WO2006016942A1

WO2006016942A1 - Predicting sand-grain composition and sand texture

Info

Publication number: WO2006016942A1
Application number: PCT/US2005/018821
Authority: WO
Inventors: Suzanne Kairo; William A. Heins; Karen M. Love
Original assignee: Exxonmobil Upstream Research Company
Priority date: 2004-07-07
Filing date: 2005-05-31
Publication date: 2006-02-16
Also published as: AU2005272112B2; US20090012746A1; CA2579011A1; US7747552B2; EP1766441A4; EP1766441A1; CA2579011C; MX2007000363A; NO20070654L; AU2005272112A1

Abstract

A method and apparatus for predicting sand-grain composition and sand texture are disclosed. A first set of system variables associated with sand-grain composition and sand texture is selected (605). A second set of system variables directly or indirectly causally related to the first set of variables is also selected (610). Data for each variable in the second set is estimated or obtained (615). A network with nodes including both sets of variables is formed (625). The network has a directional links connecting interdependent nodes. The directional links honor known causality relationships. A Bayesian network algorithm is used (630) with the data to solve the network for the first set of variables and their associated uncertainties.

Description

Predicting Sand-Grain Composition and Sand Texture

[0001] This application claims the benefit of U.S. Provisional Applications No. 60/586,061 filed on July 7, 2004 and No. 60/588,265 filed on July 15, 2004.

BACKGROUND [0002] Bayesian networks are a tool for modeling systems. A description of Bayesian networks is provided in United States Patent No. 6,408,290, which description is provided below, with omissions indicated by ellipses. Figure 1 from the 6,408,290 patent is replicated as Fig. 1 hereto:

A Bayesian network is a representation of the probabilistic relationships among distinctions about the world. Each distinction, sometimes called a variable, can take on one of a mutually exclusive and exhaustive set of possible states. A Bayesian network is expressed as an acyclic-directed graph where the variables correspond to nodes and the relationships between the nodes correspond to arcs. FIG. 1 depicts an exemplary Bayesian network 101. In FIG. 1 there are three variables, X₁, X₂, and X₃, which are represented by nodes 102, 106 and 110, respectively. This Bayesian network contains two arcs 104 and 108. Associated with each variable in a Bayesian network is a set of probability distributions. Using conditional probability notation, the set of probability distributions for a variable can be denoted by

where "p" refers to the probability distribution, where "II_i" denotes the parents of variable X_t and where "ζ" denotes the knowledge of the expert. The Greek letter "ζ" indicates that the Bayesian network reflects the knowledge of an expert in a given field. Thus, this expression reads as follows: the probability distribution for variable X_i given the parents of X₁ and the knowledge of the expert. For example, X₁ is the parent of X₂. The probability distributions specify the strength of the relationships between variables. For instance, if X₁ has two states (true and false), then associated with X₁ is a single probability distribution />(x_r|^) and associated with X₂ are two probability distributions

The arcs in a Bayesian network convey dependence between nodes. When there is an arc between two nodes, the probability distribution of the first node depends upon the value of the second node when the direction of the arc points from the second node to the first node. For example, node 106 depends upon node 102. Therefore, nodes 102 and 106 are said to be conditionally dependent. Missing arcs in a Bayesian network convey conditional independencies. For example, node 102 and node 110 are conditionally independent given node 106. However, two variables indirectly connected through intermediate variables are conditionally dependent given lack of knowledge of the values ("states") of the intermediate variables. Therefore, if the value for node 106 is known, node 102 and node 110 are conditionally dependent.

In other words, sets of variables X and Y are said to be conditionally independent, given a set of variables Z, if the probability distribution for X given Z does not depend on Y. If Z is empty, however, X and Y are said to be "independent" as opposed to conditionally independent. If X and Y are not conditionally independent, given Z, then X and Y are said to be conditionally dependent given Z.

The variables used for each node may be of different types. Specifically, variables may be of two types: discrete or continuous. A discrete variable is a variable that has a finite or countable number of states, whereas a continuous variable is a variable that has an uncountably infinite number of states. . . . An example of a discrete variable is a Boolean variable. Such a variable can assume only one of two states: "true" or "false." An example of a continuous variable is a variable that may assume any real value between -1 and 1. Discrete variables have an associated probability distribution. Continuous variables, however, have an associated probability density function ("density"). Where an event is a set of possible outcomes, the density p(x) for a variable "x" and events "α" and "b" is defined as:

where p(a ≤ x ≤ b) is the probability that x lies between a and b.

[0003] Bayesian networks also make use of Bayes Rule, which states:

p(B) ^■ p(A I B) p(B \ A) = -

P(A)

for two variables, where p(B\A) is sometimes called an a posteriori probability. Similar equations have been derived for more than two variables. The set of all variables associated with a system is known as the domain.

