Stochastic Work Flow Bridges Gap Between Subsurface and Surface Disciplines
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This paper presents an unbiased stochastic data-driven work flow in which surface and subsurface uncertainties are accounted for and their effects on facilities design and operational decisions are quantified. Unlike the traditional approach in facilities design where the most-conservative values are used typically as design input variables, the proposed work flow accounts for life-cycle variability and correlations of relevant input data.
Traditional, deterministic facilities-design methodologies, based on deterministic (single-point) conservative conditions and design margins, might not recognize the full spectrum of operational conditions throughout a field’s life cycle, resulting in significant residual risk and waste of resources during operations.
Despite efforts to standardize the process of project delivery as much as possible, industry projects remain heavily customized, intermittent (high-variety, low-volume) processes, with a high rate of diversification and complexity. On the other hand, facilities operations are expected to be high-volume, low-variety, ideally continuous processes.
In the proposed work flow, deterministic models are established to account for dependencies between design input variables (static variables such as bottomhole pressure and temperature) and the desired objective (static results, such as the chemical-injection rate). However, in field situations, the analyzed variables change because of subsurface and surface events with different levels of uncertainty (e.g., condensate banking, lean gas injection, water breakthrough). Stochastic algorithms are used to create probability distribution functions (PDFs) for all analyzed design input variables (stochastic variables). Stochastic algorithms then are applied on the deterministic model, sampling from the previously defined probability distributions. Stochastic results are assembled into insightful charts and used to analyze the most-relevant variables and their correlations affecting the model objectives.
Equipment and Processes. A deterministic model is created to calculate the baseline methanol-injection rate (QMEOH) required to mitigate the hydrate-formation risk in a wet-gas field. Both the deterministic and subsequent probabilistic modeling work is performed in a system designed for statistical computation and graphics.
Design-basis input data (static variables), considered to be conservative and covering all operational scenarios, are used in the deterministic model. Furthermore, the deterministic model assumes chemical injection as a mass/continuous process.
In the field, parameters such as bottomhole pressure and flow rates of different phases change over time. These changes are caused by subsurface and surface events that can be predicted with different levels of uncertainty. PDFs are created for all relevant parameters. Similar probability distributions are created for all relevant variables.
Random samples of each variable (stochastic variables) are assembled into input data sets and transferred as cases (scenarios) to the deterministic model. Upon completion of all cases run, the deterministic model’s outputs are assembled as statistical data sets (stochastic results), which are then used for analysis. Results of particular interest are presented in the following sections.
Data and Results. The relationship between six relevant parameters is presented in the form of a summary matrix (Fig. 1). The input parameters for this case are bottomhole pressure (BHP), bottomhole temperature (BHT), wellhead pressure (WHP), and wellhead temperature (WHT) as input, while total water rate (QWT) and QMEOH are output parameters. The number of parameters is limited in the example case to six to ensure visibility on paper, but any number and combinations of parameters can be assembled into similar charts.
The main diagonal of the summary matrix presents the histogram distributions of the selected parameters. The first and third elements of the diagonal are the histograms of BHP and WHP, respectively. The scatter plots for each combination of parameters are presented under the main diagonal.
Scatter plots are suggestive methods used to visualize the existence of correlations between various parameters. In this example, a strong positive correlation between BHT and QWT is apparent. This type of insight is virtually impossible in a deterministic approach. In correlation with surface water-rate metering, this information can provide an early indication of water breakthrough; thus, the stochastic work flow can be used as a well- and reservoir-management tool.
The WHT and QMEOH scatter plot indicates another strong correlation. The correlation factors between all investigated parameters, expressed in absolute terms, are quantified in the upper section of the summary matrix.
In general, correlation factors vary between –1 and 1, where –1 and 1 represent perfect correlation (negative or positive) and 0 means no correlation. In the summary matrix presented in Fig. 1, the correlation factors are presented in absolute terms, meaning that all negative correlations are displayed as positive. Furthermore, a larger type size is indicative of a stronger correlation for the purposes of easier visualization. The correlation factor between the BHT and QWT is 0.8, and the correlation factor between WHT and QMEOH is 0.66. This confirms the findings in the scatter plots.
Static results indicate a baseline QMEOH of 540 gal/D. However, no methanol injection is required for most of the cases. Subsequent statistical analysis of the QMEOH distribution indicates that no injection is required in 77% of cases. In addition, the mean injection rate is 150.3 gal/D, significantly lower than the baseline rate of 540 gal/D, and the median injection rate is 0 gal/D. Furthermore, in some cases, the required injection rates are higher than the baseline injection rate, reaching up to 2,000 gal/D. The statistical analysis indicates that QMEOH rates in excess of 540 gal/D are required in 11% of the cases.
These are important findings because they invalidate the conservative input-data assumption. The stochastic work flow, where the subsurface and surface uncertainties are accounted for, reveals that methanol waste is expected in 77% of cases and the system remains at risk in 11% of cases.
The QMEOH/WHT scatter plot is presented in Fig. 1 at the intersection of Row 6 and Column 4. The strong correlation (0.66) between the two parameters has already been discussed. An additional insight from this chart is that no injection is required for temperatures greater than 55°F. This finding is relevant because it enables smart-logic design of the methanol-injection control loop (e.g., IF WHT>55°F, THEN QMEOH=0).
The QMEOH/WHT scatter-plot split provides additional insights into the expected system behavior throughout its lifetime. The splits correspond to selected ranges of WHT and gas gravity (GG). The condition of WHT being greater than 55°F is expected in more than 50% of cases. The scatter-plot split reveals that, even for WHT of less than 55°F, there are cases in which methanol injection is not required. This finding can be used to improve the control-loop logic design further to account for the combinations of WHT and GG. These conditions are expected in 3.6% of cases.
In addition, the scatter-plot split reveals that QMEOH ranges between 0 and 750 gal/D when WHT is between 50 and 55°F and GG is greater than 0.65. Then, for WHT below 50°F, methanol injection doubles, up to 1,500 gal/D. QMEOH ranges between 1,500 and 2,000 gal/D in 1% of cases (outlier cases). Thus, a split-range control-loop arrangement is recommended in which the low control range (0 and 750 gal/D) is triggered by WHT between 50 and 55°F and GG greater than 0.65, and the high control range (0 and 1500 gal/D) is triggered by WHT lower than 50°F.
Statistical analysis of operating-expenditure (OPEX) distribution reveals that the mean OPEX for the revised design is approximately $8 million, or 33% lower than the baseline OPEX estimate of $12 million.
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Stochastic Work Flow Bridges Gap Between Subsurface and Surface Disciplines
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