Field development plan selection system, method and program product

A system, method and computer program product for assessing field development plans selected based on a stochastic response surface, preferably, for hydrocarbon reservoir production. Assessment begins by assessing uncertainty associated with multiple decision variable configurations. A subset of realizations is selected. An individual surrogate is constructed for each subset realization. A reduced representative realization subset is determined, where the reduced subset is representative of the behavior/performance of all realizations of decision variable configurations.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention is related to selecting a field development plan based on a stochastic response surface.

Background Description

A typical state of the art development plan selected for a hydrocarbon reservoir field provides production guidelines for a given planning horizon on a drilling schedule to maximize production, i.e., to recover reservoir contents. Thus, evaluating oil and gas production potential and economic performance over a wide range of alternate field development plans for a particular reservoir is crucial to making good decisions. When geological and petro-physical properties are known, expensive reservoir flow simulators can estimate production potential and economic performance to model any given reservoir for fairly precisely evaluating the reservoir over differing field development plan alternatives.

Normally however, available reservoir information is limited. Typically, the geological and petro-physical properties carry a quantifiable uncertainty. Consequently, major investment decisions normally are made on field development plan models that are based on this limited and uncertain information. To adequately characterize the risks associated with property uncertainties standard reservoir production models necessarily consider a large set of possible reservoir realizations across property ranges for the different properties. For example, different geological and petro-physical have property ranges that vary between best case, nominal and worst case, independently or semi-independently, of every other property. For a particular reservoir, a set of reservoir realizations and associated probabilities characterize the uncertainty associated with geological and petro-physical properties.

Consequently, arriving at a thorough evaluation of a large number of decision variables with an even larger set of reservoir realizations has been required for selecting a field development plan. Indeed evaluating all decision variable combinations and reservoir realizations using expensive reservoir simulations has been time-consuming and, frequently, an intractable activity. Moreover, ultimately selecting a single realization is somewhat arbitrary and does not appropriately reflect the geological and petro-physical uncertainty involved.

Typical risk metrics conservatively quantify economic performance using a worst case measure, e.g., Value at Risk (V@R). A typical economic performance metric is the Net Present Value (NPV), which is time varying and depends on oil and gas production profiles. Production profiles for determining NPV derive from decision variables in reservoir simulation. Since geological and petro-physical properties are different for each reservoir realization, the NPV evaluated at a given decision variable is uncertain and has a probability distribution defined by the reservoir realizations.

For example, a decision maker with a risk neutral attitude, an attitude of indifference to risk, may represent reservoir economic value for a specific field development plan as an average NPV over all reservoir realizations. By contrast another, risk averse decision maker, taking an extremely conservative approach, may represent the reservoir economic value for the same field development plan with the worst case NPV (maximum production for the minimum realizations) across all possible reservoir realizations. Thus, utility/risk measures representing the NPV valuation have depended on the risk attitude of the decision maker.

State of the art field development plan evaluation approaches have combined a set of statistical and mathematical tools, known in the art as Design of Experiments (DoE) and Response Surface Methodologies (RSM). In particular DoE identifies the most influential decision variables that affect reservoir response, and uses those decision variables to determine a representative set of candidate configurations. Initially, RSM began with choosing specific statistical/risk measures, e.g., expected value and standard deviation, to construct surrogates. Then, RSM iteratively constructs a surrogate reservoir from the DoE configuration set that approximates the reservoir as a system response within a region of interest. For example, before determining a surrogate for the standard deviation of NPV, RSM required the standard deviation for simulation results over all geological realizations for each candidate configuration of input decision variables. RSM fit those standard deviations to a mathematical model as a function of the decision variables. Thus, RSM used an aggregated approach to reflect both system performance and associated risk in surrogates. With each geological realization, however, the RSM model lost the specific response of that reservoir realization to the decision variables, which led to an inaccurate risk assessment for the reservoir.

DoE and RSM have been particularly useful where system response evaluation is computationally expensive, e.g., when evaluation requires complex reservoir flow simulations. Even so, because of the large number of expensive reservoir simulations to cover all potential combinations of reservoir realizations and decision variables may be intractable due to a possibly large number of reservoir realizations. Thus, evaluating the response for every different decision and analyzing each different reservoir realization, i.e., each input decision variable configuration, has required a large number of expensive, time consuming reservoir flow simulations. Frequently, this has proven to be intractable, especially where geological uncertainty has required a very large number of such evaluations.

