Mathematical Basin Analysis Models

(adsbygoogle = window.adsbygoogle || []).push({}); Mathematical basin analysis models are mathematical representations of physical processes that occur in sedimentary basins. These models are used to simulate the behavior of sedimentary systems, including the transport, deposition, and erosion of sediment, and to predict the distribution and character of sedimentary rocks. Introduction To Mathematical Basin Analysis Models Tissot (1984) cites the development of "basin-scale geologic and geochemical modeling which allows a quantitative approach to the generation, migration, and entrapment of hydrocarbons" as having a major impact on exploration, enabling us to address subsidence history, heat flow, thermal and maturation history, and migration. Welte and Yukler (1981) introduced an early quantitative model that combines geological, geophysical, geochemical, hydrodynamic, and thermodynamic data into a deterministic, dynamic basin model. They incorporate mass- and energy-transport equations, equations that describe the geochemical evolution of organic matter as a function of temperature, and empirical curves relating pressure and temperature, porosity and depth, and vitrinite reflectance to hydrocarbon generation. We use these equations and curves to compute pressure and temperature histories, the physical and thermal evolution of sediments, the maturation of organic matter, and hydrocarbon generation within a three-dimensional model of the basin. The results quantify hydrocarbon potential for source rocks at different stages of basin evolution. https://youtu.be/j34H3NjNqaM Welte and Yukler begin their analysis using "all available data on sedimentary thicknesses, pressure, temperature, porosity, density, thermal conductivity, specific heat, maturity of organic matter, and amount of petroleum in place" to develop mathematical models that simulate the various petroleum-generating processes. Figure 1, (Steps in development of model of real-world system: [a] conceptual and mathematical models successfully represent the real system; [b] owing to poor understanding of real system, models are inaccurate.) shows the development of these models. FIGURE 1 Steps in development of model of real-world system If data are sparse or poor quality, the models will not accurately represent the real system. Available data are input into the model, which uses a set of non-linear partial differential equations of energy and mass balance to describe geological and geochemical evolution within a three-dimensional grid. The model simulates four basic units of the petroleum-generating system -- geology, hydrodynamics, thermodynamics, and geochemistry (Figure 2, Input units for three-dimensional deterministic dynamic model). FIGURE 2 Input units for three-dimensional deterministic dynamic model Table 1 and Figure 3 summarize output from these separate units. FIGURE 3 Summarize output from these separate units We then compare the output values to the actual measured values (Figure 4), and modify the conceptual model if the solution does not match reality. FIGURE 4 Compare the output values to the actual measured values (adsbygoogle = window.adsbygoogle || []).push({}); UNITOUTPUTGeologicSediment type, source, depositional rates, etc. Depositional environments Paleobathymetry Mineralogic evolution Tectonic SubsidenceHydrodynamicDirection and rate of fluid flow Hydraulic properties of fluids Porosity Pore pressure Potential migration pathways Thermodynamic Direction and rate of heat flow Thermal properties of fluids Thermal properties of sedimentsGeochemicalType and amount of organic matter Maturity of organic matter Generation potential of organic matterTable 1: Output parameters from a deterministic basin analysis model We can apply this modeling approach at any stage of basin exploration. In frontier areas, we will have to estimate many input data, but the model can be a good planning tool for new data collection. We update the input parameters as new data become available. In more mature areas, mathematical models can provide a new, quantitative perspective on hydrocarbon generation and distribution. Figure 5, FIGURE 5 The block diagram illustrates the basin geometry Figure 6, FIGURE 6 Cross section through the mathematical model Figure 7, FIGURE 7 The solution for porosity versus depth along the cross section Figure 8, Figure 9 (adsbygoogle = window.adsbygoogle || []).push({}); FIGURE 8 Time/temperature relationships to predict source rock maturation FIGURE 9 The evolution of organic matter maturity and Figure 10 show a simplified application to a