The prior and posterior distributions of each uncertain parameter from 10,000 proxy-generated HM solutions are shown in Fig. To get a smoother posterior distribution, we also performed MCMC sampling to obtain 10,000 HM solutions using multiple response-parameter proxies. The prior and posterior distributions of each set of uncertain parameters from 64 HM solutions are shown in Fig. One can observe that only some combinations of each uncertain parameter (i.e., low fracture height values and high fracture conductivity value) are HM solutions shown as green lines. In addition, a parallel plot of 64 HM solutions is also shown together with non-HM solution cases in Fig. The best match realization of 64 HM solutions has properties as follows: matrix permeability of 0.027 md, fracture height of 40 ft, fracture conductivity of 9.9 md ft, matrix water saturation of 0.38, and fracture water saturation of 0.48. The best match case is also illustrated in Fig. The simulation results of 64 HM solutions are shown in Fig. For this study, we used 64 HM solutions for the production forecast. With a more relaxed threshold, the number of HM solutions can be as high as 98 cases, which is approximately 33% out of 300 simulation runs. Sixty-four cases passed the threshold out of 300 simulation runs, which is approximately 21%. We used the gas global error of 220 and water global error of 220 as the HM solutions threshold. The global error is specified after simulation results are available so that we can compare to production history and identify the case and maximum global error that are least acceptable as HM solutions. First, the global error used as the threshold value for screening solutions was unknown. Then, we evaluated all 300 cases from iteration 1 to the last iteration and screened them for HM solutions.

The percentage of relative discrepancies between the current and previous proxy versus iteration number ( Tripoppoom et al., 2019).Īfter that, the proxy-based MCMC algorithm generated the last iteration cases with a different filtering scheme using the lowest global error value for all 25 cases.

The objective is to maximize this determinant (if there is no correlation at all, it is equal to 1 and the design is orthogonal).įigure 4.8. This criterion is calculated using the determinant of the parameter correlation matrix. This means that they are as uncorrelated as possible (if there is a correlation between two parameters A and B, it is difficult to separate the effect of A from the effect of B). Independence: it is desirable for the parameters to be as orthogonal as possible. The objective is to maximize this distance − This criterion is calculated using the distance between the closest two points on the design. Space-filling: the trials of the LHS DOE should fill the input domain as much as possible. The main characteristics of LHS designs are: − This design is not unique and the space-filling and independence criteria are relative. In this case, a very high number of designs are generated and the design which contains the best space-filling and independence criteria is selected. LHS designs are particularly suitable for numerical designs of experiments. The objective is to maximize this determinant (if there is no correlation at all, it is equal to 1 and the design is orthogonal). This means that they are as uncorrelated as possible (if there is correlation between two parameters A and B, it is difficult to separate the effect of A from that of B). The objective is to maximize this distance – Space-filling: it is desirable for the design’s test to fill the input domain as much as possible. The main properties expected for LHS designs are: – * Values in parenthesis are design values.

Imdb hypercube