Summary of the invention
Problems to be solved by the invention
In view of the technical problems existing in the prior art, such as: precision is lower, to fluid and surrounding measurement ambient stable
Property is more demanding;The requirement of measuring condition is more harsh, generally requires sample steady shear rate with higher, and survey
Amount sensibility is lower, and spot measurement is larger etc. by influence of ambient vibration.Present invention firstly provides a kind of the online of viscosity of crude
Measuring device, of the invention can be used for is quick, accurate, convenient, and can be with on-line measurement viscosity of crude.
Further, the present invention also provides a kind of On-line Measuring Method of viscosity of crude, this method is simple and easy, and can be with
Quickly, accurately, easily measure viscosity of crude.
The solution to the problem
The present invention provides a kind of in-situ measurement equipment of viscosity of crude comprising: oil suction line, metering device and viscosity
Detection device, wherein
The oil suction line is in parallel with working connection pipeline;
The metering device is connected to the oil suction line;
The viscosity detecting device is connected to the metering device.
The in-situ measurement equipment of viscosity of crude according to the present invention, wherein the oil suction line includes the first oil circuit and the
Two oil circuits, wherein
First inlet pipeline of first oil circuit is connected with the first hydraulic fluid port of the metering device;First oil circuit
First outlet pipeline is connected with the second hydraulic fluid port of the metering device;
Second inlet pipeline of second oil circuit is connected with the second hydraulic fluid port of the metering device;Second oil circuit
Second outlet pipeline is connected with the first hydraulic fluid port of the metering device.
The in-situ measurement equipment of viscosity of crude according to the present invention, wherein go out in first inlet pipeline, described first
On mouth pipeline, second inlet pipeline and the second outlet pipeline, it is respectively arranged with valve group.
The in-situ measurement equipment of viscosity of crude according to the present invention, wherein the viscosity detecting device includes capillary, pressure
Force snesor and temperature sensor, wherein
The arrival end of the capillary is connected to the oil suction line;
The outlet end of the capillary is connected to the working connection pipeline;
The pressure sensor is set to arrival end and the outlet end of the capillary;
The temperature sensor is set to input end and/or the outlet end of the capillary.
The in-situ measurement equipment of viscosity of crude according to the present invention, wherein further include power device and/or data acquisition dress
It sets, wherein
The power device is connect with the metering device, for quantitatively to extract crude oil sample from the working connection pipeline
Product provide power;
The data acquisition device is connect with the viscosity detecting device.
The present invention also provides a kind of On-line Measuring Methods of viscosity of crude comprising following steps:
Crude oil sample is extracted from working connection pipeline using oil suction line;
The flow of the crude oil sample is controlled using metering device;
Utilize the viscosity of viscosity detecting device measurement crude oil sample.
The On-line Measuring Method of viscosity of crude according to the present invention, wherein the oil suction line includes the first oil circuit and the
Two oil circuits, wherein
When the crude oil sample in first oil circuit by when, the crude oil sample from first oil circuit first
Inlet pipeline is delivered in the metering device through the first hydraulic fluid port of the metering device, and second from the metering device is oily
Mouth outflow, through first outlet pipeline to the viscosity detecting device;
When the crude oil sample in second oil circuit by when, the crude oil sample from second oil circuit second
Inlet pipeline is delivered in the metering device through the second hydraulic fluid port of the metering device, and first from the metering device is oily
Mouth outflow, through second outlet pipeline to the viscosity detecting device.
The On-line Measuring Method of viscosity of crude according to the present invention, wherein in the first inlet pipeline, the first outlet pipe
On road, second inlet pipeline and the second outlet pipeline, it can use valve group and control above-mentioned first inlet pipeline, the
The opening and closing of one outlet conduit, the second inlet pipeline and second outlet pipeline, so that crude oil sample is in above-mentioned each pipe
Flowing is flowed or stopped in road.
The On-line Measuring Method of viscosity of crude according to the present invention, wherein described using described in viscosity detecting device measurement
The viscosity of crude oil sample includes:
The crude oil sample is delivered to the arrival end of capillary from oil suction line;
The crude oil sample is transferred out from the outlet end of the capillary;
The inlet pressure and outlet pressure of the capillary are measured using pressure sensor;
The temperature of crude oil sample described in input end using capillary described in temperature sensor measurement.