generalized basin. FIGURE 10 Simplified application to a generalized basin The block diagram in Figure 5 illustrates the basin geometry. We generate a three-dimensional mathematical model to approximate the real setting. We then divide the three-dimensional model into a horizontally and vertically gridded cube. Geologic, hydrodynamic, thermodynamic, and geochemical data are defined at each grid point in the three-dimensional grid. Next, pore pressure, temperature, physical and thermal properties, maturation, and amount of hydrocarbon generation are calculated throughout the model. Secondary migration pathways are predicted and related to potential traps. Figure 6 shows a cross section through the mathematical model, with four locations marked for reference. Figure 7 shows the solution for porosity versus depth along the cross section at the four reference points, and Figure 8 shows time/temperature relationships at the same locations. The evolution of organic matter maturity is shown in Figure 9. Figure 10 shows potential secondary migration directions and potential trap locations. This output gives us important information about the petroleum system. For example, the low porosity in the limestone units (Figure 7) forms a good top seal for the underlying units, creating a closed system of source and reservoir rocks. We can use time/temperature relationships (Figure 8) to predict source rock maturation at different times and locations within the basin (Figure 9), which we can then relate to the timing of trap formation. This early basin summary shows how mathematical modeling can quantify the generation, migration, and accumulation of hydrocarbons. More advanced models have been developed and applied during the past decade. Ungerer et al. (1984) discuss five mathematical models that lead to "quantitative predictions of the geological phenomena leading to oil accumulations." Each of the models (Figure 11 and Figure 12) FIGURE 11 Input and output mathematical models addresses a specific geological process: A backstripping model reconstructs of the sedimentary basin in time through successive cross sections. FIGURE 12 Geodynamic model A geodynamic model reconstructs heat flow histories used for basins formed by extension. A thermal model computes the temperature in the basin and is coupled to a kinetic model of organic matter maturation. A migration model computes the amounts of petroleum generated in the source rocks through time and the amounts accumulated in traps. A thermodynamic model determines the amount and composition of the hydrocarbons that may migrate in gaseous solution. We can use the first three models to effectively analyze even poorly explored sedimentary basins. To apply the last two models, we need sufficient well control to provide adequate data on source rock distribution and richness. (adsbygoogle = window.adsbygoogle || []).push({}); Backstripping Models (adsbygoogle = window.adsbygoogle || []).push({}); We use backstripping models to reconstruct the evolution of basin subsidence and sediment infill, with the goal of determining tectonic subsidence by removing the effects of sediment and water loading on the lithosphere. We do this by considering compaction effects on the sediment fill through time, as well as paleobathymetry. We can factor eustatic sea level variations into the model where such data are available. In order to compute tectonic subsidence, we must determine the response of the crust to loading by sediments and water. We do this by applying models that describe the behavior of the lithosphere when loaded. The simplest model (local or Airy isostasy) assumes that the lithosphere has no strength; this model fails to reflect the measured behavior of the lithosphere. A more realistic model (flexural isostasy) assumes the lithosphere behaves as a rigid plate overlying a fluid asthenosphere. Watts et al. (1975) determined that flexural rigidity may increase through time, depending on the thermal time/depth relationships. Karner et al. (1983) concluded that continental lithosphere responds similarly. Ungerer et al. (1985) used estimated values of elastic thickness (a measure of flexural rigidity) to compute the local and flexural isostasy models used for tectonic subsidence computations. In addition to computing tectonic subsidence (Figure 1 and Figure 2), the model of Ungerer et al. (1984) FIGURE 1 Tectonic subsidence computation local isostasy FIGURE 2 Tectonic subsidence computation regional isostasy (adsbygoogle = window.adsbygoogle || []).push({}); reconstructs the geometry of the sedimentary basin through time in the form of