nonlinear regression.

Another major focus has been the quantificaiton of uncertainty in the estimates of reservoir parameters. Starting with Rosa and Horne (1983), SUPRI-D has made frequent use of confidence intervals as a way of discriminating between valid and invalid interpretations. As an example of the way in which confidence intervals illustrate this uncertainty, consider the two interpretations shown in Figs. 2 and 3, which result in very different estimates of permeability and skin, even though the match to the data is good in both cases. The reason for the uncertainty is that this particular example has a strong correlation between k and s, as shown in Fig. 4 which illustrates the surface of the residual function (sum of sqaures of differences between the measured and calculated pressures). There is a wide range of combinations of k and s that result in similarly small values of the residual, everywhere at the bottom of the "valley" in the surface. In 1992 we started a new project that looks more closely at confidence intervals and the way that they may be used most effectively.

Well Testing for Heterogeneous Formations TOP
Another major interest in SUPRI-D has been the investigation of the requirements for well test information in reservoir characterization. Although it is already known that the degree of complexity that can be inferred from a well test interpretation is limited by the diffusive mechanism that governs pressure transmission in a porous medium, we have found several cases in which reservoir heterogeneities can be characterized. Rosa and Horne (1991) investigated the use of cyclic flow rate variations to stimulate the reservoir in a more complex fashion, and found that it is possible to estimate permeability as a function of distance from both an active and an observation well. This project has been expanded to consider higher frequency flow rate variation, for which a wave component is introduced into the reservoir impulse.

Sato (1992) considered another aspect of the reservoir characterization problem, by developing the methodology to generate highly accurate solutions for pressure transients in a heterogeneous medium. The technique used the boundary integral method (BEM) as a way of avoiding the numerical dispersion inherent in finite difference solutions. Fig. 5 illlustrates an example of a heterogeneous permeability distribution and Figs. 6 and 7 show the pressure transients and flow lines calculated for it by Sato (1992).

Optimization of Wellbore Production SystemsTOP
SUPRI-D's work in nonlinear parameter estimation led to the development of expertise within the group in the general area of nonlinear optimization. This experience was applied to the optimization of transient flow in the production system, allowing for multivariate optimization of the total income from a project over its entire design life. This work, reported in Carroll and Horne (1992) represented a considerable advance over traditional nodal analysis, which considers only one variable at a time, performs no optimization, and which does not include time dependent effects. This work was continued by Ravindran in 1992, who considered the additional aspect of decision variables which themselves could change with time (for example, and annual review of choke size). Still further work in this area is looking at the moment at optimization from multiple wells into a single separator station or platform.

Measurement of Flow RateTOP
Motivated by our interest in including flow rate information into well test interpretation, SUPRI- D has also undertaken an experimental investigation into measuring flow rate in the wellbore. In 1991 and 1992, a vertical flow loop was constructed, and tests run on an ultrasonic flow registering device. The study investigated the extent to which bubbles of gas would prevent the correct measurement of the flow rate by attenuation of the ultrasonic signal. This work will continue with the addition of a Doppler-shift device to separately register the speed of the bubbles.