The On-line Measuring Method of viscosity of crude according to the present invention, wherein further include:
Power is provided using power device quantitatively to extract crude oil sample from the working connection pipeline;And/or
The viscosity information of the crude oil sample is acquired using data acquisition device, and according to Hagen-Poiseuille law, or
The correction formula of Hagen-Poiseuille law calculates the crude oil sample viscosity;Wherein, the amendment of the Hagen-Poiseuille law
Formula is
Wherein, μ is the viscosity of the crude oil sample, mPas;
R is the radius of the capillary, mm;
p1For the pressure of the arrival end of the capillary, pa;
p2For the pressure of the outlet end of the capillary, pa;
Q is the flow of oil suction line Central Plains oil samples, mLs-1;
L is the length of the capillary, mm;
K is pressure correcting coefficient.
The effect of invention
The measurement accuracy of in-situ measurement equipment of the invention is high, requires fluid and surrounding measurement environmental stability low;
The requirement of measuring condition is low, and measurement sensitivity is high, and spot measurement is smaller by influence of ambient vibration, can be used for it is quick, accurate,
Convenient and fast on-line measurement viscosity of crude.
The On-line Measuring Method of the viscosity of crude of invention is simple and easy, and can quick, accurate, convenient and fast on-line measurement original
Oil viscosity.
Specific embodiment
Below with reference to attached drawing various exemplary embodiments, feature and the aspect that the present invention will be described in detail.It is identical in attached drawing
Appended drawing reference indicate element functionally identical or similar.Although the various aspects of embodiment are shown in the attached drawings, remove
It non-specifically points out, it is not necessary to attached drawing drawn to scale.
Dedicated word " exemplary " means " being used as example, embodiment or illustrative " herein.Here as " exemplary "
Illustrated any embodiment should not necessarily be construed as preferred or advantageous over other embodiments.
In addition, in order to better illustrate the present invention, numerous details is given in specific embodiment below.
It will be appreciated by those skilled in the art that without certain details, the present invention equally be can be implemented.In other example,
Method well known to those skilled in the art, means, equipment and step are not described in detail, in order to highlight master of the invention
Purport.
First embodiment
In first embodiment of the invention, a kind of in-situ measurement equipment of viscosity of crude is provided, comprising: oil suction line,
Metering device B and viscosity detecting device C, wherein oil suction line is in parallel with working connection pipeline A;Metering device B and oil suction line
It is connected to (series connection);Viscosity detecting device C is connected to (series connection) with metering device B by oil suction line.Specifically:
<oil suction line>
Oil suction line of the invention is arranged in parallel with working connection pipeline A, for extracting crude oil sample from working connection pipeline A
Product.In the present invention, oil suction line may include the first oil circuit and the second oil circuit, wherein
First inlet pipeline of the first oil circuit is connected with the first hydraulic fluid port of metering device B;The first outlet pipe of first oil circuit
It connects with the second hydraulic fluid port of metering device B in road;
Second inlet pipeline of the second oil circuit is connected with the second hydraulic fluid port of metering device B;The second outlet pipe of second oil circuit
It connects with the first hydraulic fluid port of metering device B in road.
Specifically, as shown in Figure 1, when crude oil sample in the first oil circuit (shown in arrow) by when, crude oil sample from
First inlet pipeline of the first oil circuit is delivered in metering device B through the first hydraulic fluid port of metering device B, and from metering device B's
Second hydraulic fluid port outflow, through first outlet pipeline to viscosity detecting device C.
As shown in Fig. 2, when crude oil sample in the second oil circuit (shown in arrow) by when, crude oil sample is from the second oil circuit
Second inlet pipeline is delivered in metering device B through the second hydraulic fluid port of metering device B, and from the first hydraulic fluid port stream of metering device B
Out, through second outlet pipeline to viscosity detecting device C.
In the present invention, when oil suction line has above-mentioned two oil circuit, the specific setting of two oil circuits is not limited specifically
It is fixed, pass through according to the above method in two oil circuits as long as being able to achieve crude oil sample.In addition, in the present invention, oil suction line
It can according to need setting multiple oil circuits, such as third oil circuit, the 4th oil circuit etc..Control device (such as: valve group) can be passed through
Crude oil sample is passed through in a specific oil circuit.
