3. METHODOLOGY
3.5 Phase 2: History Matching of Waterflooding and Polymer Flooding Models Using the
History matching is a process used in reservoir simulation to reconcile observed data from the real- system with the simulation model. It involves adjusting the model parameters so that the simulation results match the historical production data as closely as possible. The reason for conducting history matching is to verify that the simulation model reflects the actual system precisely and authentically, which is crucial for generating dependable projections concerning future performance. The process may involve iteratively adjusting various aspects of the model, such as reservoir properties, fluid characteristics, or well production rates until a satisfactory match is achieved.
Before trying to simulate and match the history of the polymer flood data, a water flood was modeled. This was a helpful exercise in order to improve comprehension of the simulator and to ensure that the initialization parameters were accurately configured. To ensure accurate results during waterflooding experiments, the cumulative oil production data must be matched with simulation results.
In this step, the relative permeability is considered the most sensitive parameter that is needed to be altered. The curves represent the relative permeability of oil and water, demonstrating the ease of flow of the phases. In the process, the rock's innate properties, such as porosity and absolute permeability constant, one can achieve a more precise depiction of total oil production.
It's important to note that the simulator performs more effectively when dealing with waterflooding data compared to chemical flooding data. In waterflooding, merely tweaking the relative permeability curves is sufficient. To sum up, the objective function for the matching will be cumulative oil production, whereas the matching parameters are relative permeability values.
To simulate the desired process using the STARS platform in Builder, the Process Wizard is utilized. The existing fluid model is used and necessary data is added to the simulation. For this specific case, the chosen process is the "alkali, surfactant and/or polymer model". The polymer flood model is selected since only one chemical component is used in the chemical flooding. Two relative permeability sets are chosen as the model options and the rock type
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selected is limestone with a density of 2.71 g/cm3. For this simulation, the polymer is defined as the adsorption component and the adsorption is set to be independent of salinity.
Additionally, the "polymer quantity decreases with time" option is selected for the simulation.
To restrict polymer flow into small pore throats, it is essential to enable polymer mobility reduction during the simulation. The relationship between the polymer concentration and viscosity should be inputted into the simulation from Mazhit's (2022) work. Polymer injection commences after 120 minutes of water injection and lasts for 54 minutes. The polymer injection rate for the entire process is 3.125 cc/min. The mole fraction of the injected fluid is illustrated in Table 4.
Table 4. The polymer concentration in injected fluid
Injected Fluid Type Component Mole Fraction
Water H2O 0.99988
Polymer 0.00012
Total 1.0
This section is concerned with history matching, which is achieved through a modeled experiment involving flaxseed gum. In most cases, the objective functions for reasonable history matching of experimental polymer floods are cumulative oil recovery, recovery factor, water cut, and pressure differential. Previous researchers have used different objective functions to match experimental and simulated saturation profiles in polymer flooding experiments. For example, Alsawafi (2015) used cumulative oil recovery and pressure differential profile as the objective functions for the history matching of polymer core floods.
Fabbri et al. (2013) estimated the relative permeability curves associated with the polymer core flooding process through a history match of a polymer core flooding experiment, using injection pressure, cumulative oil, and water cut. Zampieri et al. (2020) included histories for differential pressure, recovery factor, water cut, and cumulative produced water, oil, and liquid to compare simulation output parameters with laboratory results. In this study, cumulative oil recovery will be used as the output parameter to visualize the quality of history matching.
To adjust parameters, Pandey et al. (2008) changed the relative permeability curves during polymer flooding and used a higher adsorption value than the one measured experimentally to achieve a good match in polymer flooding experiments. Hashmet et al. (2018) calibrated relative permeability exponents and polymer reaction rates to match the oil recovery of polymer
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core flooding experiments. For the current study, adjusting parameters for history matching will involve using the Correy correlation for relative permeability to match polymer flooding and polymer adsorption values.
The CMG STARS software works with the keywords. The first parameter is the maximum adsorption capacity, which is denoted as "ADMAXT" in the CMG STARS simulator. The simulator models the irreversible adsorption behavior, which is linked to the maximum adsorption capacity, using the "ADRT" keyword. Both the maximum adsorption and the irreversible adsorption are expressed in the same units. The software's inaccessible pore volume is managed using the "PORFT" keyword, which represents the percentage of accessible pore volume more accurately. The final adsorption keyword is the permeability reduction, or
"RRFT." In the STARS simulator, setting the "RRFT" value to one indicates no reduction in permeability. The "PORFT" and "RRFT" keywords function based on how much polymer has been adsorbed relative to the stated maximum adsorption.
The STARS system employs an interpolated set of relative permeability based on two different sets of relative permeability - one defined before the polymer flood and the other defined for the polymer flood. The equations below demonstrate how STARS carries out this interpolation of the relative permeability set:
𝑘𝑟𝑤 = 𝑘𝑟𝑤𝐴× (1 − 𝑤𝑡𝑟) + 𝑘𝑟𝑤𝐵× 𝑤𝑡𝑟 (12) 𝑘𝑟𝑜 = 𝑘𝑟𝑜𝐴× (1 − 𝑜𝑖𝑙) + 𝑘𝑟𝑜𝐵× 𝑜𝑖𝑙 (13)
𝑤𝑡𝑟 = 𝑟𝑎𝑡𝑤𝑤𝑐𝑟𝑣 (14)
𝑜𝑖𝑙 = 𝑟𝑎𝑡𝑛𝑜𝑐𝑟𝑣 (15)
𝑟𝑎𝑡𝑤 = 𝑟𝑎𝑡𝑛 = 𝐷𝑇𝑅𝐴𝑃𝑊 − 𝐷𝑇𝑅𝐴𝑃𝑊𝐴 𝐷𝑇𝑅𝐴𝑃𝑊𝐴 − 𝐷𝑇𝑅𝐴𝑃𝑊𝐵
(16)
The equations described here contain subscripts A and B that represent different relative permeability sets for waterflooding and polymer flooding. The current polymer concentration is denoted as DTRAPW, while DTRAPWA and DTRAPWB represent the defined polymer concentrations for water flooding and polymer flooding, respectively. Additionally, two curvature interpolation parameters, WCRV and OCRV, are used to provide extra flexibility when interpolating between sets of curves. In this study, these last parameters are set to 1.
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The relative permeability curve and adsorption are the main factors that affect and have more influence on the history match of polymer flooding, as the other variables have constraints related to their physical meaning and experimental data. Therefore, relative permeability is the main variable in history matching for polymer flooding.
Proxy models, also known as surrogate models or reduced-order models, are simplified approximations of complex simulations that are faster to run than the original simulation. In the context of numerical simulation history matching, proxy models are used to generate a large number of plausible reservoir models that match the observed production data, while significantly reducing the computational cost of the history matching process. One of the main features of CMG CMOST for creating proxy models is the "History Matching and Optimization" module. This module includes several algorithms for generating proxy models, including the Proper Orthogonal Decomposition (POD) algorithm, which is a widely used technique for constructing reduced-order models from simulation data.
In practice, proxy models are used in a variety of ways during the history-matching process. A global optimization algorithm is used to explore the space of uncertain parameters, using the proxy model to evaluate the production data for each parameter set. This can help to identify a large number of plausible reservoir models that match the production data. Once a set of plausible models has been identified, more detailed simulations can be run on these models to refine the history-matching process. For example, a higher fidelity simulation can be run on a small number of the most promising models, in order to further refine the parameter estimates.
The application of a proxy model for this study will help to identify a larger set of plausible reservoir models that match the production data, leading to a more accurate numerical model that represents the actual experimental coreflooding.