successive cross sections Figure 3 FIGURE 3 The backstripping method and Figure 4). FIGURE 4 Tectonic subsidence history plot (adsbygoogle = window.adsbygoogle || []).push({}); Geodynamic and Thermal Models (adsbygoogle = window.adsbygoogle || []).push({}); Ungerer et al. (1984) estimate heat flow history based on models that provide quantitative predictions of subsidence and heat flow. Guidish et al. (1985) review several geodynamic models that predict the change in heat flow as a function of time, including those developed by Sleep (1971), McKenzie (1978), Falvey and Middleton (1981), and Royden et al. (1980). We can test the applicability of these geodynamic models to a given sedimentary basin by examining the differences between backstripped and predicted subsidence. We can also calibrate geodynamic models against measured thermal indicators, such as vitrinite reflectance (Lerche et al., 1984). We apply the heat flow history to determine the temperature history of rock units, and the subsequent maturation of source rocks. Two of the geodynamic models we have discussed provide subsidence predictions compatible with observed subsidence. The McKenzie crustal stretching model (1978) (Figure 1, Evolution from a simple rift to a continental margin: [a] simple rifting model; [b] extension model; [c] continental margin model.) FIGURE 1 Evolution from a simple rift to a continental margin for basin formation describes a rapid stretching of the continental lithosphere, accompanied by crustal thinning and passive upwelling of hot asthenosphere. The crust subsides through block faulting during this stage, which is followed by crustal cooling, thickening, and passive subsidence as thermal equilibrium is re-established. Royden et al. (1980) present equations for solving for various stretching factors, β. The stretching factor for "oceanization" of crust describes crust ranging from purely continental (β=0) to purely oceanic (β=1). Figure 2 (Extension and dike intrusion models: [a] theoretical surface elevation for an extensional margin), FIGURE 2 Extension and dike intrusion models Figure 3 (Theoretical heat flow for an extensional margin), FIGURE 3 Theoretical heat flow for an extensional margin Figure 4 (Theoretical surface elevation for dike intrusion), FIGURE 4 Theoretical surface elevation for dike intrusion and Figure 5 (Theoretical heat flow for dike intrusion) plot solutions showing subsidence (a) and heat flow (b) over time for the McKenzie model. FIGURE 5 Theoretical heat flow for dike intrusion (adsbygoogle = window.adsbygoogle || []).push({}); One weakness of this model is its failure to include heat input from crustal radioactive decay. Sclater and Christie (1980) input an additional heat component in the calculations of McKenzie (1978) and Royden et al. (1980). Royden et al. present a second model that produces results comparable to observed subsidence. This model proposes fracturing of continental crust and intrusion by dikes from the mantle (Figure 1 [b & c] ), with subsidence caused by replacing lighter crust with denser mantle material. Figure 2, Figure 3, Figure 4, and Figure 5. plots solutions for subsidence (c) and heat flow (d) over time for various stages of "oceanization" of the crust. Ungerer et al. (1984) also add heat produced by crustal radioactive heat decay to this model. In order to apply these geodynamic models to predict heat flow histories, we must use the backstripping model to compensate for subsidence due to loading, and to reconstruct the subsidence history. Empirical measures of tectonic subsidence and age allow us to calculate a unique value of β, or to use the graphs shown in Figure 2 and Figure 4. Once we determine the value of β, we can calculate or measure heat flow histories from Figure 3 or Figure 4. A comparison of the theoretical results shows that for end-member values of "oceanization" of crust (β=0 or β=1), heat flow histories predicted by these two models are similar. With intermediate values of b, early heat flow is higher for the dike-intrusion model. This result has implications for maturation histories, and consequently indicates the potential for using known maturation values to validate the choice of geodynamic models (Lerche et al., 1984). Once we predict the heat flow history, we can apply thermal models to determine the time/temperature history for specific sedimentary units. Royden et al. (1980) point out that the temperature at depth is directly related to heat flow, so that we can determine the temperature at a given depth based on heat flow and thermal conductivity. Using the heat flow history and a