[0004] Building a network with the nodes related by Bayes Rule allows changes in the value of variables associated with a particular node to ripple through the probabilities in the network. For example, referring to Fig. 1, assuming that Xi, ∑₂ and X₃ have probability distributions and that each of the probability distributions is related by Bayes Rule to those to which it is connected by arcs, then a change to the probability distribution of X₂ may cause a change in the probability distribution of Xj (through induction) and X₃ (through deduction). Those mechanisms also establish a full joint probability of all domain variables (i.e. Xi, X₂, X₃) while allowing the data associated with each variable to be uncertain.

[0005] Geoscientists are frequently interested in sandstone reservoir porosity and permeability, which are often related to the likelihood of producing commercial quantities of hydrocarbons from the reservoir. Some existing tools predict sandstone reservoir porosity and permeability as a function of compaction and cementation using physics- and chemistry-based numerical models. Many of these tools take sand composition and grain-size information as inputs. - A -

SUMMARY

[0006] In general, in one aspect, the invention features a casual, probabilistic method for predicting sand-grain composition and sand texture. The method includes selecting a first set of system variables associated with sand-grain composition and sand texture and a second set of system variables directly or indirectly causally related to the first set of variables. The method further includes obtaining or estimating data for each variable in the second set and forming a network with nodes including both sets of variables. The network has directional links connecting interdependent nodes. The directional links honor known causality relationships. The method includes using a Bayesian network algorithm with the data to solve the network for the first set of variables and their associated uncertainties.

[0007] Implementations of the invention may include one or more of the following. The method may include appraising the quality of selected data and including the quality appraisals in the network and in the application of the Bayesian network algorithm. The system may have a behavior and the method may further include selecting the first set of variables and the second set of variables so that together they are sufficiently complete to account for the behavior of the system.

[0008] Forming the network may include forming a third set of intermediate nodes interposed between at least some of the nodes representing the first set of system variables and at least some of the nodes representing the second set of system variables. Selecting the first set of system variables may include selecting one or more system variables associated with sand-grain composition and selecting one or more system variables associated with sand texture. Selecting the second set of system variables may include selecting one or more system variables associated with hinterland geology, selecting one or more system variables associated with hinterland weathering and transport, selecting one or more system variables associated with basin transport and deposition. [0009] In general, in another aspect, the invention features a method for predicting sand-grain composition and sand texture. The method includes establishing one or more root nodes in a Bayesian network, establishing one or more leaf nodes in the Bayesian network, coupling the root nodes to the leaf nodes to enable the Bayesian network to predict sand-grain composition and texture.

[0010] Implementations of the invention may include one or more of the following. Establishing the one or more root nodes may include establishing one or more root nodes for hinterland geology, establishing one or more root nodes for hinterland weathering and transport, and establishing one or more root nodes for basin transport and deposition. Establishing one or more root nodes for hinterland geology may include establishing a root node for tectonic setting. Establishing one or more root nodes for hinterland weathering and transport may include establishing a root node for climate, establishing a root node for rate of hinterland uplift, and establishing a root node for hinterland transport distance. Establishing one or more root nodes for basin transport and deposition may include establishing a root node for rate of basin subsidence, establishing a root node for basin fluvial transport distance, and establishing a root node for depositional facies.

[0011] Establishing one or more leaf nodes may include establishing one or more leaf nodes for sand-grain composition and establishing one or more leaf nodes for sand texture. Establishing one or more leaf nodes for sand texture may include establishing a leaf node for grain size, establishing a leaf node for degree of sorting, and establishing a leaf node for deposited matrix abundance. Establishing the leaf node for grain composition may include establishing a leaf node for final CIBU sand, establishing a leaf node for final CISU sand, establishing a leaf node for final CAMBU sand, establishing a leaf node for final CAMSU sand, establishing a leaf node for final SAMV sand, and establishing a leaf node for final SAMP sand.

[0012] The method may further include establishing one or more intermediate nodes. Coupling the root nodes to the leaf nodes to enable the Bayesian network to predict sand-grain composition and texture may include coupling at least some of the one or more root nodes to at least some of the one or more leaf nodes through the one or more intermediate nodes. Coupling the root nodes to the leaf nodes to enable the Bayesian network to predict sand-grain composition and texture may include coupling the root nodes to the leaf nodes in causal relationships that honor observations of natural systems. Coupling the root nodes to the leaf nodes to enable the Bayesian network to predict sand-grain composition and texture may include defining for each root node one or more outputs that connect to other nodes that the root node causes, and defining for each intermediate node: one or more inputs that connect to the other nodes that cause the intermediate node, one or more outputs that connect to other nodes that the intermediate node causes, and defining for each leaf node one or more inputs that connect to other nodes that cause the leaf node.

