Production logging inversion based on LFDAS/DTS

A method of optimizing oil production, said method comprising:

• a) providing one or more fiber optic cables operably coupled to one or more interrogators in a well in an oil reservoir;
• b) measuring low-frequency Distributed Acoustic Sensing (LFDAS) data in said well during a time period of constant flow and during a time period of no flow and during a time period of perturbation of flow, wherein said perturbation of flow is created by thermal perturbations;
• c) simultaneously measuring Distributed Temperature Sensing (DTS) data from said well during said time period of constant flow and during said time period of no flow and during said time period of perturbation of flow;
• d) using one or more of equations 1-6 or their mathematical equivalents:
• vR
• ⁢
• dT
• dx
• =
• v
• ⁢
• dR
• dx
• ⁢
• (
• T
• p
• -
• T
• )
• +
• U
• ⁡
• (
• T
• f
• -
• T
• )
• +
• vRG
• ⁢
• dz
• dx
• ,
• (
• 1
• )
• where v is a maximum flow velocity at a heel of said well,
• R is a spatial distribution of flow velocity profile, normalized to a range between 0 to 1,
• T is a temperature of a well fluid during stable production,
• Tp is a temperature of a produced fluid at each perforation location,
• Tf is a temperature of a surrounding formation,
• U is an overall heat transfer coefficient between said surrounding formation and said well fluid,
• G is a pressure, volume, temperature (PVT) coefficient,
• x is a measured depth of said well, and
• z is a true depth of said well;
• T
• i
• +
• 1
• -
• T
• i
• Δ
• ⁢
• x
• =
• R
• i
• +
• 1
• -
• R
• i
• Δ
• ⁢
• x
• ⁢
• T
• pi
• -
• T
• i
• R
• i
• +
• U
• vR
• i
• ⁢
• (
• T
• fi
• -
• T
• i
• )
• +
• G
• ⁢
• z
• i
• +
• 1
• -
• z
• i
• Δ
• ⁢
• x
• .
• (
• 2
• )
• where i refers to an i-th perforation cluster;
• dT
• dx
• =
• (
• dR
• dx
• +
• U
• v
• )
• ⁢
• δ
• ⁢
• T
• R
• +
• G
• ⁢
• dz
• dx
• ,
• (
• 3
• )
• where δT is a difference between temperature measurements during shut-in and stable production periods;
• R
• ⁡
• (
• x
• )
• =
• 1
• -
• (
• 1
• -
• R
• bot
• )
• ⁢
• ∑
• i
• P
• x
• <
• x
• P
• i
• ∑
• i
• =
• 1
• N
• P
• i
• ,
• (
• 4
• )
• wherein R(x) is a normalized flow velocity profile,
• wherein Pi is a normalized productivity of said i-th perforation cluster,
• Px is a perforation cluster location, and
• Rbot is a normalized flow velocity at a toe end of a sensing section;
• ∈2=∥T−T′∥2+λ∥vR−v′∥2, (5)
• wherein ∈2 is a penalty function,
• T′ is a measured flowing temperature in said well, and
• V′ is a measured flow velocity in said well;
• ∈2=∥T−T′∥2+λ∥R−R′∥2, (6)
• where R′is a normalized flow-velocity ratio measured by distributed acoustic sensing (DAS),
• i) inverting U and G using a gradient-descent based optimization while holding Pi fixed;
• ii) inverting Pi using a Markov chain Monte Carlo optimization;
• iii) repeating step i-ii) thousands of times to generate thousands of initial models;
• iv) randomly perturbing Pi of an initial model to create a new model and retaining said new model as a final model if a penalty function ∈2 for said new model is smaller than that of said initial model, and otherwise abandoning said new model;
• v) repeating step iv for each of said initial models to generate thousands of final models;
• vi) statistically analyzing said thousands of final models to obtain production allocation results;
• and
• e) using said production allocation results to optimize production of hydrocarbon from said well and future wells in said reservoir.