simple model relating temperature to depth, we can determine the temperature history of each lithologic unit after estimating the thermal conductivity of the unit. Ungerer et al. (1984) developed a more comprehensive thermal model that factors in vertical heat transfer by conduction (convection and lateral heat transfer are not modeled). Their model also accounts for vertical heat transfer by expulsion of fluids during compaction, as well as variations in thermal properties of sediments with burial. There are several models we can use to develop an understanding of the temperature history of a sedimentary basin. The input parameters for these models are both empirical and theoretical, and are based on numerous mathematical sub-models that predict such things as porosity, eustatic sea level changes, crustal response to loading, crustal thickness, heat transfer, and thermal properties of rocks. Our output from each of these models is only as reliable as the data we input. (adsbygoogle = window.adsbygoogle || []).push({}); Model Calibration (adsbygoogle = window.adsbygoogle || []).push({}); We can use empirical measurements of vitrinite reflectance to constrain and determine the heat flow history and time/temperature relationships (Guidish et al., 1985). Lerche et al. (1984) extracted a time/temperature index (TTI) from measured vitrinite reflectance data, as a function of depth. We can use this TTI to calibrate heat flow histories determined from the geodynamic models. We use the heat flow histories to compute temperature as a function of time and depth. We compare this TTI to the TTI generated using Lerche et al.’s equations, solving for known vitrinite reflectance measurements at known depths. If the TTI predicted by the geodynamic model varies significantly from that computed by the empirically-based model, we can vary the geodynamic model parameters until we obtain a least-squares fit, or we can select a different geodynamic model altogether. Tissot et al. (1987) argue for using both theoretically and empirically based models to evaluate heat flow histories. Sweeney et al. (1990) present a computer program designed to optimize heat flow histories. This program computes vitrinite reflectance data based on kinetic and temperature history data, and compares computed values to calibrate the time/temperature relationship. Maturation Modeling Once we have calculated the time/temperature/depth relationships, our next step is to perform maturation modeling. There are several common approaches to maturation modeling, including; 1) an empirical approach proposed by Lopatin (1971) and modified by Waples (1980), and 2) a kinetic model proposed by Tissot and Espitalie (1975). The empirical approach to maturation modeling is applied extensively because it calculates the combined effect of time and temperature based on the relatively simple assumption that rates of chemical reactions approximately double for every 10 degrees C rise in temperature. We plot a burial history curve using backstripped subsidence calculations, and plot paleotemperature on the burial history curve (Waples, 1980). Using this plot, we can determine the length of time any stratigraphic unit spends within a given 10 degrees C temperature interval, and the total number of intervals it has passed through in its history. We calculate the effects of increasing burial and temperature by multiplying the time in a given interval by successive powers of 2 (Table 1 [a]). We then sum the successive interval maturities to calculate a time-temperature index (TTI), which has been calibrated ( Table 1 [b] ) to vitrinite reflectance values (R0) and thermal alteration index (TAI) values. Bond (1988) details the principles and applications of the TTI method, complete with a detailed case history of maturation modeling in the Maracaibo Basin of Venezuela (Talukdar et al., 1986) and a hypothetical example of preparing a Lopatin model. Table 1: Lopatin relationships a: Temperature factor to burial temperature. Temperature Range (ºC) Temperature-Factor(γ \mathbf{\gamma} ) Temperature-Factor(γ \mathbf{\gamma} ) 30-40 2−7 2^{-7} 1128 \tfrac{1}{128} 40-50 2−6 2^{-6} 164 \tfrac{1}{64} 50-60 2−5 2^{-5} 132 \tfrac{1}{32} 60-70 2−4 2^{-4} 116 \tfrac{1}{16} 70-80 2−3 2^{-3} 18 \tfrac{1}{8} 80-90 2−2 2^{-2} 14 \tfrac{1}{4} 90-100 2−1 2^{-1} 12 \tfrac{1}{2} 100-110 20 2^0 1 110-120 21 2^1 2 120-130 22 2^2 4 130-140 23 2^3 8 140-150 24 2^4 16 150-160 25 2^5 32 160-170 26 2^6 64 b.) Cumulative TTI values to other geochemical parameters. % Vitrinite Reflectance (R0 \mathbf{R_0} ) Thermal Alteration Index (TAI) Generation 0.04 2.25 <1 