[0013] Establishing the one or more root nodes may include creating a probability table for each root node, each probability table having one or more predefined states, and each predefined state having associated with it a probability that the root node is in that state. Creating the probability table for each root node may include completing the probability table based on quantitative observations of a natural system associated with the root node. The method may further include modifying the probability table based on quantitative observations of the natural system associated with the root node.

[0014] Establishing the one or more leaf nodes may include creating a probability table for each leaf node, each probability table having a respective one or more predefined states, and each predefined state having associated with it a probability that the leaf node is in that state. Each leaf node may have a predefined number of inputs and creating the probability table for each leaf node may include creating a probability table having the respective predefined number of input dimensions. Creating the probability table for each leaf node may include completing the probability table with data reflecting quantitative observations of a natural system associated with the leaf node. The method may further include modifying the probability table based on quantitative observations of the natural system associated with the leaf node.

[0015] Establishing the one or more intermediate nodes may include creating a probability table for each intermediate node, each probability table having a respective one or more predefined states, and each predefined state having associated with it a probability that the intermediate node is in that state. Each intermediate node may have a predefined number of inputs and creating the probability table for each intermediate node may include creating a probability table having the respective predefined number of input dimensions. Creating the probability table for each intermediate node may include completing the probability table with data reflecting quantitative observations of a natural system associated with the intermediate node. The method may further include modifying the probability table based on quantitative observations of the natural system associated with the intermediate node.

[0016] In general, in another aspect, the invention features a Bayesian network including one or more root nodes and one or more leaf nodes. The root nodes are coupled to the leaf nodes to enable the Bayesian network to predict sand-grain composition and texture.

[0017] In general, in another aspect, the invention features a method for predicting porosity and permeability including predicting sand-grain composition and sand texture from tectonic setting, hinterland weathering and transport, and basin transport and deposition using a Bayesian network, and predicting porosity and permeability from the predicted sand-grain composition and sand texture.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Fig. 1 is a representation of a simple Bayesian network.

[0019] Fig. 2 is a block diagram of a system for predicting porosity and permeability using a Bayesian network to predict sand-grain composition and sand texture.

[0020] Fig. 3 is a representation of a Bayesian network to predict sand-grain composition and sand texture.

[0021] Fig. 4 is an example of a portion of the Bayesian network of Fig. 3 showing the prediction of sand texture. [0022] Fig. 5 is an example of a portion of the Bayesian network of Fig. 3 showing the prediction of sand-grain composition.

[0023] Figs. 6-14 are flowcharts illustrating the development of a Bayesian network to predict sand-grain composition and sand texture.

DETAILED DESCRIPTION

[0024] Detrital grain composition and grain-size distribution determine the initial porosity, permeability, and other petrophysical properties of a sandstone, such as for example a clastic petroleum reservoir. Grain composition and grain-size distribution also determine how petrophysical and reservoir properties evolve as the sand is buried. Understanding the composition and texture of a sandstone reservoir body can lead to a greater understanding of reservoir properties and their variation in space.

[0025] An example system to predict sand-grain composition and sand texture uses a Bayesian network to model the relationship among (1) environment (e.g. tectonic setting, topography, climate, transport/deposition systems), (2) sand generating and modifying processes (e.g. mechanical shattering and abrasion, chemical dissolution, hydrodynamic sorting), and (3) the resulting sand character (e.g. composition, texture and clay-matrix content).

[0026] Such a system can be used to predict porosity and permeability, as shown in Fig. 2. An example Bayesian network 205 has the following inputs: hinterland geology 210, hinterland weathering and transport 215, and basin transport and deposition 220. The outputs of the Bayesian network are sand-grain composition 225 and sand texture 230. The words "input" and "output" might be considered misnomers in this context. One characteristic of Bayesian networks is that the probability distributions of any node in the network can be adjusted. The adjustments may cause changes in the probability distributions associated with other nodes in the network depending on the interconnections between the nodes. Thus, for example, a user of the Bayesian network may adjust the probability distribution of the sand-grain composition "output" 225, producing an effect on the hinterland geology "input" 210. A more likely use of the Bayesian network, however, is to adjust the inputs 210, 215, and 220 and to monitor the effect on the outputs 225 and 230.

[0027] In one example system, the resulting predictions of sand-grain composition 225 and sand texture 230 are applied as inputs to an existing porosity and permeability tool 235, which produces estimates of porosity 240 and permeability 245.

