[Paper Review] Mathematical aspects of Multiwell Deconvolution and its relation to Capacitance Resistance Model

A. M. Aslanyan|arXiv (Cornell University)|Feb 24, 2022

Reservoir Engineering and Simulation Methods4 citations

TL;DR

This paper establishes a mathematical framework linking Multiwell Deconvolution (MDCV) and the Capacitance Resistance Model (CRM), showing CRM as a special case of MDCV under specific pressure response assumptions. It demonstrates that MDCV generalizes CRM by accommodating broader transient response behaviors, offering improved flexibility and accuracy in reservoir pressure and flowrate predictions under both rate and pressure control scenarios.

ABSTRACT

The paper provides introduction into the mathematical aspects of Multiwell Deconvolution (MDCV) and Capacitance Resistance Model (CRM) and connection between them. Both methods are trying to train a model over the long-term history of surface flowrates and bottomhole pressure readings and then predict bottomhole and formation pressure in response to a given production/injection flowrate scenario (called "rate control simulation") or alternatively may predict flowrate and formation pressure in response to a given bottomhole pressure scenario (called "pressure control simulation"). It has been shown that CRM can be viewed as a partial case of MDCV with a specific type of a drawdown and cross-well pressure transient responses which is not always met in practice. The paper also explains limitations which are common for both methods and specify additional limitations of CRM which MDCV can handle.

Motivation & Objective

• To formalize the mathematical relationship between Multiwell Deconvolution (MDCV) and the Capacitance Resistance Model (CRM).
• To clarify under what conditions CRM can be considered a subset of MDCV.
• To identify and contrast the limitations of CRM and MDCV in modeling reservoir pressure and flowrate responses.
• To demonstrate the broader applicability of MDCV in handling diverse drawdown and cross-well pressure transient responses.

Proposed method

• Formal derivation of MDCV as a general framework for modeling multiwell pressure and flowrate responses using long-term historical data.
• Representation of CRM as a constrained version of MDCV, where pressure responses are restricted to specific functional forms.
• Use of optimization and control theory to model both rate control and pressure control simulations within the MDCV framework.
• Mathematical analysis of transient response functions to show that CRM's assumptions are a subset of MDCV's more general formulation.
• Application of MDCV to predict formation and bottomhole pressure under varying production/injection scenarios.
• Comparison of CRM and MDCV through theoretical and structural analysis of their underlying response models.

Experimental results

Research questions

• RQ1 How is the Capacitance Resistance Model (CRM) mathematically related to Multiwell Deconvolution (MDCV)?
• RQ2 Under what conditions does CRM reduce to a special case of MDCV?
• RQ3 What are the structural limitations of CRM that MDCV can overcome?
• RQ4 How do MDCV and CRM differ in their ability to model drawdown and cross-well pressure transient responses?
• RQ5 In what ways does MDCV improve predictive accuracy in rate and pressure control simulations?

Key findings

• CRM is mathematically equivalent to MDCV under specific assumptions about the shape of drawdown and cross-well pressure transient responses.
• MDCV generalizes CRM by allowing a broader class of pressure response functions, making it applicable in cases where CRM's assumptions do not hold.
• The paper identifies that CRM's restrictive response model leads to inaccuracies when real reservoir behavior deviates from its assumed functional form.
• MDCV can handle both rate control and pressure control simulations more robustly than CRM due to its flexible response modeling.
• The framework reveals that CRM's limitations are inherent in its fixed-response structure, while MDCV's adaptability allows for better fitting to complex reservoir dynamics.