Condensate from resinite___________ 0.50 2.50 from S-rich kerogen 0.60 2.60 | \qquad early 0.65 2.65 | \qquad peak 0.70 2.70 | 0.80 2.8 Oil 0.90 2.87 | 1.00 2.90 | \qquad late 1.15 3.00 ______________ 1.35 3.27 Wet gas 1.50 3.50 ______________ 1.75 3.60 Dry gas 2.00 3.70 2.50 3.80 3.00 3.90 4.00 4.00 5.00 4.00 (adsbygoogle = window.adsbygoogle || []).push({}); Waples (1980) summarizes the applications of TTI modeling to exploration. First, we can use the data to predict present-day TTI values for potential reservoirs. For example, if the TTI value for a reservoir at 12,000 ft (3,758 m) is 1,200, the reservoir will contain dry gas according to Table 1 (b). Second, we can calculate present-day values for a known organic-rich shale at several points within a basin (Figure 1). FIGURE 1 Calculate present-day values for a known organic-rich shale at several points within a basin We can contour these values to determine the extent and location of potentially mature source rock. In this example, only limited areas have reached mature levels. A third application answers questions about timing of maturation. The model in Figure 2 shows a window defined by connecting TTI values of 15 and 160 on each of several horizons. FIGURE 2 The model in shows a window defined by connecting TTI values of 15 and 160 on each of several horizons This oil window shows that the oil source rocks began generating 180 Mya, and ceased generating 120 Mya. If traps in the region did not form until 100 to 90 Mya, oil migration would have occurred prior to their formation. If we next plot the gas window, we can make similar predictions about potential gas traps. The ease of application and limited data requirements of the Lopatin method make it an attractive first-pass method of maturation modeling (Bond, 1988). There are many computer programs on the market for developing Lopatin plots, and these plots are frequently provided as part of routine commercial geological/geochemical analyses. There are, however, several caveats to the application of Lopatin modeling (Tissot et al., 1987). The TTI model relies on the assumption that reaction rates double for every rise of 10 degrees C in temperature. This assumption is valid only within a limited range of activation energies near the onset of oil generation. At advanced stages of oil and gas generation, activation energies necessary to affect kerogen maturation are much higher, and reaction rates are multiplied by factors of 5 to 10 for each 10 degrees C rise (Tissot and Espitalie, 1975). Additionally, Lopatin’s model considers that all types of kerogen react similarly during thermal maturation. This assumption is invalid, as recognized by many authors (Tissot and Welte, 1984). Several published studies highlight shortcomings of the Lopatin method. Tissot et al. (1987) point out that kinetic models provide better agreement with known distributions of oil and gas in sedimentary basins. They recommend applying Lopatin modeling only when the computer facilities necessary for kinetic modeling are not available. Kinetic models of organic matter maturation directly calculate the amount of oil and gas generated from kerogen in sediments, where we know TOC, kerogen types, and thermal history (Figure 3). FIGURE 3 Kinetic models of organic matter maturation Kinetic modeling using the Tissot-Espitalie method calculates a transformation ratio for bitumen which is a measure of maturity. A ratio of 0:1 equals 0 percent, or immature, with all generation potential remaining. At a ratio of 1:1, (100 percent, over-mature), all generation potential has been realized (Bond, 1988). Figure 4, Figure 5, and Figure 6 show transformation ratios (as percentage conversion) for three types of kerogen. FIGURE 4 Transformation ratios as percentage conversion for kerogen type I FIGURE 5 Transformation ratios as percentage conversion for kerogen type II FIGURE 6 Transformation ratios as percentage conversion for kerogen type III Kinetic modeling is both mathematically and computer intensive (Tissot and Espitalie, 1975; Ungerer et al., 1984), taking into account several parallel reactions, with varying activation energies and reaction rates as determined in the laboratory for different types of kerogen. These models, however, allow for more realistic analysis and prediction of maturation than do non-kinetic models. Figure 7 compares the evolution of transformation ratios (maturation) for four different kerogen types subjected to the same thermal history. FIGURE 7 Compares the evolution of transformation ratios (maturation) for four different kerogen types Maturation of Type