In the present invention, on oil suction line, the first valve 1 is can be set in the position close to working connection pipeline A, for controlling
The opening and closing of oil suction line processed, when the first valve 1 is opened, crude oil sample mouth is flowed into oil suction line.
In the present invention, in the first inlet pipeline, first outlet pipeline, the second inlet pipeline and second outlet pipeline
On, be respectively arranged with valve group, the valve group for control the first inlet pipeline, first outlet pipeline, the second inlet pipeline and
The opening and closing of second outlet pipeline, so that crude oil sample can flow in above-mentioned pipeline or stop flowing.Citing
For, as shown in Figure 1, the first import can be controlled by the second valve 2, third valve 3, the 4th valve 4 and the 5th valve 5
The opening and closing of pipeline, first outlet pipeline, the second inlet pipeline and second outlet pipeline.When the second valve 2 and the 5th
When valve 5 is opened, when third valve 3 and the 4th valve 4 are closed, as shown in Figure 1, flow direction of the crude oil sample according to the first oil circuit
(shown in arrow) is conveyed;As shown in Fig. 2, when third valve 3 and the 4th valve 4 are opened, the second valve 2 and the 5th valve
When 5 closing, crude oil sample is conveyed according to the flow direction (shown in arrow) of the second oil circuit.
In addition, filter is also provided on the oil suction line, to filter out the impurity in crude oil sample.
<metering device>
Metering device B of the invention is connected to (series connection) with oil suction line, can be used for controlling the flow of crude oil sample.Metering
The first hydraulic fluid port and the second hydraulic fluid port (not shown) are provided on device B, for be connected with oil suction line (series connection).
Preferably, in the present invention, as shown in figure 3, metering device B can be metering pump.Metering pump may include cylinder
Body B1, preceding plug B2, rear plug B3 and piston (not shown).The first oil being connected with oil suction line is provided on cylinder B1
Mouth and the second hydraulic fluid port.Piston is placed in cylinder B1, the both ends of piston along the axis direction of cylinder B1 be respectively arranged with plunger rod with
Piston rod (not shown), piston rod can be identical with the diameter of plunger rod;Preceding plug B2 is separately positioned on rear plug B3
It is respectively arranged on the two sides of cylinder B1, preceding plug B2 and rear plug B3 and accommodates the through-hole that plunger rod and piston rod pass through;Plunger
Bar in the axial direction on be provided with internal screw thread.
One end of plunger rod is connected on the piston in cylinder B1;The other end of plunger rod prolongs across the through-hole of preceding plug B2
It stretches out outside the preceding plug B2 of cylinder B1, and limited block B4 can be set on the outer wall at the end of plunger rod.In general, metering
The cylinder B1 inner wall of pump is processed into using precise finiss, so that the concentricity of cylinder B1 inner wall is 0-0.02mm, cylinder B1
The circularity of inner wall is 0-0.01mm.
<viscosity detecting device>
Viscosity detecting device C of the invention connects with metering device B and (is connected by oil suction line), for measuring crude oil sample
The viscosity of product.Specifically, in the present invention, viscosity detecting device C may include that capillary, pressure sensor and temperature pass
Sensor, wherein the arrival end of capillary is connected to oil suction line;The outlet end of capillary is connected to working connection pipeline A.Described
On the arrival end of capillary to the pipeline of oil suction line, at least one valve can be set, such as: the 6th valve 6 of setting.Pressure
Force snesor is set to arrival end and the outlet end of capillary, for measuring the inlet pressure and outlet pressure of capillary.Temperature passes
Sensor is set to input end and/or the outlet end of capillary, for measuring the temperature of crude oil sample.
In general, in the present invention, capillary, pressure sensor and temperature sensor in viscosity detecting device C
It can be placed in seal thermal-insulation box, be contaminated to avoid capillary or temperature is avoided to change.
In addition, in the present invention, the outlet end of the capillary of viscosity detecting device C can be connected with working connection pipeline A,
To form fuel-displaced oil circuit, to allow crude oil sample be transmitted back in working connection pipeline A again, to be recycled.In the fuel-displaced oil
On the road, one or more valves and/or filter also can be set, such as: the 7th valve 7 of setting and the 8th valve 8.
<power device>
The in-situ measurement equipment of viscosity of crude of the invention can also include power device D.Power device D and metering device
B is connected to (series connection), for providing power quantitatively to extract crude oil sample from working connection pipeline A.
