FLUVSIM reproduces the self-organized criticality characteristics observed in natural fluvial systems ... potential for sediment storage and preservation at a particular location, and sediment supply refers ... crevasse notch will form in the channel levee. ..... Schlumberger Educational Services, Houston, Texas, USA. Vukovic ...
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Calibration and Reliability in Groundwater Modelling: A Few Steps Closer to Reality (Proceedings o f ModelCARE'2002. Prague. Czech Republic. June 2002). IAHS Publ. no. 277. 2002.
Relating flow and transport characteristics to stratigraphie process-response variables DWAINE EDINGTON & EILEEN POETER International Engineering,
Ground Water Modeling Center, Department Colorado School of Mines, Golden, Colorado
of Geology and 80401, USA
Geological
dwaine.edingtondf5jattbi.com
Abstract Fluvial stratigraphie units generated by FLUVSIM from geological process parameters are incorporated into a constant hydrological regime using MODFLOW, and particles were tracked using MODPATH. Groundwater flow and travel time are dependent on geological depositional conditions, with faster travel times in low accommodation and longer travel times in high accommodation environments. Some geologists argue that geological conditions will be the same whether sea level rises or land subsides; others have countered these arguments. These experiments illustrate that accom modation space created by sea level rise or by land subsidence causes different distributions of geological units and groundwater travel times. K e y w o r d s fluvial s e d i m e n t s ; i n v e r s i o n ; m o d e l l i n g ; M O D F L O W ; M O D P A T H ; particle tracking; stratigraphie model
INTRODUCTION The distribution of hydraulic properties is a major influence on flow and transport simulated by a groundwater model, but this distribution is difficult to determine with model calibration. Combining information from many sources reduces uncertainty associated with the distribution of hydraulic properties. One approach is to develop and invert many conceptual models that honour all of the data, and select the model(s) with the best fit(s) and least biased residuals for prediction (Poeter & McKenna, 1995). Although Anderson (1990) emphasized the importance of stratigraphie features in determining preferential flow paths, many methods for generating the distribution of hydraulic properties overlook the value and information content of stratigraphie data (Koltermann & Gorelick, 1996). We propose that joint inversion of stratigraphie and flow models will improve the conceptual models of property distributions. The problem with pursuing this route has been the lack of suitable stratigraphie simulation models. In an effort to reach that end we have developed a model of fluvial geology and, in this paper, have coupled the geological model results with flow modelling to illustrate the influence of stratigraphie processes on the flow regime. Mathematical models are capable of accurately simulating a variety of stratigraphic and sedimentological attributes (such as lithology, petrophysical properties and geometry) at scales relevant to fluid flow by operating on a set of input process parameters such as rate of sea level change, subsidence rate, river discharge, and sediment supply (expressed as mass flux, median grain size and sorting coefficient). These attributes change systematically and predictably as the stratigraphie system responds to changing accommodation-space to sediment-supply ratio (A/S) (Cross et
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al, 1993). These models reliably predict geological attributes in areas between and beyond locations where geological data are available by inverting the model to estimate optimal process parameter values (Cross & Lessenger, 1999). One commonly cited objection to stratigraphie inversion is the non-uniqueness of the solution (Burton et al., 1987). For example, it has been argued that a i m rise in sea level produces the same stratigraphie response as 1 m subsidence of the land surface. In a series of papers, Cross & Lessenger (1995, 1999, 2003) demonstrate that the stratigraphie system responds differently to such complementary changes in process parameters, exhibited as differences in sediment volume partitioning, stacking patterns, cycle symmetry, aspect ratios and frequency of hiatal surfaces. To test whether this finding extends to influence flow systems, we conducted a series of experiments to evaluate the character of flow and transport under: (a) different A/S conditions generated by changing total accommodation, and (b) similar A/S conditions by changing the dominant source of accommodation. Since the sediment supply is the same for each simulation, the net movement of land and sea level surface (i.e. the sum of the subsidence rate and the linear component of the rate of sea-level change) serves to represent the amount of A/S imposed on the model. The web site, http://www.mines.edu/~epoeter/research/FluvSim/index.shtml provides supp lementary information.