II, high-sulfur kerogen in the Monterey Formation begins at a shallow depth, while maturation of Type II kerogen in the Paris Basin begins slightly deeper. Both generate over a broad depth range. Type III kerogen in the Mahakam delta matures at a greater depth and temperature than does Type II kerogen, and the transformation ratio increases slowly due to complex activation energies. Type I kerogen in the Green River shales matures quickly, at greater depths, because of relatively simple kerogen chemistry. Figure 8 shows even more striking differences between the generation potential of the different kerogen types. FIGURE 8 Differences between the generation potential of the different kerogen types Kinetic models compute burial and hydrocarbon generation histories, and provide quantitative assessment of hydrocarbon potential in sedimentary basins. Kinetic models for analyzing oil and gas generation are now recognized as an integral part of basin modeling. Computer programs (e.g., BasinModTM) are available for personal computers. These programs require input in the form of burial and thermal histories, based on known geological and geophysical data and on model calculations. It is important to constrain the model by comparing measured maturation indices, present-day heat flow, and thermal conductivity measurements (Waples et al., 1992a, 1992b). (adsbygoogle = window.adsbygoogle || []).push({}); Migration Modeling We apply quantitative migration modeling at more advance stages of exploration, when richness and distribution of source rocks are fairly well known from well data. These data allow us to quantify the amount of hydrocarbons generated in the basin, and to model the migration, accumulation, and leakage of hydrocarbons (Ungerer et al., 1984). The migration model proposed by these authors uses input from previous thermal modeling and backstripping calculations. They compute compaction effects and create cross sections that show pressure and hydrocarbon saturation within sediments through time. Thermodynamic Modeling Thermodynamic modeling is specifically designed to determine the amount and composition of hydrocarbons that may migrate within a gaseous solution. Therefore we can use a thermodynamic model to predict the condensate content of wet gases, which is important at depths and pressures where the oil/gas mixture separates into two phases. Successively lighter oils condense out of the gas phase at successively shallower depths and pressures. The model predicts the pressure at which condensation of oil begins Figure 1, Evolution of the composition of oil and gas phases during vertical migration, as computed by the thermodynamic model. FIGURE 1 Evolution of the composition of oil and gas phases during vertical migration Initial composition is based on deep condensates of the Mahakan delta in the high pressure zones.) and computes the changing composition of the oil/gas phases during vertical migration. We should use this model relatively late in an exploration program to answer specific questions about contents of gas condensate and vertical migration. (adsbygoogle = window.adsbygoogle || []).push({}); Assessment Mathematical Basin Analysis Models (adsbygoogle = window.adsbygoogle || []).push({}); 1. _________ reconstructs heat flow histories used for basins formed by extension. A .A backstripping modelB .A geodynamic modelC .A thermal model 2. The simplest backstripping model (local or Airy isostasy) assumes that the lithosphere has no strength. A .TrueB .False 3. One can determine the temperature at a given depth based on heat flow and: A .electrical conductivityB .porosityC .thermal conductivityD .bulk density 4. A time/temperature index (TTI) as a function of depth can be used to calibrate heat flow histories determined from: A .the geomagnetic models.B .the geostratigraphic models.C .the geodynamic models. (adsbygoogle = window.adsbygoogle || []).push({}); 5. The TTI model relies on the assumption that reaction rates double for every rise of _ in temperature. A .1 degrees CB .10 degrees CC .50 degrees CD .100 degrees C 6. Migration modeling is specifically designed to determine the amount and composition of hydrocarbons that may migrate within a gaseous solution. A .TrueB .False 7. Successively lighter oils condense out of the gas phase at successively shallower depths and pressures. A .TrueB .False Recommended for You Structural Interpretation Braided Stream Environments Classification of Nonmarine Sandstones Basin Histories and Properties Alluvial Fan Environments Meandering Channel Alluvial Systems (adsbygoogle = window.adsbygoogle || []).push({});