Calibration of thermal conductivity and specific heat devices

Claim 1

A method for calibrating a system for determining thermal conductivity, k, of a fluid of interest in which the system includes heater means and sensor means in proximate position to the heater means and in thermal communication therewith through the fluid of interest, the sensor means being one having a thermally varying output signal, such that an energy input can be provided to the heater means of a level and duration such that both an interval of transient temperature change and an interval of substantially steady-state temperature occur in the sensor means in response to the energy input to the heater means, the thermal conductivity, k, of the fluid of interest being related to the sensor output at steady-state sensor temperature, the method comprising the steps of: deriving a repeatable relation between the output of the sensor means and values of k over a range of temperature based on a species of known k; and applying the derived relation to compensate the system in a manner which produces accurate determinations of k for samples of interest of unknown k.

Claim 2

A method for calibrating a system for determining thermal conductivity, k, of a fluid of interest in which the system includes heater means and sensor means in proximate position to the heater means and in thermal communication therewith through the fluid of interest, the sensor means being one having a thermally varying output signal, such that an energy input can be provided to the heater means of a level and duration such that both an interval of transient temperature change and an interval of substantially steady-state temperature occur in the sensor means in response to the energy input to the heater means, the thermal conductivity, k, of the fluid of interest being related to the sensor output at steady-state sensor temperature, the method comprising the steps of: deriving a repeatable relation between the output of the sensor means and values of k over a range of temperature based on a species of known k; and applying the derived relation to compensate the system in a manner which produces accurate determinations of k for samples of interest of unknown k.

Claim 3

A method for calibrating a system for determining thermal conductivity, k, of a fluid of interest in which the system includes heater means and sensor means in proximate position to the heater means and in thermal communication therewith through the fluid of interest, the sensor means being one having a thermally varying output signal, such that an energy input can be provided to the heater means of a level and duration such that both an interval of transient temperature change and an interval of substantially steady-state temperature occur in the sensor means in response to the energy input to the heater means, the thermal conductivity, k, of the fluid of interest being related to the sensor output at steady-state sensor temperature, and c p of the fluid of interest determined based on a relation among k, rate of change of sensor output during a transient temperature change in the sensor and c p , the method comprising the steps of: deriving a first repeatable relation between the output of the sensor means and values of k over a range of temperatures based on a species of known k; applying the derived first relation to compensate the system in a manner which produces accurate determinations of k for samples of interest of unknown k; deriving a second repeatable relation between a rate of change of sensor temperature and c p based on sensor response to a species of known k and c p ; and applying the derived second relation to compensate the system in a manner which produces accurate determination of c p for samples of interest of unknown c p .

Claim 4

A method for calibrating a system for determining thermal conductivity, k, of a fluid of interest in which the system includes heater means and sensor means in proximate position to the heater means and in thermal communication therewith through the fluid of interest, the sensor means being one having a thermally varying output signal, such that an energy input can be provided to the heater means of a level and duration such that both an interval of transient temperature change and an interval of substantially steady-state temperature occur in the sensor means in response to the energy input to the heater means, the thermal conductivity, k, of the fluid of interest being related to the sensor output at steady-state sensor temperature, and c p of the fluid of interest determined based on a relation among k, rate of change of sensor output during a transient temperature change in the sensor and c p , the method comprising the steps of: deriving a first repeatable relation between the output of the sensor means and values of k over a range of temperatures based on a species of known k; applying the derived first relation to compensate the system in a manner which produces accurate determinations of k for samples of interest of unknown k; deriving a second repeatable relation between a rate of change of sensor temperature and c p based on sensor response to a species of known k and c p ; and applying the derived second relation to compensate the system in a manner which produces accurate determination of c p for samples of interest of unknown c p .

Claim 5

A method for calibrating a system for determining thermal conductivity, k, of a fluid of interest in which the system includes heater means and sensor means in proximate position to the heater means and in thermal communication therewith through the fluid of interest, the sensor means being one having a thermally varying output signal, such that an energy input can be provided to the heater means of a level and duration such that both an interval of transient temperature change and an interval of substantially steady-state temperature occur in the sensor means in response to the energy input to the heater means, the thermal conductivity, k, of the fluid of interest being related to the sensor output at steady-state sensor temperature, and c p of the fluid of interest determined based on a relation among k, rate of change of sensor output during a transient temperature change in the sensor and c p , the method comprising the steps of: deriving a first relation between the output of the sensor means output and values of k based on linearizing the output versus k relation over a range of temperatures for a species of known k of the form: k=a.sub.r U+a.sub.5 where U is the sensor output at stead state and a 4 and a 5 are constants; applying the derived values of constants a 4 and a 5 to the determination of k with respect to observed values of U for samples of interest of unknown k; deriving a second relation between the rate of change of sensor output during a transient temperature change interval in the sensor and c p based on sensor response to a species of known k and c p of the form: c.sub.p P/P.sub.o =a.sub.1 (t.sub.2 -t.sub.1)k+a.sub.2 (t.sub.2 -t.sub.1)-a.sub.3 where a 1 , a 2 and a 3 are constants P=pressure (psia) P o =reference pressure (psia) (t 2 -t 1 )=measured elapsed time span between known temperatures; and applying derived values of the constants a 1 , a 2 and a 3 to the determination of c p with respect to known pressure and time span for samples of interest of unknown c p .

Claim 6

A method for calibrating a system for determining thermal conductivity, k, of a fluid of interest in which the system includes heater means and sensor means in proximate position to the heater means and in thermal communication therewith through the fluid of interest, the sensor means being one having a thermally varying output signal, such that an energy input can be provided to the heater means of a level and duration such that both an interval of transient temperature change and an interval of substantially steady-state temperature occur in the sensor means in response to the energy input to the heater means, the thermal conductivity, k, of the fluid of interest being related to the sensor output at steady-state sensor temperature, and c p of the fluid of interest determined based on a relation among k, rate of change of sensor output during a transient temperature change in the sensor and c p , the method comprising the steps of: deriving a first relation between the output of the sensor means output and values of k based on linearizing the output versus k relation over a range of temperatures for a species of known k of the form: k=a.sub.r U+a.sub.5 where U is the sensor output at stead state and a 4 and a 5 are constants; applying the derived values of constants a 4 and a 5 to the determination of k with respect to observed values of U for samples of interest of unknown k; deriving a second relation between the rate of change of sensor output during a transient temperature change interval in the sensor and c p based on sensor response to a species of known k and c p of the form: c.sub.p P/P.sub.o =a.sub.1 (t.sub.2 -t.sub.1)k+a.sub.2 (t.sub.2 -t.sub.1)-a.sub.3 where a 1 , a 2 and a 3 are constants P=pressure (psia) P o =reference pressure (psia) (t 2 -t 1 )=measured elapsed time span between known temperatures; and applying derived values of the constants a 1 , a 2 and a 3 to the determination of c p with respect to known pressure and time span for samples of interest of unknown c p .