An individual surrogate constructed for each selected geological realization captures the appropriate stochastic behavior of the response to decision-maker (oil company) risk preferences. Indeed, if the selected reservoir realizations are truly representative of the population and the surrogate accurately approximates the dynamic behavior of each selected realization, any descriptive statistics or even risk measures will be well approximate by surrogates constructed realization-wise. Even after selecting a surrogate, however, evaluating it is relatively inexpensive, consuming relatively little computing resources and costs to evaluate it. The surrogate may be searched relatively easily to identify a new candidate decision point for a potentially enhanced response. However, verifying surrogate accuracy has required re-simulating at each new point. Verified simulation results could be used for yet another iteration to further improve the surrogate. For these state of the art approaches, however, changing the objective function required re-starting, and constructing a new surrogate from the beginning, which has been time consuming and required significant and potentially prohibitively expensive resources. Still other state of the art approaches have evaluated every decision point (i.e., each distinct configuration of the decision variables) for every geological realization, using expensive reservoir simulations that carry high computational costs.

Thus, given volatility of results from the progressive nature of RSM surrogate construction combined with the subjective and changing nature of decision makers' attitudes to risk, there is a need for an approach to constructing reservoir surrogates that are independent of chosen risk measures.

SUMMARY OF THE INVENTION

A feature of the invention is selection of a representative set of reservoir realizations for construction of hydrocarbon reservoir surrogates that are insensitive to risk variation.

The present invention relates to a system, method and computer program product for assessing field development plans. Assessment begins by assessing uncertainty associated with multiple reservoir realizations. A subset of realizations is selected. An individual surrogate is constructed for each subset realization. A reduced representative realization subset is determined, where the reduced subset is representative of the behavior/performance of all realizations of the reservoir.

DESCRIPTION OF PREFERRED EMBODIMENTS

Turning now to the drawings and more particularly,FIG. 1shows an example of a stochastic response surface system100, e.g., for modeling a reservoir in an economic model, according to a preferred embodiment of the present invention. When applied to a hydrocarbon reservoir, the preferred system100selects a representative subset from a complete set of realizations, wherein each realization is a geographically plausible model for the reservoir. Then, the preferred system100applies Design of Experiments (DoE) to sample decision variables and identify candidate configurations. From the candidate configurations the preferred system100constructs a corresponding set of surrogates and, using the surrogates, constructs a risk measure of the surrogates and selected configurations. The risk measure quickly arrives at a proper response approximation, and captures specific behavior each reservoir realization to risk of the reservoir realizations. Thus, the preferred system quickly provides a response approximation and, further, allows for evaluating under various/varying risks without extra iterations to update the approximation.

Preferably, the stochastic response surface system100includes one or more computers102,104,106(3 in this example), wired or wirelessly, coupled to, and communicating with, each other over a network108. The network108may be, for example, a local area network (LAN), the Internet, an intranet or a combination thereof. Typically, the computers102,104,106include one or more processors, e.g., central processing unit (CPU)110, memory112and local non-volatile storage114. The system100may include additional storage, e.g., network connected storage116, and sensors118remotely collecting data.

In particular, a preferred stochastic response surface system100provides a reduced, minimized number of surrogates, f(x, ξ)≈NPV(x, ξ) for evaluation to arrive at optimal results with reduced iterations, and to significantly lower computing time costs. The flexible surrogates allow risk evaluation without re-generating new surrogates under different risk conditions or parameters. Thus, the present invention measures the risk in the reservoir realizations to capture specific behavior of each reservoir realization, and to avoid subsequent surrogate re-construction when the decision maker changes the objective function.