[0028] As mentioned above, a Bayesian network is a formal statistical structure for reasoning in the face of uncertainty, which propagates evidence (or information), along with its associated uncertainties, through cause-and-effect, correlation or functional relationships to yield the probabilities of various inferences that could be drawn from the evidence. A Bayesian network can be formulated by a variety of computational techniques, including use of commercial software, or programming directly in standard computing languages.

[0029] The Bayesian network 205 makes detailed, quantitative predictions about sand composition, texture, and matrix content simultaneously. "Sand character" may be parameterized as sand composition, mean grain size, sorting, and matrix content. "Sand composition" may be parameterized as a finite number of discrete sand compositions defined by specific ratios of grain types and discrete grain-size distributions defined by specific ratios of grain sizes.

[0030] The predictions about sand character are detailed enough to use for making further predictions about hydrocarbon reservoir properties. The simultaneous prediction of all aspects of sand character derives from the holistic, cause-and-effect geoscience thinking that underlies the model. Using the Bayesian network 205:

■ All potential states of the system are explicitly defined, through the choice of specific nodes, and defined states of each node;

■ All relationships within the system are defined and quantified, by the specific structure of the network and probability tables; ■ The model can be updated from data, via modification of the probability tables;

^■ Inferences can be drawn inductively (child nodes from parent nodes) or deductively (parent nodes from child nodes).

[0031] A detailed representation of the Bayesian network 205, shown in detail for one embodiment of the present invention in Fig. 3, includes nodes and arcs between the nodes. The network includes three varieties of nodes: (a) a root node, which has only arcs with the direction of the arc being away from the root node (i.e. the root node is only a parent node and not a child node), (b) leaf nodes, which have only arcs with the direction of the arc being toward the nodes (i.e., leaf nodes are only child nodes and not parent nodes), and (c) intermediate nodes, which have arcs directed toward the nodes and arcs directed away from the nodes (i.e., intermediate nodes are both parent nodes and child nodes).

[0032] hi one example system, each node in the Bayesian network 205 has associated with it one or more states. Each node also has associated with it a probability distribution. The following materials, which disclose an example Bayesian network 205 in detail, are included at the end of this application before the claims and are a part of this application: (a) Description of Nodes; (b) Node States; and (c) Node Probability Distribution.

[0033] Fig. 3 illustrates one embodiment of Bayesian network 205. The same relationship between the root and leaf nodes could be achieved with a different set of intermediate nodes interconnected in a different manner. The system described by the Bayesian network 205 could also be described with different root, leaf and intermediate nodes.

[0034] The details of the Bayesian network structure and conditional probabilities may be changed depending on modeling conditions and level of knowledge about the system being modeled. The model will have the greatest predictive power when input probabilities are well constrained by evidence and the conditional probabilities are well conditioned with data. [0035] Figs. 4 and 5 illustrate examples of the probability distribution for each state of the output (leaf) nodes when each input (root) node is set with probability = 1 for one state, and all others set to 0.

[0036] hi these examples, it is assumed that the seven input nodes have the following values:

1. Tectonic Setting is "Continental Interior Basement Uplift" (CIBU);

2. Climate is "Wet";

3. Uplift Rate is "Fast";

4. Hinterland Transport Distance is "Long";

5. Basin Subsidence Rate is "Slow"; and

6. Basin Transport Distance is "Long".

7. Depositional Facies is "Delta, Distributary Channel"

[0037] Fig. 4 illustrates a prediction of sand texture, hi this example, all of the input nodes except Depositional Facies influence the probability distribution for the texture of sediment delivered to the depositional environment (Delivered Grain Size and Transported Clay Abundance). The delivered texture is convolved with Depositional Facies to determine the probability distribution for the states of Deposited Matrix Abundance, Degree of Sorting, and Final Grain Size Mode.

[0038] Fig. 5 illustrates a prediction of sand composition, hi this example, the QFR ternary diagram on the left side of Fig. 5 shows the probability of initial sand composition derived from the exposed provenance-lithotype assemblage implied by the CIBU tectonic setting; the degree of shading associated with each small square in the triangle representing the associated probability, with the darkest square being the most probable. The ternary diagram on the right side of Fig. 5 represents fine, medium and coarse fractions of the final sand composition. Again, the distribution of probabilities of those fractions is represented by small squares within the triangle, with the darkest square being the most probable. In each case, the most probable initial composition has no probability of being the final composition because of evolution that happens during transport to and within the basin. Transport to the basin removes some grain types more than others (and reduces the size of surviving grains) through the collaboration of mechanical abrasion and chemical dissolution. Transport and deposition in the basin segregates sand by grain size through hydrodynamic sorting; because some grain types are naturally associated with particular sizes, sorting influences composition. For example, rock fragments tend to be more abundant in the coarsest grain sizes, and feldspar tends to be most abundant in the finest grain sizes. Thus, the Final Grain Size Mode node is both an output of the model and an intermediate node for Sand Composition Suite, Final.

