This appendix provides an example for the process of assisted-history-matching (AHM) and recreates the results for the simple example used in Appendix A. Upon the setting of the problem, at the end of a workday, an AHM procedure was initiated and a reasonable match was obtained by the next morning. By describing the process used to attain this match, the complexity and potential of this methodology is illustrated.

As described in Chapter 4, to use an AHM process, the history-matching parameters (HMPs) must first be selected and represented in a form that the simulation program can understand. For this problem Table B-1 describes the HMPs that were used and their range. The initial pressure, net thicknesses, porosity, and permeability of the two layers are all typical categories for this designation. The nature of the communication between Layers A and B (i.e., the transmissibility of the hole) is the flow area that was described in Appendix A. The location of the center of the hole was described as the grid location (I and J) in the simulation model, and the size of the hole was described as plus or minus 0–10 gridblocks, possibly varying in both I- and J-directions. It should be noted that because both the net thickness and porosity of each zone affects its pore volume, the final result cannot be unique.

In summary, the AHM process will deal with 12 HMPs. The AHM program that was used in this exercise uses orthogonal vectors for the experimental design stage, followed by artificial-intelligence-based algorithms for the investigation of the search space, and a response-surface-based optimization algorithm to converge on the final result. Postmortem analysis showed that the best answer was obtained in run number 176. The total number of simulation runs that were performed was 217, and most of them were run simultaneously.

For the AHM to guide itself through the history-matching process, it must be able to judge the quality of its results. As described in Chapter 4, this metric is called the objective function. Its purpose is to objectively measure the error (mismatch) of each simulation run by comparing it to the measured data. In this single-phase, interference example, because the only comparative information that is available is the pressure data from the observation well, it is used as the sole basis of the objective function. Instead of using root-mean-square error/objective function that minimizes the maximum error, the absolute error calculation was used for each data point. Additionally, the weights of the data in the very first hour of the test were reduced to avoid the impact of steep pressure decline. Fig. B-1 shows the observed pressure from the interference test and the best history match that was obtained through this exercise.

Fig. B-2 demonstrates the final HMP values for the same case. In this radar plot, each HMP is shown such that the inner radius corresponds to the minimum value of the range, and the outer radius to the maximum value. As can be seen, to obtain a satisfactory result, the AHM process decided that the permeability of Zone A had to be at its maximum range. As in Appendix A, we will not provide the exact values that this AHM was able to calculate so that it will not influence future exercises that use the same data set.

Fig. B-3 shows the results obtained from the best eight simulation runs, while Fig. B-4 shows the distribution of HMPs for the same runs. As can be seen in these figures, while the variation within each HMP is minimal among the cases, the sensitivity of the results to these minor variations is significant if the objective is to match the observed data points within 0.3 psi pressure difference. If the solution is deemed to be acceptable within 0.5 psi pressure difference, then all of these results can be considered to be satisfactory.

One of the advantages of the response-surface technology is the capability to investigate multiple solutions that can be acceptable. Upon completion of this history-matching exercise, the response surface around the final solution was investigated by Monte Carlo method to isolate 100 best solutions and to cluster them into three groups. Fig. B-5 shows the radar plot for these 100 best solutions, colored based on one of the three clusters they belong to. The plot indicates that the TrIPM and TrJPM parameters (that indicate the size of the hole) must be tightly constrained at the final solution value, while the remaining parameters can be slightly perturbed without impacting the final match significantly.