FIG. 2shows an example of stochastic response surface generation workflow120through computers102,104,106of the system100ofFIG. 1. An uncertainty model122characterizes the uncertainty for the random variables in plausible realizations. A sampling unit124or units, e.g., one or more of computers102,104,106inFIG. 1, samples the complete set to select a reduced subset126of N representative realizations from the uncertainty model122. A Design of Experiments (DoE) unit128identifies candidate decision variable configurations for evaluation. A surrogate construction unit130determines system responses for the decision variable configurations over the range of feasible values to generate N corresponding surrogates132from the representative realization samples126. A case selection unit134identifies a candidate decision from the surrogates132that, when applied under specific risk conditions, identifies and presents enhanced decision variable configurations136.

The preferred system generates the decision variable configurations136without expensive evaluations previously required. Moreover, the decision variable configurations136are obtained using a stochastic response surface constructed from the uncertainty model122that support selecting the hydrocarbon field development plan. In particular, this support enhancement results from properly assessing the uncertainty from all different possible configurations of (input) decision variables, independently of any pre-defined risk measure.

Initially, a new reservoir may have a large set of N possible reservoir realizations (ξj)126for M field development plans (xi), where i=1, . . . , M and j=1, . . . , N. Net Present Value (NPV) expressed as the economic response as a function of a field development plan and reservoir realization has the form NPV(x, ξ). Each realization126has a probability of occurrence characterized by Pr(ξ=ξj). So, for a given field development plan each reservoir has an expected NPV, Eξ[NPV(x, ξ)].

The sampling unit124identifies a reduced subset of N realizations from the full set of initial set of realizations. First the sampling unit124may characterize any uncertainty in random variables, analytically or as a large random variable realization set. For hydrocarbon reservoirs, for example, uncertainty may be represented over static properties, such as porosity and permeability. The sampling unit124selects members for the subset that are representative of the behavior/performance of all plausible realizations and the original uncertainty.

The DoE unit128may use reservoir flow simulators on the identified set and subsamples the configuration design variables, x∈X, to evaluate different NPV values, NPV(x,ξ), ξ∈Ξ. Thus, instead of an exhaustive enumeration of all decision variable configurations.

Preferably, the surrogate construction unit130captures the stochastic behavior of the reservoir in a respective individual surrogate from the representative realization subset. First, the surrogate construction unit130simulates well performance to determine responses associated with each decision variable configuration. Then, the surrogate construction unit130builds a stochastic surface for every selected uncertainty realization. The surrogate construction unit130, for example computer102inFIG. 1, may build an interpolation or a regression model of the configurations as surrogates132, f(x, ξ)≈NPV(x, ξ), using evaluated points as a training set.

Any risk measure, ρξ[f(x, ξ)], can be evaluated using the constructed surrogates132, which represent the whole probability distribution of the response as a function of the decision variables involved. Then, a case selection unit134is defined from the surrogates132to determine risk based on differing statistical measures. Statistical measures considered for case selection may include, for example, maximizing average output, minimizing worst-case loss, minimizing standard deviation and/or any other associated risk measure that may be selected. Preferably, the case selection unit134applies search methods using the surrogates to determine an enhanced decision variable. From application of such solution algorithms to surrogates132before evaluating risk, arrives at a different decision variable configuration depending on risk attitude of the user without needing to re-run expensive evaluations (e.g., reservoir simulations) with each change in risk attitude, unlike prior approaches.

Advantageously, the preferred system generates a stochastic response surface (a different surrogate for each reservoir realization) to more accurately approximate the specific behavior of each plausible reservoir realization. In contrast previous approaches, such as RSM, the preferred system enhances decision-making under uncertainty, especially for hydrocarbon reservoirs. These prior approaches began with computing a risk measure, followed by constructing surrogates to obtain an aggregated result. The specific response of each reservoir realization was frequently unavailable to decision makers.

By contrast, the present invention constructs a surrogate for each of a representative set of realizations, before determining the risk measure to be optimized against. Thus, the present invention captures the specific behavior of each reservoir realization and avoids any surrogate re-construction, even if the decision maker changes the risk measure. Moreover, a preferred system100may use optimization techniques to search for additional field development plans for improved performance, flexibly and accurately improved, for a chosen measure (e.g. NPV), given any constraints on risk metrics, such as, constraints on the standard deviation.

While the invention has been described in terms of preferred embodiments, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the appended claims. It is intended that all such variations and modifications fall within the scope of the appended claims. Examples and drawings are, accordingly, to be regarded as illustrative rather than restrictive.