# US 10,370,945 B2 · Method and apparatus for estimating down-hole process variables of gas lift system > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 10,370,945 B2 - Document ID: US10370945B2 - Status: Granted - Kind: B2 - Application number: 15/093,954 - Filed: 2016-04-08 - Published: 2017-10-12 - Granted: 2019-08-06 - Earliest claimed: 2016-04-08 - Assignees: Khalifa University of Science and Technology - Applicants: Khalifa University of Science and Technology - Inventors: Igor Boiko; Mohammad Luai Hammadih; Khalifa Hasan Al Hosani - Web page: https://patentgrep.com/patent/US10370945B2 ## CPC - E21B 47/06: Measuring temperature or pressure - E21B 43/123: {Gas lift valves} - G05B 13/041: {in which a variable is automatically adjusted to optimise the performance} - E21B 47/008: Monitoring of down-hole pump systems, e.g. for the detection of "pumped-off" conditions - E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS - G05B: CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS (systems for controlling or regulating non-electric variables G05D; systems for regulating electric or magnetic variables G05F; control devices or systems insofar as characterised by mechanical features only G05G) ## Abstract A method and apparatus for estimating a down-hole annulus pressure, and/or a down-hole tubing pressure, and/or a down-hole lift gas rate through a gas injection valve of gas lift system, which comprises at least one gas lift choke and at least one gas injection valve and at least one production choke. A state estimator is proposed to obtain the values of these down-hole process variables. The estimator contains a number of local estimators and an interpolation module. ## Claims ### Claim 1 A method for determining down-hole process parameters for an artificial gas lift system, comprising the following steps: measuring an annulus pressure and/or a surface tubing pressure of the gas lift system; operating a state estimator to perform the steps of: a) determining a vector signal representative of a gas lift choke opening value and/or a production choke opening value and/or a vector signal representative of the measured annulus pressure and/or the measured surface tubing pressure as input values; b) providing a vector signal representative containing estimates of a down-hole annulus pressure about a reference point of an i-th local estimator, and/or a down-hole tubing pressure about a reference point of an i-th local estimator, and/or a lift gas rate through said gas injection valve about a reference point of an i-th local estimator by means of N local estimators where N is greater than or equal to two; and c) incorporating the estimates provided by all local estimators into a single estimate by means of an interpolation module to determine estimated values of a down-hole annulus pressure, and/or of a down-hole tubing pressure, and/or of a lift gas rate through said gas injection valve; and generating an output associated with the determined estimated values; and controlling the artificial gas lift system by using the outputted estimated values of a down-hole annulus pressure, and/or of a down-hole tubing pressure, and/or of a lift gas rate through said gas injection valve. ### Claim 2 A state estimator system for determining down-hole process parameters for an artificial gas lift system, the artificial gas lift system comprising a well casing which connects a surface equipment with an oil reservoir; a tubing inserted inside said well casing and forming an annulus as a space between said well casing and said tubing; a gas lift choke installed between a source of a high-pressure gas and said annulus; a gas injection valve installed between said annulus and a volume inside said tubing; a production choke installed between a volume inside said tubing and oil processing facilities above the surface; the state estimator system comprising: a) an electronic receiver configured to receive a plurality of input parameters measured at an upper end of the artificial lift system; b) N local estimators where N is greater than or equal to two, each providing based on the plurality of input parameters an 11th vector signal representative containing estimates of a down-hole annulus pressure about a reference point of an i-th local estimator, and/or a down-hole tubing pressure about the reference point of an i-th local estimator, and/or a lift gas rate through a said gas injection valve about the reference point of an i-th local estimator; and c) an interpolation module that incorporates estimates provided by all local estimators into a single estimate to determine estimated values of a down-hole annulus pressure, of a down-hole tubing pressure, and of a lift gas rate (LGR) through said gas injection valve, in steady and transient modes; based on the input parameters measured at the upper end of the artificial gas lift system; and d) an output device configured to generate an output associated with the determined estimated values to control the artificial gas lift system using the outputted estimated values of the down-hole annulus pressure, and/or of the down-hole tubing pressure, and/or of the LGR through said gas injection valve. ### Claim 3 (depends on 2) A state estimator system as recited in claim 2, wherein the parameters measured at the upper end of the artificial gas lift system comprise a vector signal representative of a gas lift choke opening value and/or a production choke opening value; and/or a vector signal representative of a measured annulus pressure and/or a measured surface tubing pressure. ### Claim 4 (depends on 2) A state estimator system as recited in claim 2, wherein N reference points are selected as equilibrium points in a nonlinear model describing dynamics of an artificial gas lift system, for selected values of a gas lift choke and a production choke. ### Claim 5 (depends on 2) A state estimator system as recited in claim 2, wherein each of N local estimators comprises a first adder, and/or a second adder, and/or a third adder, and/or a nonlinear module, and/or a linear module, and/or a fourth adder. ### Claim 6 (depends on 5) A state estimator system as recited in claim 