In-situ permeability determining method

A method of determining the permeability of a particular stratum in an earth formation traversed by a borehole includes injecting a liquid into the borehole at a first pressure thereby causing liquid flow into the stratum. A first flow rate of the liquid is determined at the first pressure. The pressure of the liquid being injected into the borehole is then changed to a second pressure level and a second flow rate of the liquid flowing into the stratum is determined at the second pressure. An indication of the permeability of the stratum is then derived in accordance with the two pressures, the two flow rates and known characteristics of the stratum.

BACKGROUND OF THE INVENTION 
Field of the Invention 
The present invention relates to a method for determining the permeability 
of a material in general and, more particularly, to determine the 
permeability of a stratum of an earth formation from a borehole. 
SUMMARY OF THE INVENTION 
The present invention determines the permeability of a particular stratum 
in an earth formation traversed by a borehole by injecting a liquid into 
the borehole at a first pressure so as to cause liquid flow into the 
stratum. The flow rate of the liquid into the stratum is determined at the 
first pressure. The pressure of the injection liquid is changed to a 
second pressure and the flow rate of the liquid into the stratum is 
determined at the second pressure. An indication of the permeability of 
the stratum is derived in accordance with the first and second flow rates, 
the first and second pressures, and known characteristics of the stratum. 
The objects and advantages of the invention will appear more fully 
hereinafter from a consideration of the detailed description which 
follows, taken together with the accompanying drawings wherein one 
embodiment of the invention is illustrated by way of example. It is to be 
expressly understood, however, that the drawings are for illustration 
purposes only and are not to be construed as defining the limits of the 
invention.