In the present invention, power device D may include: driving motor D1, speed reducer D2 and screw rod D3, in driving motor
Under the action of D1 and speed reducer D2, power is provided quantitatively to extract crude oil sample from working connection pipeline A.Metering device B with subtract
Several pull rod D4 parallel to each other are provided between fast device D2.A righting board D5, the righting board can be set on pull rod D4
D5 and the limited block B4 of plunger rod one end cooperate.
In general, retarder D2 plays matching revolving speed between prime mover and working machine or executing agency and transmits torque
Effect.Mainly it is made of driving parts (gear or worm screw), axis, bearing, cabinet and its attachment.In the present invention, by making
Revolving speed and the transmitting torque of driving motor D1 can be reduced with retarder D2.
In the present invention, screw rod D3 is preferably ball screw D3.Ball screw D3 by screw rod, nut, steel ball, pre- tabletting,
Reverser, dust excluder composition.Rotary motion can be converted to linear motion, or torque is converted into axial repeated action power.
In the present invention, driving motor D1 can be controlled by PLC controller, and driving motor D1 on an hourly basis ten minutes daily
Automatic running and a data are automatically saved by computer daily, is provided with absolute encoder on driving motor D1.Absolutely compile
Code device, which can be, determines coding by mechanical location, without looking for reference point, and does not have to count always, in the feelings for needing location aware
Under condition, that is, the position of encoder can be read.
In the present invention, driving motor D1 is connected with retarder D2, one end phase of the output end and screw rod D3 of retarder D2
Even.The other end of screw rod D3 is connect with the screw-internal thread fit of the plunger rod of metering device B, and driving motor D1 drives screw rod D3 rotation
Plunger rod threads cooperation with metering device B with piston along the inner wall of cylinder B1 to move back and forth;Metering device B's helps
Positive plate D5 follows plunger rod along the axis side of pull rod D4 while driving motor D1 driving screw rod D3 drives plunger rod movement
To reciprocating movement.
<data acquisition device>
In the case where being provided with data acquisition device, data acquisition device of the invention is connected with viscosity detecting device C
It connects, for acquiring the viscosity information of crude oil sample.The present invention is not especially limited the structure of data acquisition device, can be this
The feasible data acquisition device in field, such as computer etc..Data acquisition device can pass through data line and viscosity detecting device C
It is connected, is also possible to be wirelessly connected.
In addition, in-situ measurement equipment of the invention is also provided with detergent line, by valve (such as: the 9th valve 9
With the tenth valve 10) control detergent line opened and closed, can use cleaning solution and in-situ measurement equipment cleaned.
In-situ measurement equipment of the invention is connect branch (in parallel with working connection pipeline A) by other on working connection pipeline A, benefit
With metering device B, viscosity detecting device C and oil suction line etc., the viscosity of crude of working connection pipeline A conveying is surveyed online
Amount, and can also acquire by computer and data transmission set, processing, record the data and result measured.
Second embodiment
Second embodiment of the present invention provides a kind of on-line measurement using the viscosity of crude in first embodiment and sets
The On-line Measuring Method of standby detection viscosity of crude, comprising the following steps: extract original from working connection pipeline A using oil suction line
Oil samples;Utilize the flow of metering device B control crude oil sample;Utilize the viscosity of viscosity detecting device C measurement crude oil sample.Tool
For body:
Oil suction line of the invention includes the first oil circuit and the second oil circuit, wherein when crude oil sample leads in the first oil circuit
Out-of-date, crude oil sample is delivered in metering device B from the first inlet pipeline of the first oil circuit through the first hydraulic fluid port of metering device B,
And flowed out from the second hydraulic fluid port of metering device B, through first outlet pipeline to viscosity detecting device C;When crude oil sample is
When passing through in two oil circuits, crude oil sample is delivered to meter through the second hydraulic fluid port of metering device B from the second inlet pipeline of the second oil circuit
It measures in device B, and is flowed out from the first hydraulic fluid port of metering device B, through second outlet pipeline to viscosity detecting device C.