[0039] One example for constructing a Bayesian network for predicting sand- grain composition and sand texture, illustrated in Fig. 6, begins by selecting a first set of system variables associated with sand-grain composition and sand texture (block 605). A second set of system variables directly or indirectly causally related to the first set of system variables is then selected (block 610). Data for each variable in the second set is then obtained or estimated (block 615). In many cases, this may involve estimating a probability distribution for some or all of the variables in the second set. As data for the variables in the second set are gathered, the probability distribution estimates may become more refined. The quality, or reliability, of selected data is then appraised (block 620). Appraising quality of selected data is optional and may occur for all, some, or none of the obtained or estimated data.

[0040] A network is then formed (block 625). The network contains nodes representing both the first and the second sets of variables and the quality appraisals.

The network also contains intermediate nodes that may be situated between the first set of nodes and the second set of nodes. The network also includes directional links connecting interdependent nodes. The directional links honor known causality relationships. By way of explanation of the requirement for honoring known causality relationships, the reader is referred to a published example of a Bayesian approach (to a different petroleum application) that does not teach or suggest this requirement. See "Stochastic Reservoir Characterization Using Prestack Seismic Data," Eidsvick, et al., Geophysics 69, pp. 978-993 (2004). The network disclosed therein contains connections of the following kind: A causes B and C, and because B and C cause D, A is an indirect cause of D. But A is also shown in the illustrated network to be a direct cause of D. For purposes of the present invention, this is considered a logical error. Such a network does not honor known causality relationships. For further elaboration of this point, the reader is referred to U.S. Patent Application No. 60/586,027, entitled Bayesian Network Applications To Geology And Geophysics, filed on July 7, 2004.

[0041] A Bayesian network algorithm is then applied to the data and quality information to solve the network for the first set of variables and their associated uncertainties (block 630). The present inventive method requires no data or other information about the first set of system variables or any similar variables associated with sand grain composition and sand texture.

[0042] An example of forming a network (block 625), shown in detail in Fig. 7, includes establishing one or more root nodes in a Bayesian network (block 705). One or more leaf nodes (block 710) and one or more intermediate nodes are also established (block 715).

[0043] The root nodes are coupled to the leaf nodes through the intermediate nodes to enable the Bayesian network to predict sand-grain composition and sand texture (block 720).

[0044] An example of establishing one or more root nodes in a Bayesian network (block 705), shown in more detail in Fig. 8, includes establishing one or more root nodes for hinterland geology (block 805), establishing one or more root nodes for hinterland weathering and transport (block 810), and establishing one or more root nodes for basin transport and deposition (block 815).

[0045] An example of establishing one or more root nodes for hinterland geology (block 805), shown in more detail in Fig. 9, includes establishing a root node for tectonic setting (block 905) and establishing a root node for dominant geologic units (block 910).

[0046] An example of establishing one or more root nodes for hinterland weathering and transport (block 810), shown in more detail in Fig. 10, includes establishing a root node for climate (block 1005), establishing a root node for Hinterland Uplift (block 1010), and establishing a root node for hinterland transport distance (block 1015).

[0047] An example of establishing one or more root nodes for basin transport and deposition (block 815), shown in more detail in Fig. 11, includes establishing a root node for rate of basin subsidence (block 1105), establishing a root node for basin fluvial transport distance (block 1110), and establishing a root node for depositional facies (block 1115).

[0048] An example of establishing one or more leaf nodes in the Bayesian network (block 710), shown in more detail in Fig. 12, includes establishing one or more leaf nodes for sand-grain composition (block 1205) and establishing one or more leaf nodes for sand texture (block 1210).

[0049] An example of establishing one or more leaf nodes for sand-grain composition (block 1205), shown in more detail in Fig. 13, includes establishing a leaf node for each of: final CIBU sand (block 1305), final CISU sand (block 1310), final CAMBU sand (block 1315), final CAMSU sand (block 1320), final SAMV sand (block 1325), and final SAMP sand (block 1330).

[0050] An example of establishing one or more leaf nodes for sand texture (block 1210), shown in more detail in Fig. 14, includes establishing a leaf node for grain size (block 1405), establishing a leaf node for degree of sorting (block 1410), and establishing a leaf node for deposited matrix abundance (block 1415).

[0051] While the present invention has been described with reference to an exemplary embodiment thereof, those skilled in the art will know of various changes in form that may be made without departing from the spirit and scope of the claimed invention as defined in the appended claims. For example, the person skilled in the art will recognize that nodes of marginal impact could be added to the network with little effect on the value of the network even if such nodes have non-causal connections. Further, while the tables following this paragraph and before the claims describe one embodiment of the invention, other embodiments of the invention are within the claims, including those with different probability distributions for the variables, different states for the variables, different variables, different Bayesian network nodes and interconnection, and approaches other than Bayesian networks for addressing full joint probability of domain variables. All such variations will be deemed included in the following claims.

