The use of numerical models for land subsidence prediction above producing hydrocarbon reservoirs has become a common and well-established practice since the early '90s. Usually, uncertainties in the deep rock behavior, which can affect the forecast capability of the models, have been taken into account by running multiple simulations with different constitutive laws and mechanical properties. Then, the most uncertain parameters were calibrated to reproduce available subsidence measurements. The objective of this work is to propose a novel methodological approach for land subsidence prediction and uncertainty quantification by integrating the available monitoring information in numerical models using ad hoc Data Assimilation techniques. The proposed approach allows to: (i) train the model with the available data and improve its accuracy as new information comes in, (ii) quantify the prediction uncertainty by providing confidence intervals and probability measures instead of deterministic outcomes, and (iii) identify the most appropriate rock constitutive model and geomechanical parameters. The methodology is tested in synthetic models of production from hydrocarbon reservoirs. The numerical experiments show that the proposed approach is a promising way to improve the effectiveness and reliability of land subsidence models.

The interest and capability of analyzing real world phenomena in a stochastic way have increased in recent years.
Focusing on land subsidence, deterministic studies do not allow to take care of uncertainties that unavoidably affect the characterization of the porous medium, e.g., the choice of the constitutive law and values of the governing mechanical parameters.
A way to address this issue relies on the integration of Data Assimilation (DA) techniques into the numerical model, in order to train the model through the available measurements and improve the reliability and accuracy of the solution by reducing the uncertainties.
In petroleum engineering, DA approaches have been originally used for history matching purposes, with recent applications for subsidence prediction

The paper is organized as follows. First, the methodological approach is described in detail, then the synthetic, but realistic, test case is presented with a discussion of the outcomes of every step of the proposed workflow. Finally, a few conclusive remarks close the presentation.

At the very beginning of a land subsidence study, the number of available pieces of information concerning the deep rock behavior is usually low.
For example, the most appropriate constitutive law that defines the behavior of the porous medium is generally unknown and the mechanical properties of the porous medium, e.g. stiffness or anisotropy, can be estimated only within a variability range by laboratory tests and preliminary in-situ analyses.
Consequently, the first step for a stochastic subsidence analysis is to propagate all these input uncertainties to the subsidence prediction, that is the output of the geomechanical model. This is done by the generation of many forecast ensembles of Monte Carlo realizations for each constitutive law that could be suitable to describe the behavior of the porous medium, and considering different variability ranges for the main mechanical parameters.
When the production program starts, displacement records are collected and used to train the model through different DA approaches in order to reduce the uncertainties and make the analysis more accurate and reliable. In particular, following the methodological approach proposed in

A way to validate the ensemble is the

After that, a cheap and fast analysis of the forecast ensembles can be performed by the RF technique, as introduced in

Finally, the ES technique is applied, a non-sequential DA algorithm originally proposed by

The methodology described in Sect.

Since a synthetic test case has been taken into consideration, the geomechanical model has been run both to create the ensembles of Monte Carlo realizations and to define a set of hypothetical measurements. Consequently, a set of statistical distributions and a true configuration of the main geomechanical parameters have to be defined. The modified Cam Clay constitutive law requires the definition of the modified compression index

Preliminarily, a model diagnostic procedure, i.e. the

Analyzed configuration sets with their associated uncertain parameters and

RF approach: maximum and minimum probabilities of occurrence

After the model diagnostic, an easy and fast technique for a preliminary analysis of the ensembles is RF. It allows to characterize every realization of the ensemble by its own probability of occurrence. In Table

ES has been applied for the three sets of uncertain parameters previously described, with the outcome shown in Fig.

Outcomes of ES for set #1

ES approach: AE and AES for the forecast ensemble and the relative variation

ES can be employed also in a predictive sense by assimilating new measurements as they are recorded. Considering set #1, effectiveness of ES improves with the increase of the number of assimilated measurements, but also few observations allow to reduce uncertainties related to parameter and to the state ensembles. Results are shown in Fig.

The same as in Fig.

Testing ES approach in a predictive sense for set #1. Variations

In this work, a novel methodological approach for a stochastic study of land subsidence due to hydrocarbon exploitation has been developed and tested in a synthetic test case inspired by the Northern Adriatic basin, Italy. The aim is to define an efficient and robust workflow that combines DA techniques and geomechanical models in order to quantify and reduce uncertainties and consequently make the model more accurate and reliable.

First, every ensemble has been evaluated considering the comparison with the available measurements through a model diagnostic procedure, i.e. the

On summary, in the context of a synthetic test case, the proposed workflow seems to be an innovative and suitable approach to study land subsidence above producing hydrocarbon reservoirs, taking into consideration the uncertainties that unavoidably affect numerical models of real world phenomena. Moreover, it allows to reduce these uncertainties in order to obtain more accurate and reliable predictions. Further analyses and improvements on these approaches are currently underway with its application on real-world reservoir problems.

This work deals with numerical modeling of a synthetic test case. All data required for the implementation and reproduction are reported in the paper and in the relevant bibliography.

All the authors have equally contributed to the development of the conceptual model. GL, FM and ZC took care of the code implementation and numerical testing. GL, FM and TP are the main contributors for paper writing and proofreading.

The authors declare that they have no conflict of interest.

This article is part of the special issue “TISOLS: the Tenth International Symposium On Land Subsidence – living with subsidence”. It is a result of the Tenth International Symposium on Land Subsidence, Delft, the Netherlands, 17–21 May 2021.