DESCRIPTION OF THE INVENTION 
The determination of the permeability of a petroleum reservoir has in the 
past involved determining the flow of fluid in an uncased injection well 
and monitoring the same fluid flow below the zone being investigated to 
determine the radial flow into the reservoir. Darcy's law for horizontal 
radial flow steady state is expressed as 
EQU 1. Q=[2.pi.kh (p.sub.w -p.sub.e)/[.mu.ln(r.sub.e /r.sub.w)], 
where k is permeability, h is a formation thickness, .mu. is a fluid 
viscosity, p.sub.w is the wellbore pressure, p.sub.e is the reservoir 
pressure, at a distance r.sub.e from the borehole center is the equivalent 
well drainage radius, and r.sub.w is the radius of the wellbore. Darcy's 
law may then be rewritten as the following expression to be solved for the 
permeability k 
EQU 2. k=[Q.mu.ln(r.sub. e /r.sub.w)]/2.pi.h (p.sub.w -p.sub.e). 
The problem with the equation 2 is that p.sub.e is an estimated value. 
The present invention permits the determination of the reservoir 
permeability without estimating the reservoir pressure p.sub.e. The 
present invention makes flow velocity measurements at two or more surface 
controlled pressure levels that renders the knowledge of p.sub.e 
unnecessary as shown in the following equations by letting Q.sub.1 be the 
flow into the permeable stratum at wellbore pressure p.sub.w1 and Q.sub.2 
will be the flow at pressure p.sub.w2 and assuming p.sub.w2 is greater 
than p.sub.w1 we can let 
EQU 3. C=[2.pi.kh]/.mu.ln (r.sub.e /r.sub.w) 
and rewrite equation 1. as follows: 
EQU 4. Q=C (p.sub.w -p.sub.e) 
EQU 5. p.sub.w -p.sub.e =Q/C, 
substituting for Q, and p.sub.w we have 
EQU 6. p.sub.w2 -p.sub.e =Q.sub.2 /C 
EQU Subtracting 7. p.sub.w1 -p.sub.e =Q.sub.1 /C. 
Substracting equation 7 from equation 6, we have 
EQU 8. p.sub.w2 -p.sub.w1 =(Q.sub.2 -Q.sub.1)/C, 
let 
EQU 9. Q.sub.1 =(Q.sub.Bore at a location B-Q.sub.Bore at a location 
A).DELTA.Q.sub.Ba1 
EQU 10. Q.sub.2 =(Q.sub.Bore at location B-Q.sub.Bore at location 
A)=.DELTA.Q.sub.BA2 
were Q.sub.Bore represents borehole liquid flow rate, .DELTA.Q.sub.BA1 and 
.DELTA.Q.sub.BA2 then represents liquid flow into the stratum for 
pressures p.sub.w1 and p.sub.w2, respectively. Rewriting equation 2, we 
have 
EQU 11. k=[(.DELTA.Q.sub.BA2 -.DELTA.Q.sub.BA1).mu. ln(r.sub.e /r.sub.w)]/2 
.pi.h (p.sub.w2 -p.sub.w1) 
The practice of the present invention may be seen readily in FIGS. 1 and 2. 
In FIG. 1 an uncased borehole 4 traverses an earth formation having 
non-permeable zones such as shale 8, and permeable zones 10. During 
reservoir flooding operations water is pumped into borehole 4 at a 
pressure p.sub.1 and flows in the direction of the arrows into the 
permeable zones to flush out and drive ahead of it the crude oil contained 
in those zones. By way of example we have just shown this section of the 
formation as having two permeable zones. The formation itself may have 
several permeable zones. The number of permeable zones does not affect the 
practice of the present invention. 
A logging tool 14 having a neutron source 17 and gamma ray detectors 19 and 
20 is intially positioned at a location A in the borehole which is below a 
permeability zone 10 of interest. It should be noted that whether the flow 
measuring is done below a zone of interest initially or above a zone of 
interest initially is immaterial from the practice of the present 
invention, although the preferred practice is to initially make the 
measurement below the permeable zone of interest and then move it up to 
above that zone to keep a proper tension on the well logging cable. Nor is 
it mandatory that the well logging tool be stationary at the time of 
measurement. There could be measuring by moving past location A and past 
location B. The actual measurement of the fluid flow will be described 
hereinafter and is fully disclosed in U.S. Pat. Nos. 4,032,781 and 
4,189,638. 
Suffice to say that at this time after the flow measurements are made at 
location A, well logging tool 14 is moved to location B and again flow 
measurements are made. The difference of flow as noted earlier, 
corresponds to the radial flow of the water .DELTA.Q.sub.BA1 into 
permeability zone 10, located between locations A and B. The flow 
.DELTA.Q.sub.BA is the Q of equations 4 and 9. Logging tool 14 can then be 
moved up to location C and again fluid measurements made with the radial 
flow of fluid into permeability zone 10 between locations B and C being 
the difference in borehole flow at locations B and C. When all the 
measurements are concluded water again is injected into borehole 4 at a 
greater pressure p.sub.2 than before and the measurements are repeated a 
second time at all of the locations for the determination of the 
permeability. The flow into permeability zone 10 at the new pressure is 
Q.sub.BA2. 
Referring now to FIG. 2, a source of drive water (not shown) pumps water 
into borehole 4 at a predetermined pressure through a pipe 15. Borehole 4 
has a metal cap 16 to seal off the borehole to prevent the water from 
rising out of the borehole. Further, as noted earlier, the pressure at 
which the water is pumped into borehole 4 can be varied by an operator. 
Well logging tool 14 includes a neutron source 17 and conventional type 
gamma ray detectors 19 and 20. Neutron source 17 is supplied by power from 
a power supply 24 while the conventional electronics connect to the power 
supply 24 and to gamma ray detectors 19 and 20. The details of the 
operation of this tool for sensing water flow is fully described in U.S. 
Pat. No. 4,032,781. The theoretical discussion in measuring the flow is 
not necessary to an understanding of the present invention. Suffice to say 
that electronics 28 provides pulses up a logging cable 30 to a pulse 
separator 34 which separates the pulses according to which gamma ray 
detector 19 or 20 provided the pulses. The pulses from one detector, such 
as detector 19, are provided to a gate 38 while the pulses from detector 
20 are provided to gate 39. It should also be noted that the 
aforementioned well logging system includes providing sync pulses downhole 
which are provided to a pulse separator 34 to sync detector and timing 
pulse generator 44. The outputs of gates 38 and 39 are provided to a 
computer 48 and to pulse height analyzers 50 and 52, respectively. The 
outputs of pulse height analyzers 50 and 52 along with the outputs from 
computer 48 are provided to a recorder 57 which is receiving a signal from 
a sheave wheel rail 60 which is cooperating with cable 30 to control 
recorder 57 in accordance with the depth of well logging tool 14 in 
borehole 4. 
Computer 48 makes the necessary flow determinations in accordance with the 
technique disclosed in U.S. Pat. No. 4,189,638 and from the flow 
determinations and data fed into the computer relating to the formation 
characteristics and the pressures of the fluid in borehole 4 to determine 
the permeability of the various zones in the earth's formation. 
It should be noted that the foregoing examples show that the operator 
increased the pressure to the predetermined value. It is possible to 
locate a pressure sensor in pipe 15 or any other convenient location and 
convert it to digital signals and provide it to computer 48. Thus the 
operator could then vary the pressure and not necessarily to a 
predetermined pressure, but that there is a sufficient change in pressure 
with the computer to then utilize the two different sensed pressures to 
derive the permeabilities. 
The present invention need not necessarily be restricted to drive water but 
could be any drive fluid, even a chemical system of drive, fluids, nor is 
the invention restricted to the use of radioactive well logging tools. The 
basic requirements are an ability to detect fluid flow above and below a 
permeable zone of interest for at least two different pressures of fluid 
being provided to borehole 4.