Preferably, in the first inlet pipeline, the first outlet pipeline, second inlet pipeline and described second
On outlet conduit, the first inlet pipeline, first outlet pipeline, the second inlet pipeline and second outlet pipeline are controlled using valve group
Opening and closing.For example, as illustrated in fig. 1 and 2, can by the second valve 2, third valve 3, the 4th valve 4 and
5th valve 5 controls unlatching and the pass of the first inlet pipeline, first outlet pipeline, the second inlet pipeline and second outlet pipeline
It closes.As shown in Figure 1, when the second valve 2 and the 5th valve 5 are opened, and when third valve 3 and the closing of the 4th valve 4, crude oil sample
It is conveyed according to the flow direction of the first oil circuit;As shown in Fig. 2, when third valve 3 and the 4th valve 4 are opened, and 2 He of the second valve
When 5th valve 5 is closed, crude oil sample is conveyed according to the flow direction of the second oil circuit.
In fact, the first oil circuit and the second oil circuit of oil suction line of the invention and the piston (plunger) of metering device B are past
What multiple movement was equipped with.In piston (plunger) uplink, the second valve 2 and the 5th valve 5 are opened, and third valve 3 and the
Four valves 4 are closed, and crude oil sample is conveyed according to the flow direction of the first oil circuit.In piston (plunger) downlink, 3 He of third valve
4th valve 4 is opened, and the second valve 2 and the 5th valve 5 are closed, and crude oil sample is conveyed according to the flow direction of the second oil circuit.
It is of course also possible to which third valve 3 and the 4th valve 4 are opened, and 2 He of the second valve in piston (plunger) uplink
5th valve 5 is closed, and crude oil sample is conveyed according to the flow direction of the second oil circuit.In piston (plunger) downlink, the second valve 2
It is opened with the 5th valve 5, and third valve 3 and the 4th valve 4 are closed, crude oil sample carries out defeated according to the flow direction of the first oil circuit
It send.
The On-line Measuring Method of viscosity of crude according to the present invention, it is described to measure the crude oil using viscosity detecting device C
The viscosity of sample includes: the arrival end that the crude oil sample is delivered to capillary from oil suction line;The crude oil sample is from described
The outlet end of capillary transfers out;The inlet pressure and outlet pressure of the capillary are measured using pressure sensor;Utilize temperature
Spend the temperature of crude oil sample described in the input end of capillary described in sensor measurement.
It is from the master that the On-line Measuring Method of viscosity of crude according to the present invention, which can also include: using power device D,
Crude oil sample is quantitatively extracted in oil line pipe A, and power is provided.The power device D is the power device D in first embodiment.
The On-line Measuring Method of viscosity of crude according to the present invention, further includes: acquire the original using data acquisition device
The viscosity information of oil samples, and calculated according to Hagen-Poiseuille law, or according to the correction formula of Hagen-Poiseuille law
The crude oil sample viscosity.
In general, when fluid flows through the tiny pipe of caliber, if it is able to satisfy following conditions: (1) tubule is very
It is long and linearly, and internal diameter is impartial;(2) flow regime of fluid is fully developed stable laminar flow, any point in fluid
Flow velocity be only its radius r function;(3) fluid is incompressible homogeneous fluid;(4) fluid being in contact with thin tube inner wall
Do not slide;(5) fluid rheology property is unrelated with the time, and there is one-to-one close between shear stress and shear rate
System;(6) fluid is isothermal.It, theoretically can be according to Hagen-Poiseuille law when meeting above-mentioned condition:
By determining geometric dimension R, L of capillary, experiment measures pressure and the outlet end of the input end at capillary both ends
Pressure between pressure difference △ p (that is: p1-p2) and corresponding flow Q, the dynamic viscosity μ of fluid can be obtained.
But in the case where viscosity is in the range of 10-100mPas, many of actual measurement condition deviates reason
Think situation, such as: there are mismachining tolerances, it cannot be guaranteed that pipeline section internal diameter is impartial;Caliber change at fluid inlet and outlet, making measurement, there are ends
Portion's effect;There are the temperature difference between oil product and environment, oil product constantly exchanges heat with environment in flow process in viscosity detecting device C, leads
Cause temperature in oil product flow process unstable etc..Since there are above-mentioned intrinsic systematic errors, so that crude oil sample be caused to flow through
Pressure measurement when viscosity detecting device C is unable to actual response fluid behaviour, therefore, viscosity in a certain range when, can be with
Hagen-Poiseuille law is modified, the viscosity of crude oil sample is obtained using modified Hagen-Poiseuille law.