Description of Nodes

Table A1- Root Nodes of the Network

cf. Figure 3 for a picture of network structure.

Table A2.1- Intermediate Nodes of the Network

Table A2.2-- Intermediate Nodes of the Network

cf. Figure 3 for a picture of network structure.

cf. Figure 3 for a picture of network structure. Table A4 - SandGEM Network Structure

cf. Figure 3 for a picture of network structure; cf. Table Al for node codes.

Look across rows to see the parent nodes for a given node.

Look down columns to see the child nodes for a given node.

Normal text indicates root nodes; there are no root-node rows, because root nodes have no parents

Italicized text indicates intermediate nodes

Bold text indicates leaf nodes; there are no leaf-node columns because leaf nodes have no children

Node States

Table B1-- Root-Node States

Table B2.1-- Intermediate-Node States

Table B2.2-- Intermediate-Node States

-25-

Table B3- Final-Node States

Table B4- Grain Types

Figure B1

Table B6- States of ICAMBU MCAMBU FCAMBU

Table B8- States of ISAMV, MSAMV, FSAMV

Table BlO- States of ICISU, MCISU, FCISU

-34-

Node Probability Distribution

- 36 -

Table C2- Probabilit table for Node CCA

Table C3- Probabilit table for Node CRO

Table C4-- Probabilit table for Node IWI

-37-

-38-

Table C10.1- Probability table for Node ICIBU

Table C12.1- Probability table for Node ISAMP

Table C14.1- Probabilit table for Node ICAMSU

-42-

Table C16- Probability table for Node FSP

-44-

Table C19-- Probabilit table for Node ODFP

-45-

Table C20.1.3- Probabilit table for Node MCIBU

Table C20.1.4- Probability table for Node MCIBU

Table C20.2.1- Probability table for Node MCIBU

O

Table C20.2.2- Probability table for Node MCIBU

Table C20.2.3- Probabilit table for Node MCIBU

Table C20.2.4- Probabilit table for Node MCIBU

Table C21.1.2- Probabilit table for Node MCAMBU

Table C24.1.1- Probability table for Node MCAMSU

Table C24.1.3- Probabilit table for Node MCAMSU

Table C25.1.2- Probability table for Node MCISU

Table C25.1.3- Probabilit table for Node MCISU

Table C25.2.3- Probability table for Node MCISU

Table C26.2- Probabilit table for Node GST

Table C27.1- Probability table for Node GSD

Table C27.2- Probability table for Node GSD

Table C27.3- Probabilit table for Node GSP

Table C27.5- Probabilit table for Node GSP

Table C29- Probabilit table for Node GSG

Table C30- Probabilit table for Node DMA

Table C31.3- Probability table for Node DS

Table C31.4- Probabilit table for Node DS

Table C32.1.1- Probabilit table for Node FCIBU

Table C32.1.2- Probability table for Node FCIBU

Table C32.1.4- Probability table for Node FCESU

Table C32.2.1- Probability table for Node FCIBU

Table C32.2.2- Probabilit table for Node FCIBU

Table C32.2.3- Probability table for Node FCEBU

Table C33.2.1- Probabilit table for Node FCAMBU

Table C34.1.1- Probability table for Node FSAMP

Table C34.1.2- Probability table for Node FSAMP

Table C36.1.1- Probability table for Node FCAMSU

90

Table C37.1.1- Probability table for Node FCISU

Table C37.1.2- Probability table for Node FCISU

Table C37.1.3- Probability table for Node FCISU

κ>

Table C37.2.3- Probability table for Node FCISU

Claims

CLAIMSWhat is claimed is:

1. A method for predicting sand-grain composition and sand texture comprising:

selecting a first set of system variables, said first set associated with sand- grain composition and sand texture;

selecting a second set of system variables, said second set being directly or indirectly causally related to said first set of variables;

obtaining or estimating data for each variable in the second set;

forming a network with nodes comprising both sets of variables, having directional links connecting interdependent nodes, said directional links honoring known causality relationships; and

using a Bayesian Network algorithm with said data to solve the network for said first set of variables and their associated uncertainties.

2. The method of claim 1 further comprising:

appraising the quality of selected data; and

including the quality appraisals in the network and in the application of the Bayesian Network algorithm.

3. The method of claim 1, where the system has a behavior, the method further comprising:

selecting the first set of variables and the second set of variables so that together they are sufficiently complete to account for the behavior of the system.