PROCEDURE FLUVSIM is a deterministic model based on fuzzy logic that simulates threedimensional (3-D) sediment accumulation in fluvial environments at the channelbelt/flood-plain scale. Sub-environments (facies tracts) in the model include main channel belt, abandoned main channel, and splay complexes with proximal, distal, delta and pond elements. FLUVSIM determines sedimentological (e.g. grain size, environment of deposition) and stratigraphie (e.g. thickness, geometry, facies distribution) attributes and determines petrophysical properties, such as porosity and hydraulic conductivity based on textural characteristics of the deposited sediment. FLUVSIM uses fuzzy logic to simulate where, how much, and what type of sediment is deposited on the flood plain. Advantages of fuzzy logic include: the ability to simulate multiple, nonlinear, interdependent processes and responses; the ability to incorporate qualitative data, empirical generalizations, and knowledge lacking in robust numerical formulations; and the ability to incorporate complex, nonlinear functions without using more precision than necessary to solve the problem. FLUVSIM reproduces the self-organized criticality characteristics observed in natural fluvial systems by incorporating nonlinear dynamics, feedback, buffers, thresholds, memory, and mass conservation. Self-organized critical behaviour ensures that the simulated model results are internally consistent so that information available in one part of the model infers geology in other parts of the model. This internal consistency is a necessary condition for stratigraphie inversion. Changes in stratigraphie attributes reflect changes in the accommodation to sediment supply (A/S) ratio (Fig. 1). Accommodation space refers to the potential for sediment storage and preservation at a particular location, and sediment supply refers
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Dwaine Edington & Eileen Poeter
(a) High Accommodation
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'""' 10 km
i—j Active
j
!—J Channels
I—i Splays
j Proximal
r—iDistal
••Abandoned
-•—"Splays
^Channels
Fig. 1 Contrasting stratigraphie architecture, results from different A/S conditions. High A/S systems (a) produce isolated main channel sand bodies surrounded by splaycomplex sediments, while low A/S systems (b) produce extensive sheets of sand due to lateral channel migration.
to processes that produce and transport sediment. FLUVSIM minimizes the number of input parameters and direct forcing functions to just four user-defined input curves that describe fluxes of energy and mass entering the model as a function of time: sea level, subsidence, river discharge, sediment flux (amount and texture). The first two parameters affect accommodation and the last two parameters affect sediment supply. Given these energy and mass fluxes defined at the model boundary, internal processes redistribute the energy (accommodation) and flux (sediment supply) according to rules specified by the stratigraphie process-response system. When accommodation is high, the typical life cycle of a fluvial system begins with alluvial ridge aggradation. Aggradation on alluvial ridges is a function of the amount of accommodation added to the system through sea level fluctuations and subsidence. As the alluvial ridge grows in height, the lateral gradient may exceed the down channel gradient. If the discharge in the channel exceeds a threshold during a flood event, a crevasse notch will form in the channel levee. If conditions are right, water and sediment transfer to splay complexes allowing for crevasse splay evolution. Ultimately, the splay complex may capture all of the water and sediment flow from the main channel in a process called avulsion, resulting in abandonment of the main channel. Aggradation of the new main channel commences and the cycle continues. The stratigraphie record in this case is one of isolated main-channel sand bodies s u i T O u n d e d by splay complex deposits (Fig. 1(a)). Under low A/S conditions, aggradation of the main channel does not occur. Splays will not develop without a gradient advantage, so avulsions do not occur. The dominant process in this case is lateral channel migration. As the channel sweeps across the flood plain, it consumes pre-existing sediments and replaces them with coarse-grained channel deposits, resulting in laterally extensive sheets of sand (Fig. 1(b)). FLUVSIM generated a series of simulations on a 40 x 40 grid of 2500 m x 2500 m cells, each using a unique set of process parameters as delineated in Table 1 and organized in two suites. Each suite investigates flow and transport characteristics with respect to the stratigraphie attributes resulting from changes in a single geological
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Table 1 Input process parameters describe energy or mass flux entering the model space. The sum of the linear component of the sea level function and subsidence function are consistent between suites. Sea level Subsidence
Suite 1
Suite 2
Sinusoidal plus lonj» term linear ranging from +20 cm kyear" to -10 cm kyear"' Long term linear 2 cm kyear"'
Sinusoid only Long term linear ranging from +22 cm kyear" to - 8 cm kyear" 500 + / - 150 m V 1200 kg s"' 0.200 mm 4.5 1
River discharge Sediment flux Median grain size Sorting coefficient
5 0 0 + / - 150 m V 1200 kg s" 0.200 mm 4.5 1
1
process parameter over a range of A/S values. One suite of simulations investigates the stratigraphie response to a range of rates of sea-level rise and fall. The sea-level function consists of a sinusoidal curve superimposed on a long-term linear trend. The long-term trend ranges from -10 to +20 centimetres per kilo-year (cm kyear" ). Subsidence was held constant at +2 cm kyear" . The second suite evaluates a range of subsidence rates from - 8 to +22 cm kyear"'. The long-term linear trend of sea level was fixed at 0 cm kyear"' for all runs in this suite. The rates are such that the sums of the rate of sea-level change and the rate of subsidence are identical in both suites. All other model inputs were constant between the runs in each suite. The FLUVSIM simulations generate distributions of horizontal and vertical hydraulic conductivity and effective porosity for input into MODFLOW (McDonald & Harbaugh, 1988) and MODPATH (Pollock, 1989). Information from the grain size distribution is used to estimate the hydraulic conductivity using the Kozeny-Carmen equation (Vukovic & Soro, 1992). Determination of effective porosity from the grain size distribution involves three steps. 1
1
2
3
cp, = (- 0.3340 C + 0.0153475 C - 0.000097025 C + 37.130ô)/l00
(1)
9 . =q>, -0.601806 C
(2)
ty
3
3