In the present invention, the online viscosity that can use in-situ measurement equipment measurement standard viscosity liquid of the invention, according to
Then difference between the online viscosity of standard viscosity liquid and the normal viscosity of the standard viscosity liquid utilizes Ha Gen-poiseuille
Law obtains pressure correcting coefficient k, and then obtains the correction formula of hage oiseuillelaw.
Specifically, in the present invention, the correction formula of the Hagen-Poiseuille law is
Wherein, μ is the viscosity of the crude oil sample, mPas;
R is the radius of the capillary, mm;
p1For the pressure of the arrival end of the capillary, Pa;
p2For the pressure of the outlet end of the capillary, Pa;
Q is the flow of oil suction line Central Plains oil samples, mLs-1;
L is the length of the capillary, mm;
K is pressure correcting coefficient.
Wherein, the pressure correcting coefficient can carry out repeatedly testing under corresponding specific environment according to normal viscosity
It arrives.I.e. the radius of capillary, the inlet port pressure of capillary and outlet pressures, oil suction line Central Plains oil samples flow,
In the case that the length of capillary determines, using the viscosity of known standard viscosity liquid, above-mentioned Hagen-Poiseuille law is utilized
Correction formula obtains pressure correcting coefficient k.
In the present invention, the standard viscosity liquid used can be GBW (E) 130202, and viscosity is about 9.135mPas;GBW
(E) 130203, viscosity is about 18.27mPas, GBW (E) 130204, and viscosity is about 45.675mPas, GBW (E) 130205,
Viscosity is about 106.325mPas etc..
In addition, in the present invention, the viscosity of based on crude sample can choose whether to repair Hagen-Poiseuille law
Just.Such as: when the viscosity of crude oil sample is in 10-100mPas, Hagen-Poiseuille law can be modified, utilize Kazakhstan
Root-Poiseuille's law correction formula measures its online viscosity;It, can pressure when the viscosity of crude oil sample is more than 100mPas
Power correction factor k measures for 1, it can is calculated, i.e., also can get accurate using Hagen-Poiseuille law
Online viscosity.
In addition, in on-line viscosity measurement, also there is more applicable flow according to used capillary, flow compared with
In the case where being suitable for, error is smaller.
Specifically, as depicted in figs. 1 and 2, the On-line Measuring Method of viscosity of crude of the invention may comprise steps of:
When a measurement is started, the first valve 1 is opened, and oil product enters oil suction line by working connection pipeline A;Start power device D, is measuring
During piston (plunger) uplink in device B, the second valve 2 and the 5th valve 5 are opened, and third valve 3 and the 4th valve 4 close
It closes, so that the first oil circuit of crude oil sample as shown in Figure 1 is entered viscosity detecting device with constant flow using metering device B
C.After the piston (plunger) in metering device B goes upward to the limit, downlink process is switched to, third valve 3 and the 4th valve 4 are beaten
It opens, the second valve 2 and the 5th valve 5 are closed, and make crude oil sample still can be with constant flow rate as shown in Figure 2 using metering device B
The second oil circuit enter viscosity detecting device C.Utilize the first valve 1, the second valve 2, third valve 3 and the 4th valve 4
It opens and closes the door, realize that piston (plunger) the uplink and downlink process of metering device B can provide always for viscosity detecting device C
The crude oil sample of constant flow rate.
Further, the 6th valve 6 is opened, so that crude oil sample is flowed through viscosity detecting device C, is remembered using pressure sensor
Crude oil sample is recorded in the pressure of viscosity detecting device C arrival end and the pressure of outlet end, records crude oil sample using temperature sensor
Temperature of the product in arrival end and/or outlet end.
Finally, the lift that crude oil sample utilizes metering device B to provide, opens the 7th valve 7 and the 8th valve 8, makes crude oil
Back flow of sample is to working connection pipeline A;After device runs some cycles, the 9th valve 9 and 10 pairs of the tenth valve measurements can control
Pipeline is cleaned.
Using the online viscosity of in-situ measurement equipment measurement standard viscosity liquid of the invention, according to the online of standard viscosity liquid
Then Kazakhstan root is calculated using Hagen-Poiseuille law in difference between viscosity and the normal viscosity of the standard viscosity liquid
The correction formula of Poiseuille's law.