4. The method of claim 1, where forming the network comprises: forming a third set of intermediate nodes interposed between at least some of the nodes representing the first set of system variables and at least some of the nodes representing the second set of system variables.

5. The method of claim 1, where selecting the first set of system variables comprises:

selecting one or more system variables associated with sand-grain composition; and

selecting one or more system variables associated with sand texture.

6. The method of claim 1 where selecting the second set of system variables comprises:

selecting one or more system variables associated with hinterland geology;

selecting one or more system variables associated with hinterland weathering and transport; and

selecting one or more system variables associated with basin transport and deposition.

7. A method for predicting sand-grain composition and sand texture comprising:

establishing one or more root nodes in a Bayesian network;

establishing one or more leaf nodes in the Bayesian network;

coupling the root nodes to the leaf nodes to enable the Bayesian network to predict sand-grain composition and texture.

8. The method of claim 7 where establishing the one or more root nodes comprises:

establishing one or more root nodes for hinterland geology; establishing one or more root nodes for hinterland weathering and transport; and

establishing one or more root nodes for basin transport and deposition.

9. The method of claim 8 where establishing one or more root nodes for hinterland geology comprises:

establishing a root node for tectonic setting.

10. The method of claim 8 where establishing one or more root nodes for hinterland weathering and transport comprises:

establishing a root node for climate;

establishing a root node for rate of hinterland uplift; and

establishing a root node for hinterland transport distance.

11. The method of claim 8 where establishing one or more root nodes for basin transport and deposition comprises:

establishing a root node for rate of basin subsidence;

establishing a root node for basin fluvial transport distance; and

establishing a root node for depositional facies.

12. The method of claim 7 where establishing one or more leaf nodes comprises:

establishing one or more leaf nodes for sand-grain composition; and

establishing one or more leaf nodes for sand texture.

13. The method of claim 12 where establishing one or more leaf nodes for sand texture comprises:

establishing a leaf node for grain size; establishing a leaf node for degree of sorting; and

establishing a leaf node for deposited matrix abundance.

14. The method of claim 12 where establishing the leaf node for grain composition comprises:

establishing a leaf node for final CIBU sand;

establishing a leaf node for final CISU sand;

establishing a leaf node for final CAMBU sand;

establishing a leaf node for final CAMSU sand;

establishing a leaf node for final SAMV sand; and

establishing a leaf node for final SAMP sand.

15. The method of claim 7 further comprising:

establishing one or more intermediate nodes; and

where coupling the root nodes to the leaf nodes to enable the Bayesian network to predict sand-grain composition and texture comprises:

coupling at least some of the one or more root nodes to at least some of the one or more leaf nodes through the one or more intermediate nodes.

16. The method of claim 15 where coupling the root nodes to the leaf nodes to enable the Bayesian network to predict sand-grain composition and texture comprises:

coupling the root nodes to the leaf nodes in causal relationships that honor observations of natural systems.

17. The method of claim 15 where coupling the root nodes to the leaf nodes to enable the Bayesian network to predict sand-grain composition and texture comprises:

defining for each root node one or more outputs that connect to other nodes that the root node causes;

defining for each intermediate node:

one or more inputs that connect to the other nodes that cause the intermediate node;

one or more outputs that connect to other nodes that the intermediate node causes; and

defining for each leaf node one or more inputs that connect to other nodes that cause the leaf node.

18. The method of claim 15 where establishing the one or more root nodes comprises:

creating a probability table for each root node;

each probability table having one or more predefined states; and

each predefined state having associated with it a probability that the root node is in that state.

19. The method of claim 18 where creating the probability table for each root node comprises:

completing the probability table based on quantitative observations of a natural system associated with the root node.

20. The method of claim 19 further comprising:

modifying the probability table based on quantitative observations of the natural system associated with the root node.

21. The method of claim 15 where establishing the one or more leaf nodes comprises:

creating a probability table for each leaf node;

each probability table having a respective one or more predefined states; and

each predefined state having associated with it a probability that the leaf node is in that state.

22. The method of claim 15where each leaf node has a predefined number of inputs and where creating the probability table for each leaf node comprises:

creating a probability table having the respective predefined number of input dimensions.

23. The method of claim 22 where creating the probability table for each leaf node comprises:

completing the probability table with data reflecting quantitative observations of a natural system associated with the leaf node.

24. The method of claim 23 further comprising:

modifying the probability table based on quantitative observations of the natural system associated with the leaf node.

25. The method of claim 15 where establishing the one or more intermediate nodes comprises:

creating a probability table for each intermediate node;

each probability table having a respective one or more predefined states; and

each predefined state having associated with it a probability that the intermediate node is in that state.