5, wherein at least one of the N local estimators comprises the first adder, and wherein the first adder produces a 1st vector signal representative containing a deviation of a gas lift choke opening and a deviation of a production choke opening, by subtracting a 2nd vector signal representative containing a gas lift choke opening and a production coke opening about a reference point of an i-th local estimator from a 3rd vector signal representative containing a gas lift choke opening and a production choke opening. ### Claim 7 (depends on 5) A state estimator system as recited in claim 5, wherein at least one of the N local estimators comprises the second adder, and wherein the second adder produces a 4th vector signal representative containing a deviation of a surface annulus pressure and a deviation of a surface tubing pressure, by subtracting a 5th vector signal representative containing a surface annulus pressure and a surface tubing pressure about a reference point of an i-th local estimator from a 6th vector signal representative containing a measured surface annulus pressure and a measured surface tubing pressure. ### Claim 8 (depends on 5) A state estimator system as recited in claim 5, wherein at least one of the N local estimators comprises the third adder, and wherein the third adder produces a 7th vector error signal representative by subtracting an 8th vector signal representative containing an estimate of a deviation of a surface annulus pressure and an estimate of a deviation of a surface tubing pressure from a 4th vector signal representative containing a deviation of a surface annulus pressure and a deviation of a surface tubing pressure. ### Claim 9 (depends on 5) A state estimator system as recited in claim 5, wherein at least one of the N local estimators comprises the nonlinear module, and wherein the nonlinear module further contains a relay nonlinearity, produces a 9th vector control signal representative based on a said seventh vector error signal representative as per formula: vi=h·sign ei where vi is an i-th vector control signal, h is an amplitude of the relay, h=1 in a preferred embodiment, and ei is an i-th vector error signal. ### Claim 10 (depends on 5) A state estimator system as recited in claim 5, wherein at least one of the N local estimators comprises the linear module, and wherein the linear module realizes computation of a 10th vector signal representative containing an estimate of a deviation of a down-hole annulus pressure, an estimate of a deviation of a down-hole tubing pressure and an estimate of a deviation of a lift gas rate through a said gas injection valve (6), according to equations: {circumflex over ({dot over (x)})}=A{circumflex over (x)}+Bũ+Lv, and ŷ=C{circumflex over (x)}+Dũ, where A∈R3×3, B∈R3×3, C∈R1×3, and D∈R3×2 are matrices computed as A = ∂ f ∂ x  p , B = ∂ f ∂ u  p , C = ∂ y ∂ x  p , and ⁢ ⁢ D = ∂ y ∂ u  p where f is the right-hand side of the equation {dot over (x)}=f(x,u) describing the dynamics of the gas lift system, y is a vector signal containing a deviation of a surface annulus pressure and a deviation of a surface tubing pressure, p is an i-th equilibrium point, L∈R3×2 is a matrix containing constant coefficients, {circumflex over (x)} is a vector containing an estimate of a deviation of a down-hole annulus pressure, an estimate of a deviation of a down-hole tubing pressure and an estimate of a deviation of a lift gas rate through a said gas injection valve, ũ is a vector containing a deviation of a controller command of a gas lift choke opening and a deviation of a controller command of a production choke opening. ### Claim 11 (depends on 5) A state estimator system as recited in claim 5, wherein at least one of the N local estimators comprises the fourth adder, and wherein the fourth adder produces an 11th vector signal representative containing estimates of a down-hole annulus pressure about a reference point of an i-th local estimator, a down-hole tubing pressure about a reference point of an i-th local estimator, and a lift gas rate through a said gas injection valve about a reference point of an i-th local estimator, by adding a 10th vector signal representative containing an estimate of a deviation of a down-hole annulus pressure, an estimate of a deviation of a down-hole tubing pressure and an estimate of a deviation of a lift gas rate through a said gas injection valve, and a 12th vector signal representative containing a down-hole annulus pressure, a down-hole tubing pressure, and a lift gas rate through a said gas injection valve about a reference point of an i-th local estimator. ### Claim 12 (depends on 2) A state estimator system as recited in claim 2, wherein an interpolation module incorporates a said 11th vector signal representative containing estimates of a down-hole annulus pressure about a reference point of an i-th local estimator, a down-hole tubing pressure about a reference point of an i-th local estimator, and a lift gas rate through a said gas injection valve about a reference point of an i-th local estimator, from all local estimators into a single estimate. ### Claim 13 (depends on 12) A state estimator system as recited in claim 12, wherein the interpolation module produces a single estimate based on the following steps; Selection of two local estimators with reference points closest to the current operating point of a gas lift system, Computation of said single estimate from said two estimates based on the closeness of the actual operating point to reference points of these said two estimates; wherein the computation of a said single estimate is done per formula: x ^ f = { x ^ i ⁢ ⁢ if ⁢ ⁢ y ≤ r i α ⁢ x ^ i + ( 1 - α ) ⁢ x ^ i + 1 ⁢ ⁢ if ⁢ ⁢ r i < y ≤ r i + 1 x ^ i + 1 ⁢ ⁢ if ⁢ ⁢ y > r i + 1 where {circumflex over (x)}i is an estimate of an i-th local estimator, {circumflex over (x)}i+1 is an estimate of an i-th+1 local estimator, {circumflex over (x)}f is a single estimate from all local estimators, ri is an i-th reference point of an i-th local estimator, ri+1 is an i-th+1 reference point of an i-th+1 local estimator, α is an interpolation coefficient and 0<α<1, which preferably is equal to 0.3.