26. The method of claim 15 where each intermediate node has a predefined number of inputs and where creating the probability table for each intermediate node comprises:

27. The method of claim 26 where creating the probability table for each intermediate node comprises:

completing the probability table with data reflecting quantitative observations of a natural system associated with the intermediate node.

28. The method of claim 27 further comprising:

modifying the probability table based on quantitative observations of the natural system associated with the intermediate node.

29. A Bayesian network comprising:

one or more root nodes;

one or more leaf nodes;

the root nodes being coupled to the leaf nodes to enable the Bayesian network to predict sand-grain composition and texture.

30. The Bayesian network of claim 31 the one or more root nodes comprise:

one or more root nodes for hinterland geology;

one or more root nodes for hinterland weathering and transport; and

one or more root nodes for basin transport and deposition.

31. The Bayesian network of claim 32 where the one or more root nodes for hinterland geology comprise: a root node for tectonic setting; and

a root node for dominant geologic units.

32. The Bayesian network of claim 30 where the one or more root nodes for hinterland weathering and transport comprise:

a root node for climate;

a root node for rate of hinterland uplift; and

a root node for hinterland transport distance.

33. The Bayesian network of claim 30 where the one or more root nodes for basin transport and deposition comprise:

a root node for rate of basis subsidence;

a root node for basin fluvial transport distance; and

a root node for depositional facies.

34. The Bayesian network of claim 29 where the one or more root nodes comprise:

one or more leaf nodes for sand-grain composition; and

one or more leaf nodes for sand texture.

35. The Bayesian network of claim 34 where the one or more root nodes for sand texture comprise:

a leaf node for grain size;

a leaf node for degree of sorting; and

a leaf node for deposited matrix abundance.

36. The Bayesian network of claim 35 where the leaf node for grain size comprises:

a leaf node for final CIBU sand;

a leaf node for final CISU sand;

a leaf node for final CAMBU sand;

a leaf node for final CAMSU sand;

a leaf node for final SAMV sand; and

a leaf node for final SAMP sand.

37. The Bayesian network of claim 29 further comprising:

one or more intermediate nodes; and

where the coupling between the root nodes and the leaf nodes to enable the

Bayesian network to predict sand-grain composition and texture comprises:

at least some of the one or more root nodes be coupled to at least some of the one or more leaf nodes through the one or more intermediate nodes.

38. The Bayesian network of claim 37 where the coupling between the root nodes and the leaf nodes to enable the Bayesian network to predict sand-grain composition and texture comprises:

the root nodes being coupled to the leaf nodes in causal relationships that honor observations of natural systems.

39. The Bayesian network of claim 37 where the coupling between the root nodes and the leaf nodes to enable the Bayesian network to predict sand-grain composition and texture comprises:

for each root node, one or more outputs that connect to other nodes that the root node causes;

for each intermediate node:

for each leaf node one or more inputs that connect to other nodes that cause the leaf node.

40. The Bayesian network of claim 37 where the one or more root nodes comprises:

a probability table for each root node;

each probability table having one or more predefined states; and

41. The Bayesian network of claim 40 where the probability table for each root node comprises:

data reflecting quantitative observations of a natural system associated with the root node.

42. The Bayesian network of claim 41 further comprising:

modifications to the probability table based on quantitative observations of the natural system associated with the root node.

43. The Bayesian network of claim 38 where the one or more leaf nodes comprises:

a probability table for each leaf node;

each probability table having a respective one or more predefined states; and

44. The Bayesian network of claim 38 where each leaf node has a predefined number of inputs and where creating a probability table for each leaf node comprises:

45. The Bayesian network of claim 44 where creating the probability table for each leaf node comprises:

data reflecting quantitative observations of a natural system associated with the leaf node.

46. The Bayesian network of claim 45 further comprising:

modifications the probability table based on quantitative observations of the natural system associated with the leaf node.

47. The Bayesian network of claim 38 where the one or more intermediate nodes comprises:

a probability table for each intermediate node;

each probability table having a respective one or more predefined states; and

48. The Bayesian network of claim 38 where each intermediate node has a predefined number of inputs and where the probability table for each intermediate node comprises:

a respective predefined number of input dimensions.

49. The Bayesian network of claim 48 where the probability table for each intermediate node comprises:

data reflecting quantitative observations of a natural system associated with the intermediate node.

50. The Bayesian network of claim 49 further comprising:

modifications to the probability table based on quantitative observations of the natural system associated with the intermediate node.

51. A method for predicting porosity and permeability comprising:

predicting sand-grain composition and sand texture from tectonic setting, hinterland weathering and transport and basin transport and deposition using a Bayesian network; and

predicting porosity and permeability from the predicted sand-grain composition and sand texture.